Numerical analysis of the surface and geometry of plate fin heat exchangers for increasing heat transfer rate

Numerical analysis of the surface and geometry of plate fin heat exchangers for increasing heat... This paper investigates the flow field and turbulent flow heat transfer around an array of plain and perforated fin using Flu - ent software within the range of 20,000–50,000 Reynolds. Regarding the turbulent flow, the k-ε RNG turbulence model was implemented, and SIMPLE algorithm was used for solving the equations of three-dimensional, steady, and incompressible flow. In the simulation process, air was considered as the working fluid with consistent physical properties. The results revealed that perforated fins increase the heat transfer coefficient as well as Nusselt number. The highest heat transfer coef - ficient and Nusselt number was achieved for perforated fins with two square holes. Moreover, it was concluded that increase of Reynolds number notably increases the heat transfer coec ffi ient and Nusselt number. The total drag force imposed to plain fins was higher than the force imposed to perforated fins. As a result, by changing plain fins into perforated fins, the pressure decreases due to passage of the flow through the pins, and accordingly, the total drag force imposed to the fins decreases. Finally, it was revealed that attaching some pins on the plain fins along the passing flow will decrease the pressure, while notably increase the heat transfer. Furthermore, it can reduce the fins’ weight and price. Keywords Convection heat transfer · Reynolds number · Nusselt number · Total drag force · Turbulent flow Introduction A heat exchanger is a machine that transfers the heat of a fluid to one or more other fluids with different tempera - Since 1973 oil crisis (when the members of the Organiza- tures. As a result, the heat exchangers are implemented in tion of Arab Petroleum Exporting Countries announced an all industrial and commercial usages, and even those aspects oil sanction), environmental issues including energy saving of normal life that are related to energy transfer. Each living has increasingly found importance. Moreover, world popula- creature is somehow equipped with a heat exchanger. Heat tion growth has led to increase of energy demand. Although exchangers are manufactured in very small and very huge energy consumption has brought about great profits, such sizes. The smallest heat exchangers (less than 1 W) are used issues as environmental pollution and the effects of con - for superconductor electronic applications, guiding mis- suming energy resources over human health has caused a siles controlled by the thermal source, etc. The biggest heat number of concerns to emerge. One of the keys to resolve exchangers (more than 1000 mW) are implemented in large this problem is “Meaningful Energy Conservation”, and a power plants as boiler, condenser or cooling tower. Heat precondition of realizing this concept is design and defini - exchangers are widely used in different industrial units like tion of operational conditions for heat exchangers. power plants, refineries, metal molding and glass industries, food and medicine industries, paper making, petro chemis- try, cold storage, heating and cooling systems for buildings, * Farivar Fazelpour gas congestion industries, land, sea and space vehicles, and f_fazelpour@azad.ac.ir finally electronic industries. Smaller size of a heat exchanger is a measurement of Department of Mechanical Engineering, Faculty of Engineering, Islamic Azad University, South Tehran industrial growth at present [1]. Regarding the increasing Branch, Tehran, Iran growth of cryogenics, plate fin heat exchangers are usually Department of Energy Systems Engineering, Faculty appropriate for implementation in a wide range of indus- of Engineering, Islamic Azad University, South Tehran tries. The plate fin units are usually used in counter flow Branch, Tehran, Iran Vol.:(0123456789) 1 3 156 International Journal of Energy and Environmental Engineering (2018) 9:155–167 heat exchangers. This type of heat exchangers have thin Wais analyzed the influence of fin thickness and winglet corrugated fins or corrugated heat transfer surface of the orientation on mass and thermal efficiency of cross-flow heat plates [2]. The density of small heat exchangers’ surface exchanger. In this study, the fin thickness, length, and orien- is very high, and it can be as much as 1800 . Due to its tation of winglet were the major parameters under analysis. high heat transfer rate, plate fin heat exchangers are highly Numerical analyses were undertaken to analyze the finned important now, and are widely used [3]. tube heat exchanger with and without winglets at the fin Regarding the energy transfer, efficiency of heat surface. It was concluded that fin thickness is influential exchangers in satisfaction of the requirements for energy over the mass of whole heat exchanger as well as the manu- standards (based on low cost and environmental impact) is facturing costs, while proper orientation of the winglet can highly important [4]. In this paper, first, the plate fin heat improve the heat transfer. The correlation between the heat exchangers and their performance has been considered, exchanger’s weight and heat transfer was also investigated in and then a plate fin heat exchanger in Ansys-Fluent was this research for different fin configurations. 3D models were simulated to analyze the geometry of different fins, heat utilized for obtaining the properties of heat transfer between transfer, and pressure drop in different Reynolds numbers. finned tube and the air. The results of this study revealed Finally, the simulation results will be compared with each that optimization cannot be undertaken for merely one cri- other to obtain the highest rate of heat transfer among terion, and more than one parameter should be considered to Reynolds numbers. improve the heat exchanger’s efficiency. All the calculations There are well-cited researches in this regard. Johnson in this study revealed that the ratio of heat exchanger’s mass and Moshfegh made an experiment on seven different types to heat transfer is an essential parameter to which careful of thermal performance of plate fin, strip fin, and pin fin attentions must be paid in the process of the heat exchanger heat sinks in a wind tunnel with turbulent flow. The authors design [19]. investigated thermal resistance and pressure drop [5]. Kays Han et al. undertook a numerical analysis of the fluid flow and London conducted a number of integrated experiments and heat transfer characteristics in finned tube heat exchang- to obtain such factors as friction and heat transfer for differ - ers through analysis of different oval and circular tubes. ent types of plate fin heat exchangers [6 ]. Velayati and Yag- Three different models of tube with two types of enhanced houbi conducted a numerical study on an array of parallel fins (wavy and louvered fins) were used. The results of this fins, and calculated the Nusselt number and pressure drop in study showed that usage of oval fin-tube is not only able to the turbulent flow by changing the width of the fins and the reduce flow resistance, but also able to improve the heat distance among them. By decreasing the proportion of fins’ transfer capacity of the heat exchangers. This issue can width to the distance among them, the Nusselt number and improve the efficiency of the fin’s performance too. Regard - friction coefficient increased both [7 ]. Razelos and Kakat- ing the heat transfer rate for the louvered fins, it was revealed sios obtained the optimal dimensions of the fins with Heat that heat transfer coefficient is more important than the heat transfer and radiation heat transfer. The authors investigated transfer area [20]. hyperbolic fins and achieved the results by simplifying the Čarija et al. in their study investigated the fluid flow and equations [8]. heat transfer in a fin and tube heat exchanger. A comparison Computational fluid dynamics has a good flexibility in between the characteristics of fin and tube heat exchanger formation of computational models, in a way that required and flat and louvered fins exchangers within the range physical conditions will be prepared for the model, without of 70–350 of Reynolds number. The results of the study any need to construct an experimental model. Wang, et al. reflected that louvered heat exchangers show better heat conducted a numerical study on fluid flow and heat trans- transfer characteristics and lower pressure drop. Computa- fer in plain and offset plate fin heat exchangers within the tional fluid dynamics was validated through comparing the quiet Reynolds number range. The researchers compared the results of numerical simulation and the experimental results. results of their study with the results of Kays and London [6] The output of the research reflected minimum average of at the end [9]. Asako and Faghri analyzed the heat transfer Nusselt number deviation, and almost complete correspond- characteristics in a turbulent flow around arrays of heated ing pressure drop [21]. blocks encountered on the wall of two parallel sheets on a Yeom et al. studied the heat transfer and pressure drop channel. A wide range of geometrical parameters were con- characteristics of micro pin fin arrays in a narrow rectangu- sidered in this study, and k-ε turbulence model was imple- lar channel with an air through flow. In this study, the flow mented to solve the equations [10]. Flow behavior in plate rate moved from laminar flow toward turbulent flow. Cop- fin heat exchangers has been analytically and experimentally per micro pin fins with 150–400 µm length and 75–700 µm analyzed due to the complexities of this subject [11–17]. diameter were made. Furthermore, the performance pro- Moreover, Mueller and Chiou studied different types of flow portions that calculate the heat transfer characteristics with distribution in heat exchangers [18]. respect to the pressure drop were employed to study the 1 3 International Journal of Energy and Environmental Engineering (2018) 9:155–167 157 performance of micro pin fins surface. The results of this each other by means of some fins with different shapes study revealed that role of the fluid dynamic effects gener - and geometries. These finned paths are in fact the path ated around micro pin fins is more important than the area from which the flow passes in the heat exchanger. Thicker increase due to micro pin fins in improvement of heat trans- plates are selected for blocking the sideways of the flow fer. The maximum amount of heat transfer improvement for passage path. Offset strip fins are among the most com- plain surface was equal to 79% that due to the micro pin–fin monly used fins in these heat exchangers. A schematic surface with 250 µm height and 400 µm diameter [22, 23]. view of this type of fin is depicted in Fig.  2. This type of Manufacturing heat wells has widely been studied, and fin has high heat transfer efficiency, acceptable compac- so far, a number of methods are presented for improving tion, and high reliability. That is why offset strip fins are this procedure. However, there is not much study conducted widely used in cooling systems of airplanes, automobiles, on perforated fins in turbulent flow fluid. According to and other industrial cooling systems. Offset strip fins are the results of the previous research, the best performance more efficient than pin fins regarding the heat transfer. of external fins is achieved through the use of hyperbolic- Moreover, the offset strips are better than perforated fins shaped fins. However, due to difficulty of manufacturing as regarding the strength and reliability [25]. well as manufacturing high costs of hyperbolic fins, simple Shell–tube heat exchanger which is considered as a type rectangular fins are used in industry. As a result, it can be of tube heat exchangers. This heat exchanger is one of mentioned that novelty of the present research is in analyz- the most common equipment of heat transfer in industry ing the perforated fins in turbulent flow. [26]. Almost 85% of the heat exchangers used in refiner - ies, petro chemistries, and power plants are shell–tube heat exchangers [27]. Although this heat exchanger is Concept not necessarily compact, its high capacity and structural formation has made it suitable for most of the industrial Heat exchangers are equipment that enables heat flow among applications [26]. two or more fluids with different temperatures. Heat transfer Air cooler is a heat exchanger with tube equipment for in a heat exchanger usually occurs as heat exchange in each heat transfer. The tubes are exposed to air, and the pass- fluid, and thermal conductivity through separating wall. ing air works as a cooler of the fluid inside the tubes [26]. Double pipe heat exchanger which is made up of a Types of heat exchangers straight pipe or a finned pipe that is placed into another pipe with higher diameter. In some types of this heat Heat exchangers are made according to different measures exchanger, a group of pipes are placed into larger pipes. like transfer procedure, structural geometry and component This heat exchanger is specifically appropriate for low arrangement [24]. Different types of heat exchangers will be capacity, interoperability and high pressure cases [26]. mentioned in this section. Heat pipe heat exchangers which consists of an envelope, working fluid, and in most cases, a wick that must form Compact heat exchangers in which the heat exchange rate a consistent and strong bond with the surface of internal per unit volume is high (higher than 700). This type of case [26]. heat exchangers includes a compact set of tubes or finned Plate heat exchangers which are made of thin metal flat surfaces [24]. Plate fin heat exchangers are a type of plates attached to each other closely with a distance of compact heat exchangers that are composed of a number 3–6  mm. The heat exchanger fluid flows through the of parallel plates (which are usually known as separat- plates interchangeably [24]. ing plates), as shown in Fig. 1. The plates are attached to Different types of plate heat exchanger: Plate-and-frame heat exchangers, gasketed plate heat exchangers, spiral Fig. 1 A schematic view of plate fin heat exchanger for turbulent flow [25] Fig. 2 An offset strip fin [25] 1 3 158 International Journal of Energy and Environmental Engineering (2018) 9:155–167 plate heat exchangers, lamella heat exchangers, panel coil around an array of fins will be solved by numerical method. heat exchangers [24]. The governing equations are solved through finite volume method, by use of SIMPLE algorithm, and by applying k-ε turbulence model. After obtaining simulation results, they Different types of fin will be compared with the experimental results to provide a validated model with a particular error percentage. The Corrugated plates that are placed between the flat plates to provided model can be used later for analysis and modeling increase the heat transfer surface, and provide a mainstay of other problems. for the flat plates too. There are different types of corrugated plates used in heat exchangers; however, the most commonly used types are plain fin, perforated fin, serrated fin, and her - Preprocessing ringbone fin. By use of the fins, the boundary layers will break and disrupt completely. If the surface is wavy along Preprocessing is a phase in which the aims of modeling (like the flow direction, boundary layers become thin or break; geometry creation) and meshing creation are done. The next and, the result will be higher heat transfer coefficient and phase will be definition of numerical models and boundary higher pressure drop [24]. conditions for beginning equation solution. The solver will Fast heat transfer from hot surface, reduction of pressure go on till a complete convergence is achieved in the solu- drop, reduction of weight and cost of the heat exchanger are tion. When the solver is done, the results will be analyzed the goals of designers. Extended surfaces are good equip- numerically and graphically. The former phase is called ment for heat transfer between fluid and environment, and post-processing. are extensively used in industries. Rectangular plain fins are Figure 3a depicts the components of the computational used in industries for cooling hot surfaces. domain for a plain rectangular fin. Figures  3b and 3c, respec- tively, depict a rectangular fin with two square holes, and a rectangular fin with one rectangular hole. Methodology Computational domain is a rectangular cube with 86 mm of length, 46 mm of width, and 31 mm of height. The fin In this paper, first the plate fin heat exchangers and their material is aluminum, and their dimension is 24 mm for performance is studied. After data collection, a plate fin heat length, 4 mm for width, and 12 mm for height. The distance exchanger will be modeled through a CFD commercial code between the fins is 10 mm. The dimension of holes in the (Ansys Fluent); geometry of different fins, heat transfer, and fin with two square holes is 3 × 3 mm, and the dimension pressure drop in different Reynolds numbers will be esti- of the hole in the fin with one rectangular hole is 2 × 9 mm. mated; and finally, the obtained results will be compared and The second section of preprocessing is creation of com- analyzed to find the highest rate of heat transfer for Reyn- putational cells. Definition of computational cells or mesh- olds numbers. A great number of meshing are considered for ing is an important phase in an accurate numerical solution. evaluation of the simulation method, and the result will be The meshing section of the ANSYS software is equipped selection of a meshing with appropriate dimension. Simula- with different algorithms for meshing. In this paper, a trian- tion will be done after selection of the meshing with suitable gle grid was considered for rectangular cube area and for the number and dimension. In this regard, the flow equations are fins. Figure  4 displays a general view of the meshing, and solved in a 3D manner, and the equations of heat transfer Fig. 5 displays a close view of the meshing. Fig. 3 Computational domain for a plain rectangular fin (a), for a rectangular fin with two square holes (b), for a rectangular fin with one rectan- gular hole (c) 1 3 International Journal of Energy and Environmental Engineering (2018) 9:155–167 159 Fig. 4 A General view of the meshing recording the results, to save time in calculation process. Table 1 and Fig. 6 display the details of grid independence. Boundary conditions After preparing meshing of the problem, it is time to process it by the Fluent software. In this regard, boundary conditions must be defined, and this phase is one of the most essen- tial phases in the modeling problems. Boundary conditions define the flow and heat characteristics in boundaries, with regard to the problem physics. Boundary conditions play an important role in computational fluid dynamics (CFD) solutions. The boundary conditions are categorized as follows: Fig. 5 A close view of the meshing Output and input flow to the border: input pressure, out- put pressure, velocity input, velocity output, input mass Grid independence flow, output mass flow, free entrance (ventilation), free output (ventilation), blower or fan, far-reaching pressure In this study, five different meshing for analysis of the grid, field, and blower output. independence were made in meshing section of the ANSYS, • Pair and repeating boundaries and wall: wall, axisymmet- and all the results were compared with each other. The num- ric boundary, symmetric boundary, periodic boundary ber of meshing were, respectively, 30,651, 77,345, 90,143, • Internal areas and cells: fluid, solid 105,741, and 167,947. To calculate the average Nusselt Boundaries of internal plates: blower, radiator, wall, number in Reynolds, 50,000 was used for plain fin. While internal area. comparing the obtained results with other meshing, a very slight difference between the results of smallest meshing and the results of meshing with 105,741 cells was witnessed. As a result, the meshing with 105,741 cells was used for Table 1 Analysis of grid Number of mesh Average independence for calculation Nusselt of Nusselt number in Reynolds number 50,000 30,651 57.91 77,345 79.02 90,143 97.12 105,741 110.78 Fig. 6 Analysis of grid independence for calculation of Nusselt num- 167,947 111.23 ber in Reynolds 50,000 1 3 160 International Journal of Energy and Environmental Engineering (2018) 9:155–167 In this research, the entrance side is considered as the needed to obtain them by use of the existing methods and boundary condition for velocity input; and the exit side models. was considered as the boundary condition for output pres- RANS utilizes all the volatility measurements in transi- sure. The wall with no-slip condition was considered for tional quantities as average. As a result, this method notably other sides. The flow was considered as 3D, steady and decreases the required calculations, and is appropriate for a incompressible. The fluid flow occurs parallel with the wide range of engineering problems. fins, and free air temperature is 25 °C. The temperature for the surface below the fins was considered to be steady RANS and equal to be 70 °C. The fluid motion is mathematically described by three equa- Governing equations tions of mass conservation, momentum, and energy. Under the assumption that flow is incompressible, and there is a Incompressible and steady flow equations in turbulence con- linear correlation between gradient of velocity and stress ditions can be defined as below. The following equations are, (Newtonian fluid), fluid motion can be expressed by respectively, continuity, momentum, and energy equations. Navier–Stokes equations in a tensor form, as below: u ̄ = 0 i,j (1) u  u u i i j =− − t x x � � j i 𝜌 ū ū =− p̄ + 𝜇 ū + ū − 𝜌u u j i,j i i,j j,i i j (2) ,j Acceleration Pr essure gradient Displacement (6) ̄ ̄ � 𝜌 C (u ̄ T )=(kT − 𝜌C u T ) +  + + F (3) p j ,j j p ,j i x x x j j i External forces Equation below is used for calculation of heat transfer Viscosity effects coefficient: = 0 (7) − k (4) h = T − T s ∞ On the above equations, ρ denotes air density, U denotes fluid velocity, P denotes static pressure, μ denotes viscosity, In above equation, h is the heat transfer coefficient. and F denotes external forces imposed to the object. The Another parameter defined in this regard is the dimension- above-mentioned equations are valid as long as the flow is less Nusselt number, which is defined as below: laminar and without any turbulence. However, when turbu- hl lence occurs in flow entrance and vortices grow, transient Nu = (5) region (and turbulence afterward) is formed in the flow, and Reynolds number exceeds the critical value. Under this con- If we put the average heat transfer coefficient in this equa- dition, utilizing Navier–Stokes equations is not permissible, tion, average Nusselt number will be achieved. and there is a need for an equation that is able to model tur- bulence. The solution suggested for this problem is changing Modeling turbulent flows the whole time-dependent variables into time-averaged com- ponents and fluctuating component. For example, instanta- With regard to the increasing need of the engineers to have neous velocity can be defined as below: required parameters of fluid flow, finding an applied solu- tion for solving turbulent flow problems is necessary. It is u = u + u (8) i i not possible to solve time-dependent Navier–Stokes equa- In the above equation, u denotes velocity average time, tions when there are high Reynolds numbers or complex and u is its fluctuating component. The u value can be eas- geometries. However, there are two methods for solving ily calculated by the equation below: Navier–Stokes equations when the fluctuations of turbulent t +Δt flows are not directly involved in the equations: u =  u dt (9) i i Δt 1. Reynolds Average Navier–Stokes (RANS) After replacing the velocity and pressure variables, and 2. Large Eddy Simulation (LES) time integrating of equations, the average flow equation is obtained. Due to the fact that integration of linear terms of In both above-mentioned methods, additional and new the equations in fluctuating component in momentum and variables are added to the governing equations, and it is 1 3 International Journal of Energy and Environmental Engineering (2018) 9:155–167 161 conservation equations equals to zero, the only change that Standard k‑ε model is made in these equations due to turbulence will be for the displacement term of the momentum equation (in which Standard k-ε model was proposed by Launder-Spalding [29]. multiplication of velocity to its derivatives brings about This model has relatively good accuracy for analysis of Reyn- a non-linear answer). With regard to displacement term, olds stress due to turbulent flow. The model is defined by two replacement of fluctuating component and average velocity, quantities of Turbulent Kinetic Energy (K) and Dissipation we will have: Rate of Turbulent Kinetic Energy (ε). Knowing the values of K and ε, eddy viscosity is obtained through the formula below: � � � u u = u + u u + u = u u + u u j i j i j i j j i i = C (15) (10) � � � � � + u u + u u = u u + u u i j i j j i j i The Standard k-ε model equations are: Achieved equation after the above-mentioned calculations Kinetic energy of turbulence (K) will be RANS that is as below: k k  k + u =  −  + ( +  ∕ ) j ij t k (16) 𝜕 𝜌̄u ū 𝜕 u 𝜕 (𝜌 u ) ̄ 𝜕 u j i j 𝜕 P 𝜕 i i t x x x x � � j j j j =− − + 𝜇 + − 𝜌 u u + F j i 𝜕 t 𝜕 x 𝜕 x 𝜕 x 𝜕 x 𝜕 x j i j j i (11) Dissipation Rate of Turbulent Kinetic Energy (ε) The RANS equation that models turbulence in system has one further term than the Navier–Stokes equations that + u = C  − C  + ( +  ∕ ) 1 ij 2 t t x k x k x x j j i j is called Reynolds Stress Tensor. In fact, the added term to (17) Navier–Stokes equation is due to separation of the field into In the above equation,  is the Reynolds stress tensor, and two parts of laminar and turbulent. However, as defining the ij it equals with: value of this component is impossible by means of analytical calculations, a model must be found by which writing Reyn- = 2 S − ∕ k ij t ij 3 ij olds stresses based on average quantities would be possible. (18) Boussinesq presented a model entitled as “Eddy Viscosity”, in which Reynolds stresses become related to average strains On Eq. (18),  denotes Kronecker Delta, k denotes mean due to eddy viscosity, by the equation below: turbulent kinematic energy, and S denotes strain rate tensor. The following equations are defined for the above-mentioned i parameters: � � =− u u =  + (12) ij t i j x x j i = 1(i = j = 1) ij (19) Replacing the above-mentioned equation into Eq. 12, the � � k = u u (20) average flow equation will be as follows: i i 𝜕 𝜌 u ū 𝜕 u 𝜕 (𝜌 u ) ̄ 𝜕 u j i j 𝜕 P 𝜕 i i =− − + 𝜇 + + F eff i 1 j 𝜕 t 𝜕 x 𝜕 x 𝜕 x 𝜕 x 𝜕 x S = + j i j j i (21) ij 2 x x j i (13) On which: Moreover, the constant values of  ,  , C , C and C k  1 2 =  + that are usually obtained from wind tunnel test are displayed eff t (14) on Table 2. Analyzing this equation, it can be concluded that the value As observed, Reynolds stress tensor in standard k-ε model of  increased due to consideration of turbulence over vis- has an additional term (third sentence) than the Boussinesq cosity value [28]. Now, if can obtain the value of turbulence equation. Adding this term to Reynolds stress equation is due viscosity (or eddy viscosity) by use of the correlations among to consideration of vertical Reynolds stresses in k-ε model. It variables, the phases of mathematical modeling of fluid motion will be complete. There are different methods for calculation of eddy viscosity in Fluent software, including single-equation Table 2 Constant values for eddy viscosity equations, K , and models like Spalart–Allmaras model, two-equation models like k-ω and k-ε, and seven-equation models like Reynolds Model C C 1 2 k stress. In the following, k-ε model (that are used in the simula- Standard k-ε 0.09 1.44 1.92 1 1.3 tion process of the present research) will be explained. 1 3 162 International Journal of Energy and Environmental Engineering (2018) 9:155–167 is needed to be mentioned that k-ε model is only valid for quite characteristics. As depicted in Fig. 7, there is an accept- turbulent flow, and is not able to predict the transitional phase able conformity between the results of the present study of the flow around the wall. k -ε RNG model is used for solving and the study of El-Sayed et al. [30]. the problem in the present study. Numerical analysis Results Within the model under analysis, a triangle grid was con- sidered for rectangular cube area and the fins too. Standard The results of the numerical method and convergence are method was used for pressure discretization, and the First- discussed in this section. For validation of the results, they order upwind method was used for momentum and turbu- were compared with the results of El-Sayed et al. [30]. lence discretization. Moreover, second-order upwind method Afterward, the results of numerical analysis of a plate fin was used for energy discretization. By use of this method, the exchanger with different geometries with Fluent software results obtained have higher accuracy. As the model is a steady are represented. The working fluid was considered to be model, and regular grids are used, simple algorithm is used air, and fins’ material was considered to be aluminum in for the pressure–velocity coupling pattern. In this article, the this study. The flow developed and flow conditions were convergence measure for reduction of remainder for such vari- considered steady. Moreover, the fluid flow parallel to fins −3 ables as momentum and mass was considered lower than 10 , passed on the surface. The fluid flow was turbulent, and −6 and for energy was considered 10 . As mentioned before, k-ε Reynolds number was between 20,000 and 50,000. The RNG turbulence model was used in this study, as this model is input air temperature was 300 K, and the fins were placed more accurate than others. on a plate with constant heat flux of 1200 w/m . Validation Fluctuations of average heat transfer coefficients in the fins Due to lack of experimental results regarding plain perfo- rated fins in turbulent flow, the plain fin in turbulent flow Figure 8 displays fluctuations of average heat transfer coef- model was used to compare the results of this study with ficients in the plain fins, fins with one hole and two holes, the results achieved in the experimental study of El-Sayed according to Reynolds number. As observed, the fin with et al. [30]. In this regard, fluctuations of average Nusselt two holes has a higher heat transfer rate than others. Making number relative to Reynolds number were compared in a hole in rectangular fin, the heat transfer surface increases both studies. In the experimental study of El-Sayed et al. notably, and heat transfer increases accordingly, in a way that [30], an array of rectangular parallel fins were placed in in Reynolds number 50,000, heat transfer coefficient for the different direction, and the results were compared with fin with two holes was about 7% higher than the plain fin, each other. The best result was achieved under the parallel and the heat transfer coec ffi ient for the fin with one hole was flow condition. El-Sayed et al. [30] studied the geomet- about 6% higher than the plain fin. Also, it can be concluded ric effects of an array of fins as well as the heat transfer that by increase of Reynolds number, the heat transfer coef- ficient increased in all fins. Fig. 7 Comparing fluctuations of average Nusselt number relative to Reynolds number in the present study and the study of El-Sayed et al. [30] Fig. 8 Fluctuations of average heat transfer coefficients in the fins 1 3 International Journal of Energy and Environmental Engineering (2018) 9:155–167 163 fin had a higher pressure drag force than the other fins, and Fluctuations of average Nusselt number in fins the fin with one hole had a higher pressure drag force than the fin with two holes. Moreover, the pressure drag force Figure 9 displays the fluctuations of average Nusselt number for plain fins, fins with one hole and two holes relative to increased with the increase of Reynolds number, and the increase slope is more intensive for the plain fin than the Reynolds number. As observed, the value of average Nusselt number increases with a high slope, as the Reynolds number other two fins. Decrease of pressure drag force in the per - forated fins is due to passage of a part of the flow from the increases. The highest amount of increase is seen at Reyn- olds number 50,000. With the increase of Reynolds number hole. With the passage of the flow from the holes, a part of the created weak behind the fins is lost, and as the rotational up to 50,000, average Nusselt number increased as much as 84% compared to Reynolds number 20,000 for the fin flow decreases behind the fins, pressure difference decreases; and accordingly, pressure drag force decreases. with two holes. With the increase of Reynolds number from 20,000 to 50,000, average Nusselt number increased 82% for Fluctuations of viscous drag force in the fins the fin with one hole, and 75% for the plain fin. Important point here is that higher average of Nusselt number for the Figure 11 displays fluctuations of viscous drag force relative fin with two holes (than the other two fins) is due to passage of the flow from the fins and increase of heat transfer. to Reynolds number in the plain fins, the fin with one hole, and the fin with two holes. It is clear that the perforated Fluctuations of pressure drag force in the fins fins had a higher viscous drag force than the plain fin, and the fin with one hole had a higher viscous drag force than Figure 10 displays the fluctuations of pressure drag force the fin with two holes. The imposed force to perforated fins was higher than the imposed force to the plain fin. Increase relative to Reynolds number in the plain fin, the fin with one hole, and the fin with two holes. It is obvious that plain of viscous drag is due to increase of the fin contact sur - face in the holes. In fact, by passage of the flow from the holes, a higher surface of the fluid is touched by the fins. Moreover, the viscous drag force increased as the Reynolds number boosted. The highest amount of viscous drag force is observed at Reynolds number 50,000. Fluctuations of total drag force imposed to fins Figure 12 depicts fluctuations of total drag force imposed to the three fins (that is obtained by summing up pressure drag force and viscous drag force). Analysis of the figure reveals that total drag force imposed to the plain fin is higher than the total drag force imposed to perorated fins, and the reason is increase of the imposed pressure on the fin contact Fig. 9 Fluctuations of average Nusselt number according to Reynolds surface due to the strike of the flow to the fin. However, with number in the fins passage of the flow form the holes in perforated fins, the Fig. 10 Fluctuations of pressure drag force according to Reynolds Fig. 11 Fluctuations of viscous drag force in the fins according to number in the fins Reynolds number 1 3 164 International Journal of Energy and Environmental Engineering (2018) 9:155–167 Comparison of the temperature distribution along the fins Figures 16, 17, 18 display the fluctuations of temperature distribution along the plain fin, the fin with one hole, and the fin with two holes based on Reynolds number. As observed in the figures below, temperature increases with the increase of fins’ length, and the highest amount is for fin number 2 that is surrounded by the other two fins. Simultaneous analy - sis of the three cases under analysis revealed that plain fins has higher temperature than the perforated fins. Fig. 12 Fluctuations of total drag force imposed to fins according to Reynolds number Conclusion pressure decreases notably. Moreover, the total drag force increases with the increase of Reynolds number. The fin with The author in this paper conducted a numerical analysis two holes had the lowest amount of total drag force. of heat transfer around an array of plain and perforated fins that were placed on a plate with constant thermal flux Comparison of the highest pressure imposed on the Reynolds range of 20,000–50,000. The flow was to the fins assumed to be 3D, steady, incompressible, and turbulent. To solve equations, First-order and second-order discre- Table 3 displays the results of comparing the highest pres- tization method were used; and, SIMPLE algorithm with sure imposed to the fins with regard to the Reynolds number. the help of Fluent software was used for obtaining pres- Analysis of the table reveals that with a constant Reynolds sure–velocity coupling pattern. The results of the study number, plain fin had the highest amount of maximum pres- revealed that k-ε RNG turbulence model is an appropriate sure (pascal). By making holes on the plain fins along the model for solving the problem of flow around the fins, and flow direction, the amount of pressure decreases due to pas- analysis of the fins’ thermal characteristics. The results sage of the flow from the holes. Furthermore, the fins with of the study confirmed that changing plain fins into per - two square holes had the lowest amount of maximum pres- forated fins brings about an increase of convection heat sure. Figures 13, 14 and 15 display the distribution of static transfer coefficient and Nusselt number—in a way that fins pressure on the three fins under study at Reynolds number with two square holes had the highest amount of convec- tion heat transfer coefficient and Nusselt number. Increase of Reynolds number leads in an outstanding increase of heat transfer coefficient and Nusselt number in a way that Table 3 Comparing the highest pressure imposed to the fins based on Reynolds number mentioned parameters in the fins with two square holes increased 84%. The point to be careful is that the total Fin Maximum pressure Reynolds number drag force imposed to the plain fins is higher than the total (pascal) drag force imposed to perforated fins. By making holes Plain fin 2191 20,000 on the plain fins and passage of the flow from the holes, 4907 30,000 the pressure marvelously decreases; and, the total drag 8668 40,000 force imposed to the fins decreases accordingly. Moreo- 13,503 50,000 ver, the total drag force imposed to the fins increases as Fin with one hole 2092 20,000 the Reynolds number increases; as a result, the fins with 4680 30,000 two holes have the lowest imposed total drag force. Com- 8263 40,000 paring the temperature distribution along the fins made it 12,866 50000 clear that increase of the fin length leads in increase of the 2056 20,000 Fin with two holes temperature, and the highest temperature belonged to the 4490 30,000 middle fin that was surrounded by the fins beside it. The 7942 40,000 essential point to mention is that most of the previously 12,581 50,000 conducted research with the aim of increasing heat transfer 20,000. 1 3 International Journal of Energy and Environmental Engineering (2018) 9:155–167 165 Fig. 13 Distribution of static pressure on plain fin on Reynolds number 20,000 Fig. 14 Distribution of static pressure on the fin with one rectangular hole on Reynolds number 20,000 led to an increase of pressure drop. It was concluded in transfer improves outstandingly. Therefore, doing will also this study that by making some holes along the passing decrease the weight and the cost of the fins. flow on the plain fins, pressure drop decreases, while heat 1 3 166 International Journal of Energy and Environmental Engineering (2018) 9:155–167 Fig. 15 Distribution of static pressure on the fin with two square hole on Reynolds number 20,000 Fig. 16 Temperature distribution along plain fin in Reynolds number Fig. 18 Temperature distribution along the fin with two square holes 30,000 in Reynolds number 30,000 Compliance with ethical standards Conflict of interest The authors declare no conflict of interests. Open Access This article is distributed under the terms of the Crea- tive Commons Attribution 4.0 International License (http://creat iveco mmons.or g/licenses/b y/4.0/), which permits unrestricted use, distribu- tion, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Fig. 17 Temperature distribution along the fin with a rectangular hole in Reynolds number 30,000 1 3 International Journal of Energy and Environmental Engineering (2018) 9:155–167 167 17. Cho, D.H., Seo, S.K., Lee, C.J., Lim, Y.: Optimization of layer References patterning on a plate fin heat exchanger considering abnormal operating conditions. Appl. Therm. Eng. 127, 1036–1048 (2017) 1. Zohuri, B.: Nuclear Energy for Hydrogen Generation Through 18. Mueller, A., Chiou, J.: Review of various types of flow maldistri- Intermediate Heat Exchangers: A Renewable Source of Energy. bution in heat exchangers. Heat Transfer Eng. 9, 36–50 (1988) Springer, New York (2016) 19. Wais, P.: Influence of fin thickness and winglet orientation on 2. Sahu, A.K., Sahu, N.K., Sahu, A.K.: Benchmarking CNC mass and thermal efficiency of cross-flow heat exchanger. Appl. machine tool using hybrid-fuzzy methodology: a multi-indices Therm. Eng. 102, 184–195 (2016) decision making (MCDM) approach. Int. J. Fuzzy Syst. Appl. 20. Han, H., He, Y.L., Li, Y.S., Wang, Y., Wu, M.: A numerical study (IJFSA) 4, 28–46 (2015) on compact enhanced fin-and-tube heat exchangers with oval 3. Tahseen, T.A., Ishak, M., Rahman, M.M.: Performance predic- and circular tube configurations. Int. J. Heat Mass Transfer 65, tions of laminar heat transfer and Pressure drop in an in-line 686–695 (2013) flat tube bundle using an adaptive neuro-fuzzy inference system 21. Čarija, Z., Franković, B., Perčić, M., Čavrak, M.: Heat transfer (ANFIS) model. Int. Commun. Heat Mass Transfer 50, 85–97 analysis of fin-and-tube heat exchangers with flat and louvered (2014) fin geometries. Int. J. Refrig 45, 160–167 (2014) 4. Sinha, A., Chattopadhyay, H., Iyengar, A.K., Biswas, G.: 22. Yeom, T., Simon, T., Zhang, T., Zhang, M., North, M., Cui, T.: Enhancement of heat transfer in a fin-tube heat exchanger using Enhanced heat transfer of heat sink channels with micro pin fin rectangular winglet type vortex generators. Int. J. Heat Mass roughened walls. Int. J. Heat Mass Transfer 92, 617–627 (2016) Transfer 101, 667–681 (2016) 23. Wang, G.L., Yang, D.W., Wang, Y., Niu, D., Zhao, X.L., Ding, 5. Jonsson, H., Moshfegh, B.: Modeling of the thermal and hydrau- G.F.: Heat transfer and friction characteristics of the microfluidic lic performance of plate fin, strip fin, and pin fin heat sinks- heat sink with variously-shaped ribs for chip cooling. Sensors. 15, influence of flow bypass. IEEE Trans. Compon. Packag. Tech- 9547–9562 (2015) nol. 24, 142–149 (2001) 24. Salehi, S.: Simulation of Air-to-Air Plate Heat Exchangers for 6. Kays, W.M., London, A.L.: Compact Heat Exchangers. Analyzing the Possibility of Baffle Installation, Analyzing the McGraw-Hill, New York (1984) Effects of Input Duct Shape and Geometry of Used Fins on the 7. Velayati, E., Yaghoubi, M.: Numerical study of convective heat Heat Exchanger Performance, Master’s thesis, Sharif Industrial transfer from an array of parallel bluff plates. Int. J. Heat Fluid University, Tehran, Iran (2012) Flow 26, 80–91 (2005) 25. Das, P., Ghosh, I.: Thermal design of multistream plate fin heat 8. Razelos, P., Kakatsios, X.: Optimum dimensions of convecting- exchangers-a state-of-the-art review. Heat Transfer Eng. 33, 284– radiating fins: part I—longitudinal fins. Appl. Therm. Eng. 20, 300 (2012) 1161–1192 (2000) 26. Mohammad Zamani, G.: Modeling and Controlling Plate Heat 9. Wang, Y.Q., Dong, Q.W., Liu, M.S., Wang, D.: Numerical study Exchanger, Master’s thesis, Sharif Industrial University, Tehran, on plate-fin heat exchangers with plain fins and serrated fins at low Iran (1994) reynolds number. Chem. Eng. Technol. 32, 1219–1226 (2009) 27. Butterworth D.: Design and application of twisted tube exchang- 10. Asako, Y., Faghri, M.: Parametric study of turbulent three-dimen- ers. In: European Research Meeting on the Future Needs and sional heat transfer of arrays of heated blocks encountered in elec- Developments in Heat Exchanger Technology—Advances in tronic equipment. Int. J. Heat Mass Transfer 37, 469–478 (1994) Industrial Heat Transfer, IChemE, pp. 87–95 (1996) 11. Kitto, J., Robertson, J.: Effects of maldistribution of flow on heat 28. Chen, Y.S., Kim, S.W.: Computation of Turbulent Flows Using transfer equipment performance. Heat Transfer Eng. 10, 18–25 an Extended k-ε Turbulence Closure Model, Report No. NASA (1989) CR-179204, Universities Space Research Association, Washing- 12. Ranganayakulu, C., Seetharamu, K.: The combined effects of lon - ton, D.C., USA (1987) gitudinal heat conduction, flow nonuniformity and temperature 29. Launder, B., Spalding, D.: The numerical computation of turbu- nonuniformity in crossflow plate-fin heat exchangers. Int. Com- lent o fl ws. Comput. Methods Appl. Mech. Eng. 3, 269–289 (1974) mun. Heat Mass Transfer 26, 669–678 (1999) 30. El-Sayed, S.A., Mohamed, S.M., Abdel-latif, A.M., Abdel-hamid, 13. Ranganayakulu, C., Seetharamu, K.: The combined effects of wall E.A.: Investigation of turbulent heat transfer and fluid flow in longitudinal heat conduction, inlet fluid flow nonuniformity and longitudinal rectangular-fin arrays of different geometries and temperature nonuniformity in compact tube-fin heat exchangers: shrouded fin array. Exp. Therm. Fluid Sci. 26, 879–900 (2002) a finite element method. Int. J. Heat Mass Transfer 42, 263–273 (1999) Publisher’s Note Springer Nature remains neutral with regard to 14. Mueller, A.: Effects of some types of maldistribution on the per - urisdictional claims in published maps and institutional affiliations. formance of heat exchangers. Heat Transfer Eng. 8, 75–86 (1987) 15. Shah, R., London, A.: Effects of nonuniform passages on compact heat exchanger performance. J. Eng. Power 102, 653–659 (1980) 16. Khan, T.A., Li, W.: Optimal design of plate-fin heat exchanger by combining multi-objective algorithms. Int. J. Heat Mass Transfer 108, 1560–1572 (2017) 1 3 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Energy and Environmental Engineering Springer Journals

Numerical analysis of the surface and geometry of plate fin heat exchangers for increasing heat transfer rate

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Engineering; Renewable and Green Energy
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Abstract

This paper investigates the flow field and turbulent flow heat transfer around an array of plain and perforated fin using Flu - ent software within the range of 20,000–50,000 Reynolds. Regarding the turbulent flow, the k-ε RNG turbulence model was implemented, and SIMPLE algorithm was used for solving the equations of three-dimensional, steady, and incompressible flow. In the simulation process, air was considered as the working fluid with consistent physical properties. The results revealed that perforated fins increase the heat transfer coefficient as well as Nusselt number. The highest heat transfer coef - ficient and Nusselt number was achieved for perforated fins with two square holes. Moreover, it was concluded that increase of Reynolds number notably increases the heat transfer coec ffi ient and Nusselt number. The total drag force imposed to plain fins was higher than the force imposed to perforated fins. As a result, by changing plain fins into perforated fins, the pressure decreases due to passage of the flow through the pins, and accordingly, the total drag force imposed to the fins decreases. Finally, it was revealed that attaching some pins on the plain fins along the passing flow will decrease the pressure, while notably increase the heat transfer. Furthermore, it can reduce the fins’ weight and price. Keywords Convection heat transfer · Reynolds number · Nusselt number · Total drag force · Turbulent flow Introduction A heat exchanger is a machine that transfers the heat of a fluid to one or more other fluids with different tempera - Since 1973 oil crisis (when the members of the Organiza- tures. As a result, the heat exchangers are implemented in tion of Arab Petroleum Exporting Countries announced an all industrial and commercial usages, and even those aspects oil sanction), environmental issues including energy saving of normal life that are related to energy transfer. Each living has increasingly found importance. Moreover, world popula- creature is somehow equipped with a heat exchanger. Heat tion growth has led to increase of energy demand. Although exchangers are manufactured in very small and very huge energy consumption has brought about great profits, such sizes. The smallest heat exchangers (less than 1 W) are used issues as environmental pollution and the effects of con - for superconductor electronic applications, guiding mis- suming energy resources over human health has caused a siles controlled by the thermal source, etc. The biggest heat number of concerns to emerge. One of the keys to resolve exchangers (more than 1000 mW) are implemented in large this problem is “Meaningful Energy Conservation”, and a power plants as boiler, condenser or cooling tower. Heat precondition of realizing this concept is design and defini - exchangers are widely used in different industrial units like tion of operational conditions for heat exchangers. power plants, refineries, metal molding and glass industries, food and medicine industries, paper making, petro chemis- try, cold storage, heating and cooling systems for buildings, * Farivar Fazelpour gas congestion industries, land, sea and space vehicles, and f_fazelpour@azad.ac.ir finally electronic industries. Smaller size of a heat exchanger is a measurement of Department of Mechanical Engineering, Faculty of Engineering, Islamic Azad University, South Tehran industrial growth at present [1]. Regarding the increasing Branch, Tehran, Iran growth of cryogenics, plate fin heat exchangers are usually Department of Energy Systems Engineering, Faculty appropriate for implementation in a wide range of indus- of Engineering, Islamic Azad University, South Tehran tries. The plate fin units are usually used in counter flow Branch, Tehran, Iran Vol.:(0123456789) 1 3 156 International Journal of Energy and Environmental Engineering (2018) 9:155–167 heat exchangers. This type of heat exchangers have thin Wais analyzed the influence of fin thickness and winglet corrugated fins or corrugated heat transfer surface of the orientation on mass and thermal efficiency of cross-flow heat plates [2]. The density of small heat exchangers’ surface exchanger. In this study, the fin thickness, length, and orien- is very high, and it can be as much as 1800 . Due to its tation of winglet were the major parameters under analysis. high heat transfer rate, plate fin heat exchangers are highly Numerical analyses were undertaken to analyze the finned important now, and are widely used [3]. tube heat exchanger with and without winglets at the fin Regarding the energy transfer, efficiency of heat surface. It was concluded that fin thickness is influential exchangers in satisfaction of the requirements for energy over the mass of whole heat exchanger as well as the manu- standards (based on low cost and environmental impact) is facturing costs, while proper orientation of the winglet can highly important [4]. In this paper, first, the plate fin heat improve the heat transfer. The correlation between the heat exchangers and their performance has been considered, exchanger’s weight and heat transfer was also investigated in and then a plate fin heat exchanger in Ansys-Fluent was this research for different fin configurations. 3D models were simulated to analyze the geometry of different fins, heat utilized for obtaining the properties of heat transfer between transfer, and pressure drop in different Reynolds numbers. finned tube and the air. The results of this study revealed Finally, the simulation results will be compared with each that optimization cannot be undertaken for merely one cri- other to obtain the highest rate of heat transfer among terion, and more than one parameter should be considered to Reynolds numbers. improve the heat exchanger’s efficiency. All the calculations There are well-cited researches in this regard. Johnson in this study revealed that the ratio of heat exchanger’s mass and Moshfegh made an experiment on seven different types to heat transfer is an essential parameter to which careful of thermal performance of plate fin, strip fin, and pin fin attentions must be paid in the process of the heat exchanger heat sinks in a wind tunnel with turbulent flow. The authors design [19]. investigated thermal resistance and pressure drop [5]. Kays Han et al. undertook a numerical analysis of the fluid flow and London conducted a number of integrated experiments and heat transfer characteristics in finned tube heat exchang- to obtain such factors as friction and heat transfer for differ - ers through analysis of different oval and circular tubes. ent types of plate fin heat exchangers [6 ]. Velayati and Yag- Three different models of tube with two types of enhanced houbi conducted a numerical study on an array of parallel fins (wavy and louvered fins) were used. The results of this fins, and calculated the Nusselt number and pressure drop in study showed that usage of oval fin-tube is not only able to the turbulent flow by changing the width of the fins and the reduce flow resistance, but also able to improve the heat distance among them. By decreasing the proportion of fins’ transfer capacity of the heat exchangers. This issue can width to the distance among them, the Nusselt number and improve the efficiency of the fin’s performance too. Regard - friction coefficient increased both [7 ]. Razelos and Kakat- ing the heat transfer rate for the louvered fins, it was revealed sios obtained the optimal dimensions of the fins with Heat that heat transfer coefficient is more important than the heat transfer and radiation heat transfer. The authors investigated transfer area [20]. hyperbolic fins and achieved the results by simplifying the Čarija et al. in their study investigated the fluid flow and equations [8]. heat transfer in a fin and tube heat exchanger. A comparison Computational fluid dynamics has a good flexibility in between the characteristics of fin and tube heat exchanger formation of computational models, in a way that required and flat and louvered fins exchangers within the range physical conditions will be prepared for the model, without of 70–350 of Reynolds number. The results of the study any need to construct an experimental model. Wang, et al. reflected that louvered heat exchangers show better heat conducted a numerical study on fluid flow and heat trans- transfer characteristics and lower pressure drop. Computa- fer in plain and offset plate fin heat exchangers within the tional fluid dynamics was validated through comparing the quiet Reynolds number range. The researchers compared the results of numerical simulation and the experimental results. results of their study with the results of Kays and London [6] The output of the research reflected minimum average of at the end [9]. Asako and Faghri analyzed the heat transfer Nusselt number deviation, and almost complete correspond- characteristics in a turbulent flow around arrays of heated ing pressure drop [21]. blocks encountered on the wall of two parallel sheets on a Yeom et al. studied the heat transfer and pressure drop channel. A wide range of geometrical parameters were con- characteristics of micro pin fin arrays in a narrow rectangu- sidered in this study, and k-ε turbulence model was imple- lar channel with an air through flow. In this study, the flow mented to solve the equations [10]. Flow behavior in plate rate moved from laminar flow toward turbulent flow. Cop- fin heat exchangers has been analytically and experimentally per micro pin fins with 150–400 µm length and 75–700 µm analyzed due to the complexities of this subject [11–17]. diameter were made. Furthermore, the performance pro- Moreover, Mueller and Chiou studied different types of flow portions that calculate the heat transfer characteristics with distribution in heat exchangers [18]. respect to the pressure drop were employed to study the 1 3 International Journal of Energy and Environmental Engineering (2018) 9:155–167 157 performance of micro pin fins surface. The results of this each other by means of some fins with different shapes study revealed that role of the fluid dynamic effects gener - and geometries. These finned paths are in fact the path ated around micro pin fins is more important than the area from which the flow passes in the heat exchanger. Thicker increase due to micro pin fins in improvement of heat trans- plates are selected for blocking the sideways of the flow fer. The maximum amount of heat transfer improvement for passage path. Offset strip fins are among the most com- plain surface was equal to 79% that due to the micro pin–fin monly used fins in these heat exchangers. A schematic surface with 250 µm height and 400 µm diameter [22, 23]. view of this type of fin is depicted in Fig.  2. This type of Manufacturing heat wells has widely been studied, and fin has high heat transfer efficiency, acceptable compac- so far, a number of methods are presented for improving tion, and high reliability. That is why offset strip fins are this procedure. However, there is not much study conducted widely used in cooling systems of airplanes, automobiles, on perforated fins in turbulent flow fluid. According to and other industrial cooling systems. Offset strip fins are the results of the previous research, the best performance more efficient than pin fins regarding the heat transfer. of external fins is achieved through the use of hyperbolic- Moreover, the offset strips are better than perforated fins shaped fins. However, due to difficulty of manufacturing as regarding the strength and reliability [25]. well as manufacturing high costs of hyperbolic fins, simple Shell–tube heat exchanger which is considered as a type rectangular fins are used in industry. As a result, it can be of tube heat exchangers. This heat exchanger is one of mentioned that novelty of the present research is in analyz- the most common equipment of heat transfer in industry ing the perforated fins in turbulent flow. [26]. Almost 85% of the heat exchangers used in refiner - ies, petro chemistries, and power plants are shell–tube heat exchangers [27]. Although this heat exchanger is Concept not necessarily compact, its high capacity and structural formation has made it suitable for most of the industrial Heat exchangers are equipment that enables heat flow among applications [26]. two or more fluids with different temperatures. Heat transfer Air cooler is a heat exchanger with tube equipment for in a heat exchanger usually occurs as heat exchange in each heat transfer. The tubes are exposed to air, and the pass- fluid, and thermal conductivity through separating wall. ing air works as a cooler of the fluid inside the tubes [26]. Double pipe heat exchanger which is made up of a Types of heat exchangers straight pipe or a finned pipe that is placed into another pipe with higher diameter. In some types of this heat Heat exchangers are made according to different measures exchanger, a group of pipes are placed into larger pipes. like transfer procedure, structural geometry and component This heat exchanger is specifically appropriate for low arrangement [24]. Different types of heat exchangers will be capacity, interoperability and high pressure cases [26]. mentioned in this section. Heat pipe heat exchangers which consists of an envelope, working fluid, and in most cases, a wick that must form Compact heat exchangers in which the heat exchange rate a consistent and strong bond with the surface of internal per unit volume is high (higher than 700). This type of case [26]. heat exchangers includes a compact set of tubes or finned Plate heat exchangers which are made of thin metal flat surfaces [24]. Plate fin heat exchangers are a type of plates attached to each other closely with a distance of compact heat exchangers that are composed of a number 3–6  mm. The heat exchanger fluid flows through the of parallel plates (which are usually known as separat- plates interchangeably [24]. ing plates), as shown in Fig. 1. The plates are attached to Different types of plate heat exchanger: Plate-and-frame heat exchangers, gasketed plate heat exchangers, spiral Fig. 1 A schematic view of plate fin heat exchanger for turbulent flow [25] Fig. 2 An offset strip fin [25] 1 3 158 International Journal of Energy and Environmental Engineering (2018) 9:155–167 plate heat exchangers, lamella heat exchangers, panel coil around an array of fins will be solved by numerical method. heat exchangers [24]. The governing equations are solved through finite volume method, by use of SIMPLE algorithm, and by applying k-ε turbulence model. After obtaining simulation results, they Different types of fin will be compared with the experimental results to provide a validated model with a particular error percentage. The Corrugated plates that are placed between the flat plates to provided model can be used later for analysis and modeling increase the heat transfer surface, and provide a mainstay of other problems. for the flat plates too. There are different types of corrugated plates used in heat exchangers; however, the most commonly used types are plain fin, perforated fin, serrated fin, and her - Preprocessing ringbone fin. By use of the fins, the boundary layers will break and disrupt completely. If the surface is wavy along Preprocessing is a phase in which the aims of modeling (like the flow direction, boundary layers become thin or break; geometry creation) and meshing creation are done. The next and, the result will be higher heat transfer coefficient and phase will be definition of numerical models and boundary higher pressure drop [24]. conditions for beginning equation solution. The solver will Fast heat transfer from hot surface, reduction of pressure go on till a complete convergence is achieved in the solu- drop, reduction of weight and cost of the heat exchanger are tion. When the solver is done, the results will be analyzed the goals of designers. Extended surfaces are good equip- numerically and graphically. The former phase is called ment for heat transfer between fluid and environment, and post-processing. are extensively used in industries. Rectangular plain fins are Figure 3a depicts the components of the computational used in industries for cooling hot surfaces. domain for a plain rectangular fin. Figures  3b and 3c, respec- tively, depict a rectangular fin with two square holes, and a rectangular fin with one rectangular hole. Methodology Computational domain is a rectangular cube with 86 mm of length, 46 mm of width, and 31 mm of height. The fin In this paper, first the plate fin heat exchangers and their material is aluminum, and their dimension is 24 mm for performance is studied. After data collection, a plate fin heat length, 4 mm for width, and 12 mm for height. The distance exchanger will be modeled through a CFD commercial code between the fins is 10 mm. The dimension of holes in the (Ansys Fluent); geometry of different fins, heat transfer, and fin with two square holes is 3 × 3 mm, and the dimension pressure drop in different Reynolds numbers will be esti- of the hole in the fin with one rectangular hole is 2 × 9 mm. mated; and finally, the obtained results will be compared and The second section of preprocessing is creation of com- analyzed to find the highest rate of heat transfer for Reyn- putational cells. Definition of computational cells or mesh- olds numbers. A great number of meshing are considered for ing is an important phase in an accurate numerical solution. evaluation of the simulation method, and the result will be The meshing section of the ANSYS software is equipped selection of a meshing with appropriate dimension. Simula- with different algorithms for meshing. In this paper, a trian- tion will be done after selection of the meshing with suitable gle grid was considered for rectangular cube area and for the number and dimension. In this regard, the flow equations are fins. Figure  4 displays a general view of the meshing, and solved in a 3D manner, and the equations of heat transfer Fig. 5 displays a close view of the meshing. Fig. 3 Computational domain for a plain rectangular fin (a), for a rectangular fin with two square holes (b), for a rectangular fin with one rectan- gular hole (c) 1 3 International Journal of Energy and Environmental Engineering (2018) 9:155–167 159 Fig. 4 A General view of the meshing recording the results, to save time in calculation process. Table 1 and Fig. 6 display the details of grid independence. Boundary conditions After preparing meshing of the problem, it is time to process it by the Fluent software. In this regard, boundary conditions must be defined, and this phase is one of the most essen- tial phases in the modeling problems. Boundary conditions define the flow and heat characteristics in boundaries, with regard to the problem physics. Boundary conditions play an important role in computational fluid dynamics (CFD) solutions. The boundary conditions are categorized as follows: Fig. 5 A close view of the meshing Output and input flow to the border: input pressure, out- put pressure, velocity input, velocity output, input mass Grid independence flow, output mass flow, free entrance (ventilation), free output (ventilation), blower or fan, far-reaching pressure In this study, five different meshing for analysis of the grid, field, and blower output. independence were made in meshing section of the ANSYS, • Pair and repeating boundaries and wall: wall, axisymmet- and all the results were compared with each other. The num- ric boundary, symmetric boundary, periodic boundary ber of meshing were, respectively, 30,651, 77,345, 90,143, • Internal areas and cells: fluid, solid 105,741, and 167,947. To calculate the average Nusselt Boundaries of internal plates: blower, radiator, wall, number in Reynolds, 50,000 was used for plain fin. While internal area. comparing the obtained results with other meshing, a very slight difference between the results of smallest meshing and the results of meshing with 105,741 cells was witnessed. As a result, the meshing with 105,741 cells was used for Table 1 Analysis of grid Number of mesh Average independence for calculation Nusselt of Nusselt number in Reynolds number 50,000 30,651 57.91 77,345 79.02 90,143 97.12 105,741 110.78 Fig. 6 Analysis of grid independence for calculation of Nusselt num- 167,947 111.23 ber in Reynolds 50,000 1 3 160 International Journal of Energy and Environmental Engineering (2018) 9:155–167 In this research, the entrance side is considered as the needed to obtain them by use of the existing methods and boundary condition for velocity input; and the exit side models. was considered as the boundary condition for output pres- RANS utilizes all the volatility measurements in transi- sure. The wall with no-slip condition was considered for tional quantities as average. As a result, this method notably other sides. The flow was considered as 3D, steady and decreases the required calculations, and is appropriate for a incompressible. The fluid flow occurs parallel with the wide range of engineering problems. fins, and free air temperature is 25 °C. The temperature for the surface below the fins was considered to be steady RANS and equal to be 70 °C. The fluid motion is mathematically described by three equa- Governing equations tions of mass conservation, momentum, and energy. Under the assumption that flow is incompressible, and there is a Incompressible and steady flow equations in turbulence con- linear correlation between gradient of velocity and stress ditions can be defined as below. The following equations are, (Newtonian fluid), fluid motion can be expressed by respectively, continuity, momentum, and energy equations. Navier–Stokes equations in a tensor form, as below: u ̄ = 0 i,j (1) u  u u i i j =− − t x x � � j i 𝜌 ū ū =− p̄ + 𝜇 ū + ū − 𝜌u u j i,j i i,j j,i i j (2) ,j Acceleration Pr essure gradient Displacement (6) ̄ ̄ � 𝜌 C (u ̄ T )=(kT − 𝜌C u T ) +  + + F (3) p j ,j j p ,j i x x x j j i External forces Equation below is used for calculation of heat transfer Viscosity effects coefficient: = 0 (7) − k (4) h = T − T s ∞ On the above equations, ρ denotes air density, U denotes fluid velocity, P denotes static pressure, μ denotes viscosity, In above equation, h is the heat transfer coefficient. and F denotes external forces imposed to the object. The Another parameter defined in this regard is the dimension- above-mentioned equations are valid as long as the flow is less Nusselt number, which is defined as below: laminar and without any turbulence. However, when turbu- hl lence occurs in flow entrance and vortices grow, transient Nu = (5) region (and turbulence afterward) is formed in the flow, and Reynolds number exceeds the critical value. Under this con- If we put the average heat transfer coefficient in this equa- dition, utilizing Navier–Stokes equations is not permissible, tion, average Nusselt number will be achieved. and there is a need for an equation that is able to model tur- bulence. The solution suggested for this problem is changing Modeling turbulent flows the whole time-dependent variables into time-averaged com- ponents and fluctuating component. For example, instanta- With regard to the increasing need of the engineers to have neous velocity can be defined as below: required parameters of fluid flow, finding an applied solu- tion for solving turbulent flow problems is necessary. It is u = u + u (8) i i not possible to solve time-dependent Navier–Stokes equa- In the above equation, u denotes velocity average time, tions when there are high Reynolds numbers or complex and u is its fluctuating component. The u value can be eas- geometries. However, there are two methods for solving ily calculated by the equation below: Navier–Stokes equations when the fluctuations of turbulent t +Δt flows are not directly involved in the equations: u =  u dt (9) i i Δt 1. Reynolds Average Navier–Stokes (RANS) After replacing the velocity and pressure variables, and 2. Large Eddy Simulation (LES) time integrating of equations, the average flow equation is obtained. Due to the fact that integration of linear terms of In both above-mentioned methods, additional and new the equations in fluctuating component in momentum and variables are added to the governing equations, and it is 1 3 International Journal of Energy and Environmental Engineering (2018) 9:155–167 161 conservation equations equals to zero, the only change that Standard k‑ε model is made in these equations due to turbulence will be for the displacement term of the momentum equation (in which Standard k-ε model was proposed by Launder-Spalding [29]. multiplication of velocity to its derivatives brings about This model has relatively good accuracy for analysis of Reyn- a non-linear answer). With regard to displacement term, olds stress due to turbulent flow. The model is defined by two replacement of fluctuating component and average velocity, quantities of Turbulent Kinetic Energy (K) and Dissipation we will have: Rate of Turbulent Kinetic Energy (ε). Knowing the values of K and ε, eddy viscosity is obtained through the formula below: � � � u u = u + u u + u = u u + u u j i j i j i j j i i = C (15) (10) � � � � � + u u + u u = u u + u u i j i j j i j i The Standard k-ε model equations are: Achieved equation after the above-mentioned calculations Kinetic energy of turbulence (K) will be RANS that is as below: k k  k + u =  −  + ( +  ∕ ) j ij t k (16) 𝜕 𝜌̄u ū 𝜕 u 𝜕 (𝜌 u ) ̄ 𝜕 u j i j 𝜕 P 𝜕 i i t x x x x � � j j j j =− − + 𝜇 + − 𝜌 u u + F j i 𝜕 t 𝜕 x 𝜕 x 𝜕 x 𝜕 x 𝜕 x j i j j i (11) Dissipation Rate of Turbulent Kinetic Energy (ε) The RANS equation that models turbulence in system has one further term than the Navier–Stokes equations that + u = C  − C  + ( +  ∕ ) 1 ij 2 t t x k x k x x j j i j is called Reynolds Stress Tensor. In fact, the added term to (17) Navier–Stokes equation is due to separation of the field into In the above equation,  is the Reynolds stress tensor, and two parts of laminar and turbulent. However, as defining the ij it equals with: value of this component is impossible by means of analytical calculations, a model must be found by which writing Reyn- = 2 S − ∕ k ij t ij 3 ij olds stresses based on average quantities would be possible. (18) Boussinesq presented a model entitled as “Eddy Viscosity”, in which Reynolds stresses become related to average strains On Eq. (18),  denotes Kronecker Delta, k denotes mean due to eddy viscosity, by the equation below: turbulent kinematic energy, and S denotes strain rate tensor. The following equations are defined for the above-mentioned i parameters: � � =− u u =  + (12) ij t i j x x j i = 1(i = j = 1) ij (19) Replacing the above-mentioned equation into Eq. 12, the � � k = u u (20) average flow equation will be as follows: i i 𝜕 𝜌 u ū 𝜕 u 𝜕 (𝜌 u ) ̄ 𝜕 u j i j 𝜕 P 𝜕 i i =− − + 𝜇 + + F eff i 1 j 𝜕 t 𝜕 x 𝜕 x 𝜕 x 𝜕 x 𝜕 x S = + j i j j i (21) ij 2 x x j i (13) On which: Moreover, the constant values of  ,  , C , C and C k  1 2 =  + that are usually obtained from wind tunnel test are displayed eff t (14) on Table 2. Analyzing this equation, it can be concluded that the value As observed, Reynolds stress tensor in standard k-ε model of  increased due to consideration of turbulence over vis- has an additional term (third sentence) than the Boussinesq cosity value [28]. Now, if can obtain the value of turbulence equation. Adding this term to Reynolds stress equation is due viscosity (or eddy viscosity) by use of the correlations among to consideration of vertical Reynolds stresses in k-ε model. It variables, the phases of mathematical modeling of fluid motion will be complete. There are different methods for calculation of eddy viscosity in Fluent software, including single-equation Table 2 Constant values for eddy viscosity equations, K , and models like Spalart–Allmaras model, two-equation models like k-ω and k-ε, and seven-equation models like Reynolds Model C C 1 2 k stress. In the following, k-ε model (that are used in the simula- Standard k-ε 0.09 1.44 1.92 1 1.3 tion process of the present research) will be explained. 1 3 162 International Journal of Energy and Environmental Engineering (2018) 9:155–167 is needed to be mentioned that k-ε model is only valid for quite characteristics. As depicted in Fig. 7, there is an accept- turbulent flow, and is not able to predict the transitional phase able conformity between the results of the present study of the flow around the wall. k -ε RNG model is used for solving and the study of El-Sayed et al. [30]. the problem in the present study. Numerical analysis Results Within the model under analysis, a triangle grid was con- sidered for rectangular cube area and the fins too. Standard The results of the numerical method and convergence are method was used for pressure discretization, and the First- discussed in this section. For validation of the results, they order upwind method was used for momentum and turbu- were compared with the results of El-Sayed et al. [30]. lence discretization. Moreover, second-order upwind method Afterward, the results of numerical analysis of a plate fin was used for energy discretization. By use of this method, the exchanger with different geometries with Fluent software results obtained have higher accuracy. As the model is a steady are represented. The working fluid was considered to be model, and regular grids are used, simple algorithm is used air, and fins’ material was considered to be aluminum in for the pressure–velocity coupling pattern. In this article, the this study. The flow developed and flow conditions were convergence measure for reduction of remainder for such vari- considered steady. Moreover, the fluid flow parallel to fins −3 ables as momentum and mass was considered lower than 10 , passed on the surface. The fluid flow was turbulent, and −6 and for energy was considered 10 . As mentioned before, k-ε Reynolds number was between 20,000 and 50,000. The RNG turbulence model was used in this study, as this model is input air temperature was 300 K, and the fins were placed more accurate than others. on a plate with constant heat flux of 1200 w/m . Validation Fluctuations of average heat transfer coefficients in the fins Due to lack of experimental results regarding plain perfo- rated fins in turbulent flow, the plain fin in turbulent flow Figure 8 displays fluctuations of average heat transfer coef- model was used to compare the results of this study with ficients in the plain fins, fins with one hole and two holes, the results achieved in the experimental study of El-Sayed according to Reynolds number. As observed, the fin with et al. [30]. In this regard, fluctuations of average Nusselt two holes has a higher heat transfer rate than others. Making number relative to Reynolds number were compared in a hole in rectangular fin, the heat transfer surface increases both studies. In the experimental study of El-Sayed et al. notably, and heat transfer increases accordingly, in a way that [30], an array of rectangular parallel fins were placed in in Reynolds number 50,000, heat transfer coefficient for the different direction, and the results were compared with fin with two holes was about 7% higher than the plain fin, each other. The best result was achieved under the parallel and the heat transfer coec ffi ient for the fin with one hole was flow condition. El-Sayed et al. [30] studied the geomet- about 6% higher than the plain fin. Also, it can be concluded ric effects of an array of fins as well as the heat transfer that by increase of Reynolds number, the heat transfer coef- ficient increased in all fins. Fig. 7 Comparing fluctuations of average Nusselt number relative to Reynolds number in the present study and the study of El-Sayed et al. [30] Fig. 8 Fluctuations of average heat transfer coefficients in the fins 1 3 International Journal of Energy and Environmental Engineering (2018) 9:155–167 163 fin had a higher pressure drag force than the other fins, and Fluctuations of average Nusselt number in fins the fin with one hole had a higher pressure drag force than the fin with two holes. Moreover, the pressure drag force Figure 9 displays the fluctuations of average Nusselt number for plain fins, fins with one hole and two holes relative to increased with the increase of Reynolds number, and the increase slope is more intensive for the plain fin than the Reynolds number. As observed, the value of average Nusselt number increases with a high slope, as the Reynolds number other two fins. Decrease of pressure drag force in the per - forated fins is due to passage of a part of the flow from the increases. The highest amount of increase is seen at Reyn- olds number 50,000. With the increase of Reynolds number hole. With the passage of the flow from the holes, a part of the created weak behind the fins is lost, and as the rotational up to 50,000, average Nusselt number increased as much as 84% compared to Reynolds number 20,000 for the fin flow decreases behind the fins, pressure difference decreases; and accordingly, pressure drag force decreases. with two holes. With the increase of Reynolds number from 20,000 to 50,000, average Nusselt number increased 82% for Fluctuations of viscous drag force in the fins the fin with one hole, and 75% for the plain fin. Important point here is that higher average of Nusselt number for the Figure 11 displays fluctuations of viscous drag force relative fin with two holes (than the other two fins) is due to passage of the flow from the fins and increase of heat transfer. to Reynolds number in the plain fins, the fin with one hole, and the fin with two holes. It is clear that the perforated Fluctuations of pressure drag force in the fins fins had a higher viscous drag force than the plain fin, and the fin with one hole had a higher viscous drag force than Figure 10 displays the fluctuations of pressure drag force the fin with two holes. The imposed force to perforated fins was higher than the imposed force to the plain fin. Increase relative to Reynolds number in the plain fin, the fin with one hole, and the fin with two holes. It is obvious that plain of viscous drag is due to increase of the fin contact sur - face in the holes. In fact, by passage of the flow from the holes, a higher surface of the fluid is touched by the fins. Moreover, the viscous drag force increased as the Reynolds number boosted. The highest amount of viscous drag force is observed at Reynolds number 50,000. Fluctuations of total drag force imposed to fins Figure 12 depicts fluctuations of total drag force imposed to the three fins (that is obtained by summing up pressure drag force and viscous drag force). Analysis of the figure reveals that total drag force imposed to the plain fin is higher than the total drag force imposed to perorated fins, and the reason is increase of the imposed pressure on the fin contact Fig. 9 Fluctuations of average Nusselt number according to Reynolds surface due to the strike of the flow to the fin. However, with number in the fins passage of the flow form the holes in perforated fins, the Fig. 10 Fluctuations of pressure drag force according to Reynolds Fig. 11 Fluctuations of viscous drag force in the fins according to number in the fins Reynolds number 1 3 164 International Journal of Energy and Environmental Engineering (2018) 9:155–167 Comparison of the temperature distribution along the fins Figures 16, 17, 18 display the fluctuations of temperature distribution along the plain fin, the fin with one hole, and the fin with two holes based on Reynolds number. As observed in the figures below, temperature increases with the increase of fins’ length, and the highest amount is for fin number 2 that is surrounded by the other two fins. Simultaneous analy - sis of the three cases under analysis revealed that plain fins has higher temperature than the perforated fins. Fig. 12 Fluctuations of total drag force imposed to fins according to Reynolds number Conclusion pressure decreases notably. Moreover, the total drag force increases with the increase of Reynolds number. The fin with The author in this paper conducted a numerical analysis two holes had the lowest amount of total drag force. of heat transfer around an array of plain and perforated fins that were placed on a plate with constant thermal flux Comparison of the highest pressure imposed on the Reynolds range of 20,000–50,000. The flow was to the fins assumed to be 3D, steady, incompressible, and turbulent. To solve equations, First-order and second-order discre- Table 3 displays the results of comparing the highest pres- tization method were used; and, SIMPLE algorithm with sure imposed to the fins with regard to the Reynolds number. the help of Fluent software was used for obtaining pres- Analysis of the table reveals that with a constant Reynolds sure–velocity coupling pattern. The results of the study number, plain fin had the highest amount of maximum pres- revealed that k-ε RNG turbulence model is an appropriate sure (pascal). By making holes on the plain fins along the model for solving the problem of flow around the fins, and flow direction, the amount of pressure decreases due to pas- analysis of the fins’ thermal characteristics. The results sage of the flow from the holes. Furthermore, the fins with of the study confirmed that changing plain fins into per - two square holes had the lowest amount of maximum pres- forated fins brings about an increase of convection heat sure. Figures 13, 14 and 15 display the distribution of static transfer coefficient and Nusselt number—in a way that fins pressure on the three fins under study at Reynolds number with two square holes had the highest amount of convec- tion heat transfer coefficient and Nusselt number. Increase of Reynolds number leads in an outstanding increase of heat transfer coefficient and Nusselt number in a way that Table 3 Comparing the highest pressure imposed to the fins based on Reynolds number mentioned parameters in the fins with two square holes increased 84%. The point to be careful is that the total Fin Maximum pressure Reynolds number drag force imposed to the plain fins is higher than the total (pascal) drag force imposed to perforated fins. By making holes Plain fin 2191 20,000 on the plain fins and passage of the flow from the holes, 4907 30,000 the pressure marvelously decreases; and, the total drag 8668 40,000 force imposed to the fins decreases accordingly. Moreo- 13,503 50,000 ver, the total drag force imposed to the fins increases as Fin with one hole 2092 20,000 the Reynolds number increases; as a result, the fins with 4680 30,000 two holes have the lowest imposed total drag force. Com- 8263 40,000 paring the temperature distribution along the fins made it 12,866 50000 clear that increase of the fin length leads in increase of the 2056 20,000 Fin with two holes temperature, and the highest temperature belonged to the 4490 30,000 middle fin that was surrounded by the fins beside it. The 7942 40,000 essential point to mention is that most of the previously 12,581 50,000 conducted research with the aim of increasing heat transfer 20,000. 1 3 International Journal of Energy and Environmental Engineering (2018) 9:155–167 165 Fig. 13 Distribution of static pressure on plain fin on Reynolds number 20,000 Fig. 14 Distribution of static pressure on the fin with one rectangular hole on Reynolds number 20,000 led to an increase of pressure drop. It was concluded in transfer improves outstandingly. Therefore, doing will also this study that by making some holes along the passing decrease the weight and the cost of the fins. flow on the plain fins, pressure drop decreases, while heat 1 3 166 International Journal of Energy and Environmental Engineering (2018) 9:155–167 Fig. 15 Distribution of static pressure on the fin with two square hole on Reynolds number 20,000 Fig. 16 Temperature distribution along plain fin in Reynolds number Fig. 18 Temperature distribution along the fin with two square holes 30,000 in Reynolds number 30,000 Compliance with ethical standards Conflict of interest The authors declare no conflict of interests. Open Access This article is distributed under the terms of the Crea- tive Commons Attribution 4.0 International License (http://creat iveco mmons.or g/licenses/b y/4.0/), which permits unrestricted use, distribu- tion, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Fig. 17 Temperature distribution along the fin with a rectangular hole in Reynolds number 30,000 1 3 International Journal of Energy and Environmental Engineering (2018) 9:155–167 167 17. Cho, D.H., Seo, S.K., Lee, C.J., Lim, Y.: Optimization of layer References patterning on a plate fin heat exchanger considering abnormal operating conditions. Appl. Therm. Eng. 127, 1036–1048 (2017) 1. Zohuri, B.: Nuclear Energy for Hydrogen Generation Through 18. Mueller, A., Chiou, J.: Review of various types of flow maldistri- Intermediate Heat Exchangers: A Renewable Source of Energy. bution in heat exchangers. Heat Transfer Eng. 9, 36–50 (1988) Springer, New York (2016) 19. Wais, P.: Influence of fin thickness and winglet orientation on 2. Sahu, A.K., Sahu, N.K., Sahu, A.K.: Benchmarking CNC mass and thermal efficiency of cross-flow heat exchanger. Appl. machine tool using hybrid-fuzzy methodology: a multi-indices Therm. Eng. 102, 184–195 (2016) decision making (MCDM) approach. Int. J. Fuzzy Syst. Appl. 20. Han, H., He, Y.L., Li, Y.S., Wang, Y., Wu, M.: A numerical study (IJFSA) 4, 28–46 (2015) on compact enhanced fin-and-tube heat exchangers with oval 3. Tahseen, T.A., Ishak, M., Rahman, M.M.: Performance predic- and circular tube configurations. Int. J. Heat Mass Transfer 65, tions of laminar heat transfer and Pressure drop in an in-line 686–695 (2013) flat tube bundle using an adaptive neuro-fuzzy inference system 21. Čarija, Z., Franković, B., Perčić, M., Čavrak, M.: Heat transfer (ANFIS) model. Int. Commun. Heat Mass Transfer 50, 85–97 analysis of fin-and-tube heat exchangers with flat and louvered (2014) fin geometries. Int. J. Refrig 45, 160–167 (2014) 4. Sinha, A., Chattopadhyay, H., Iyengar, A.K., Biswas, G.: 22. Yeom, T., Simon, T., Zhang, T., Zhang, M., North, M., Cui, T.: Enhancement of heat transfer in a fin-tube heat exchanger using Enhanced heat transfer of heat sink channels with micro pin fin rectangular winglet type vortex generators. Int. J. Heat Mass roughened walls. Int. J. Heat Mass Transfer 92, 617–627 (2016) Transfer 101, 667–681 (2016) 23. Wang, G.L., Yang, D.W., Wang, Y., Niu, D., Zhao, X.L., Ding, 5. Jonsson, H., Moshfegh, B.: Modeling of the thermal and hydrau- G.F.: Heat transfer and friction characteristics of the microfluidic lic performance of plate fin, strip fin, and pin fin heat sinks- heat sink with variously-shaped ribs for chip cooling. Sensors. 15, influence of flow bypass. IEEE Trans. Compon. Packag. Tech- 9547–9562 (2015) nol. 24, 142–149 (2001) 24. Salehi, S.: Simulation of Air-to-Air Plate Heat Exchangers for 6. Kays, W.M., London, A.L.: Compact Heat Exchangers. Analyzing the Possibility of Baffle Installation, Analyzing the McGraw-Hill, New York (1984) Effects of Input Duct Shape and Geometry of Used Fins on the 7. Velayati, E., Yaghoubi, M.: Numerical study of convective heat Heat Exchanger Performance, Master’s thesis, Sharif Industrial transfer from an array of parallel bluff plates. Int. J. Heat Fluid University, Tehran, Iran (2012) Flow 26, 80–91 (2005) 25. Das, P., Ghosh, I.: Thermal design of multistream plate fin heat 8. Razelos, P., Kakatsios, X.: Optimum dimensions of convecting- exchangers-a state-of-the-art review. Heat Transfer Eng. 33, 284– radiating fins: part I—longitudinal fins. Appl. Therm. Eng. 20, 300 (2012) 1161–1192 (2000) 26. Mohammad Zamani, G.: Modeling and Controlling Plate Heat 9. Wang, Y.Q., Dong, Q.W., Liu, M.S., Wang, D.: Numerical study Exchanger, Master’s thesis, Sharif Industrial University, Tehran, on plate-fin heat exchangers with plain fins and serrated fins at low Iran (1994) reynolds number. Chem. Eng. Technol. 32, 1219–1226 (2009) 27. Butterworth D.: Design and application of twisted tube exchang- 10. Asako, Y., Faghri, M.: Parametric study of turbulent three-dimen- ers. In: European Research Meeting on the Future Needs and sional heat transfer of arrays of heated blocks encountered in elec- Developments in Heat Exchanger Technology—Advances in tronic equipment. Int. J. Heat Mass Transfer 37, 469–478 (1994) Industrial Heat Transfer, IChemE, pp. 87–95 (1996) 11. Kitto, J., Robertson, J.: Effects of maldistribution of flow on heat 28. Chen, Y.S., Kim, S.W.: Computation of Turbulent Flows Using transfer equipment performance. Heat Transfer Eng. 10, 18–25 an Extended k-ε Turbulence Closure Model, Report No. NASA (1989) CR-179204, Universities Space Research Association, Washing- 12. Ranganayakulu, C., Seetharamu, K.: The combined effects of lon - ton, D.C., USA (1987) gitudinal heat conduction, flow nonuniformity and temperature 29. Launder, B., Spalding, D.: The numerical computation of turbu- nonuniformity in crossflow plate-fin heat exchangers. Int. Com- lent o fl ws. Comput. Methods Appl. Mech. Eng. 3, 269–289 (1974) mun. Heat Mass Transfer 26, 669–678 (1999) 30. El-Sayed, S.A., Mohamed, S.M., Abdel-latif, A.M., Abdel-hamid, 13. Ranganayakulu, C., Seetharamu, K.: The combined effects of wall E.A.: Investigation of turbulent heat transfer and fluid flow in longitudinal heat conduction, inlet fluid flow nonuniformity and longitudinal rectangular-fin arrays of different geometries and temperature nonuniformity in compact tube-fin heat exchangers: shrouded fin array. Exp. Therm. Fluid Sci. 26, 879–900 (2002) a finite element method. Int. J. Heat Mass Transfer 42, 263–273 (1999) Publisher’s Note Springer Nature remains neutral with regard to 14. Mueller, A.: Effects of some types of maldistribution on the per - urisdictional claims in published maps and institutional affiliations. formance of heat exchangers. Heat Transfer Eng. 8, 75–86 (1987) 15. Shah, R., London, A.: Effects of nonuniform passages on compact heat exchanger performance. J. Eng. Power 102, 653–659 (1980) 16. Khan, T.A., Li, W.: Optimal design of plate-fin heat exchanger by combining multi-objective algorithms. Int. J. Heat Mass Transfer 108, 1560–1572 (2017) 1 3

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International Journal of Energy and Environmental EngineeringSpringer Journals

Published: Mar 19, 2018

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