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The objective of this study is to develop a mathematical model for a two-pot enclosed mud cookstove. A new model has been developed combining transient heat transfer, combustion chemistry and fluid flow. The model can be used for variation of the operation and design parameters. The model predicts performance parameters such as efficiency, boiling time, excess air ratio (EAR), transient wall, flame and char temperature. For an input power of 5.1 kW, the estimated overall efficiency, EAR and boiling time were 17.1%, 1.97 and 43 minutes, respectively. The model outcome is compared with experimental results. Further, 10 parameters are varied and their impact on cookstove performance is analysed. The optimum dimension for the door opening, combustion- chamber height and wall thickness are suggested. Therefore, this study can serve as an effective tool for cookstove design. Keywords: improved cookstove; modelling; MATLAB; transient heat transfer; wood were based on a trial-and-error approach. Therefore, lo- Introduction cally available stoves do not match the best design that The use of biomass resources for cooking and heating is modern engineering can offer. Lately, researchers have as old as human civilization. Currently, more than 3 billion used numerical modelling and computational fluid dy- people in the world rely on biomass for cooking and space- namics (CFD) tools for cookstove design, with better heating purposes . The fuelwood demand has created understanding of guiding principles . Globally, only a stress on forest cover over the world. Moreover, the indoor handful of researchers have adopted the numerical mod- burning of fuelwood releases particulate matter, carbon elling technique of the heat-transfer and combustion pro- monoxide (CO) and other toxic pollutants, which is leading cess in solid-fuel cooking stoves . to pressing global health issues . In Nepal, the majority of the population (i.e. 65%) depend The last 40 years have witnessed an increase in the on firewood for cooking. The situation might not change in awareness level on the social and environmental impact the future considering the country’s unstable economy and of traditional cookstoves. This has enhanced the focus of poverty. The position of Nepal’s dependency on firewood the public and the government sector on addressing the and the challenges are similar to most underdeveloped associated challenges. Studies on cookstoves have come countries, where traditional cooking stoves are preva- up with strategies to reduce the usage of fuel and harmful lent. The majority of cooking stoves used in low-income emissions. However, design modifications of the cookstove Received: 3 March, 2019; Accepted: 24 June, 2019 © The Author(s) 2019. Published by Oxford University Press on behalf of National Institute of Clean-and-Low-Carbon Energy This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact firstname.lastname@example.org Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 Parajuli et al. | 289 countries are made of clay, since it is readily available and model for enclosed-type stoves [1415 , ]. Sharma compiled has null cost. More than 1.2 million families in Nepal use basic design principles for a cookstove including combus- the two-pot improved mud cookstove (ICS), which is dis- tion, fluid flow and heat transfer . These studies gave seminated by the Nepal government . Such stoves were a rough guideline on how one should approach a better originally based on the ‘Hydrabad or Magan Stove’ and mathematical model. modified through a series of trials. Cookstove-design prin- A pause occurred between the 1990s and early 2000s. ciples and engineering of the model being disseminated The researchers in this field were focused on the use of have yet to be discussed. To counter this problem, this CFD tools. A CFD tool, although it has high fidelity com- study has been conducted in view of the development of a pared to a simple model, has a higher computational mathematical model for the two-pot mud ICS. cost. Because of this, CFD was not suitable for a para- Review of the available literature suggests that mod- metric variation study. In 2010, Pandit et al. developed elling of the cooking stove has not yet reached a level at a theoretical model for solid-fuel combustion in the which it can be used as a tool for stove design. The true Harsha Cookstove. This work incorporated steady-state utility of mathematical modelling of a cooking stove and transient combustion models for solid-fuel burning. would become evident if the model could help to per - The model focused on the details of the combustion pro- form a parametric analysis of the stove and identify the cess but parametric variation was not concerned . optimum dimension for the cooking stove for any given Agenbroad et al. developed a simple steady-state model configuration. A proper theoretical model able to deliver for a rocket stove and solved iteratively for the airflow this purpose is not available. Therefore, modelling of the rate and flue-gas temperature . Shah and Date intro- cooking stove remains a major challenge considering duced a four-step Hautmann reaction to model the com- the fact that it is a non-linear system. The mathematical bustion of the gas phase. The model could accurately model developed in this study is a pioneer for addressing define the heat transfer for a shielded-type cookstove transient heat-transfer behaviour incorporating fluid flow . Kshirsagar et al. presented the most promising and combustion. Further, the model can be used for para- model for cookstoves alongside its experimental veri- metric variation and performance evaluation, which jus- fication . They developed a performance-prediction tifies its purpose. tool for shielded stoves. Heat-transfer and mass-transfer models were combined in a MS Excel Spreadsheet that predicted the effect on 31 stove output parameters for 20 input variables (geometry, material and operation). 1 Literature review MacCarty developed a steady-state computational zonal Early modelling efforts were initiated by the wood-burning model of a wood-burning, natural-draft, single-pot, stove group at Eindhoven University in the 1980s. De shielded-fire stove to predict the fluid-flow and heat- Lepeleire et al. presented common design principles for transfer behaviour inside the stove [, 3 21]. Recently, cookstove-performance improvement . Verhaart et al. Gogoi et al. developed a steady-state heat-transfer model explained cookstove design in a novel way using gen- to predict cookstove performance, varying the operating eral principles of engineering, which was supported by and design conditions for the Harsha Stove . A new Bussmann . Bussmann et al. also presented an ad hoc approach was developed where the flame was considered theoretical model for the calculation of convective and ra- as a cylinder of separate temperatures. diative heat transfer to the pan . The first step towards The literature review is summarized in Table 1. The type modern modelling techniques was taken by De Lepeleire of stove studied, model characteristics and capability for and Christiaens. They introduced a mathematical model parametric variation are shown in the table. It is shown coupling convective heat transfer with simple flue-gas that a model that permits carrying out parametric analysis flow . Prasad et al. calculated the combustion-chamber of the stove to identify the optimal dimension for a given wall losses for three different materials, namely dried clay, configuration, incorporating combustion, transient heat ceramic and metal, assuming one-dimensional transient transfer and fluid flow, is still lacking. heat conduction in a plane wall . Baldwin presented rough guidelines for the design of biomass cookstoves and investigated wall losses . Date developed a theoretical 2 The model framework for predicting the performance of the CTARA 2.1 Model geometry cookstove . He assumed complete chemical combus- tion and calculated the heat transfer for a packed-bed Fig. 1 shows the schematic of the stove used for math- model and gas-phase model. Various parameters were ematical modelling in this work. The stove is divided into varied for shielded-type cookstoves to study the effect and three zones. The combustion zone (volume beneath the the model was verified with experimentation published in first pot) is designated as zone 1. It is assumed that the Part I . Bussman conducted an experiment in which he combustion occurs only in this zone. The flue gas then studied the parametric variation for a shielded-fire stove passes through the baffle geometry, comes into contact . Kumar and Schutte separately developed a theoretical with the second pot and enters the chimney. This region Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 290 | Clean Energy, 2019, Vol. 3, No. 4 Table 1 Characteristics of different research Parametric Reference Stove type Model characteristics variation De Lepeleire, 1981 Enclosed Air-inlet-area calculation No Verhaart, 1982 Enclosed Simple calculation of firepower No Bussmann et al., 1983 Open Fire Simple heat-transfer model No De Lepeleire and Shielded Basic flue-flow modelling combined with convective No Christiaens, 1983 heat-transfer model Prasad et al., 1985 Shielded Transient heat-transfer model; conduction only No Baldwin, 1987 Shielded Coupled combustion modelling and heat-transfer Yes modelling Date, 1988 Shielded Coupled heat-transfer modelling and flue-flow modelling Yes Bussmann et al., 1988 Shielded Coupled simple heat-transfer and flue-flow modelling Yes (Exp. only) Kumar et al., 1990 Enclosed Coupled flue-flow modelling and heat-transfer modelling No (without radiation) Schutte et al., 1991 Enclosed Use of combustion stoichiometry predicting flue-gas No composition Pandit et al., 2010 Shielded Steady-state and transient combustion modelling Yes Agenbroad et al., 2011 Shielded Use of simple flue-flow modelling and introduction of di- No mensionless analysis Shah and Date, 2011 Shielded Coupled heat-transfer, combustion and flue-flow modelling Yes Kshirsagar et al., 2015 Shielded Detailed heat-transfer coupled with flue-flow modelling No Gogoi et al., 2016 Shielded Detailed heat-transfer modelling assuming flame as a cy- No linder of uniform temperature volatile release/char formation (pyrolysis), burning of volatiles and oxidation of char . This model separates wood combustion into two subzones inside the combus- tion chamber. The fuel-bed area is one subzone where Zone 2 moisture evaporation, pyrolysis and char oxidation take Zone 3 place. Volatile combustion takes place above the fuel-bed region. Zone 1 Moisture evaporation. Biomass usually contains moisture as liquid water stored in the fuel-particle pores; moisture is evaporated along with the rise in the wood-surface tem- perature. In this model, it is assumed that all the moisture content (f) in the wood is evaporated instantaneously. The rate of evaporation of the moisture is given by: ˙ ˙ m = m × f H2O, moisture fuel (1) Fig. 1 Schematic drawing of cookstove showing different zones Pyrolysis. Under a limited supply of air, only the thermal in the stove is termed zone 2. Zone 3 comprises the space disintegration of organic matter occurs, leading to a re- inside the chimney. lease of volatiles and the formation of char. The wood p -yr olysis begins at around 200 C of wood-surface temperature. Above 450 C, all wood components end their volatile emis- 2.2 Basic principles of mathematical modelling sion . The volatiles are mainly composed of CO, CO , Precise mathematical modelling of the cookstove shall H , H O and higher hydrocarbons (CH ) . In this model, 2 2 x y represent the real-life situation with accuracy. The basic C H represents the higher hydrocarbons, as it effectively 7 16 phenomena occurring inside the cookstove are combus- represents both light and heavy (soot and tar) hydrocar - tion, heat transfer and fluid flow. bons. Mass fractions of various species are taken from the study of Ragaland et al. for dry wood . The rate of for - 2.2.1 Combustion model mation of different products from pyrolysis is: The solid-fuel-combustion process involves four ˙ ˙ m =(mass fraction) × m (2) j, vol fuel overlapping subprocesses: evaporation of moisture, Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 Parajuli et al. | 291 Å ã m ˙ =(mass fraction) × m ˙ (3) E char fuel x a a b c char R = −10 exp − [C H ] [O ] [C H ](11) C H 2 4 2 7 16 2 4 R T where j represents individual species CO, CO, H , H O and 2 2 2 Å ã C H . 7 16 a x a b c R = −10 exp − [CO] [O ] [H O](12) CO 2 2 R T Char oxidation. The char-burning rate is controlled by mixed Å ã a a b c gas-film diffusion and chemical reaction. This depends on R = −10 exp − [H ] [O ] [C H ](13) H 2 2 2 4 R T the partial pressure of the oxygen at the solid surface and in the gas, fluid-flow velocity, diameter of char, its porosity, The value of exponents x, a, b, c and E are taken as sug- surface temperature, etc. It is understood from the litera- gested by Hautman . R is the universal gas constant ture that char-burning produces CO, CO and H in various 2 2 and T is the temperature of the combustion zone. The net ratios. Stimley et al. explain hydrogen release as a func- rate of the production of species (R ) after the volatile j,net tion of temperature and, above 700 C, char does not release combustion can be evaluated using: hydrogen . As the temperature of the char during wood R = R − 2 R (14) CO,net CO C H ° 2 4 combustion is above 700C, the study excludes H in char combustion. Evans et al. have proposed an overall reaction R = −R (15) CO ,net CO of char combustion : 1 1 Å ã Å ã (16) 1 R = R + R + R 1 2 O ,net CO H C H 2 2 2 4 (4) C + O → 2 1 − CO + − 1 CO 2 2 2 2 Φ Φ Φ R = R − 2R − R (17) H ,net H C H C H where Ф is the stoichiometric air requirement for the com- 2 2 2 4 7 16 plete combustion of the char. R = −R (18) H O,net H 2 2 1 + rc Φ= (5) (19) 0.5 + R = R − R C H ,net C H C H rc 2 4 2 4 7 16 where rc is the ratio of CO and CO formation and Pederson R = −R (20) C H ,net C H 7 16 7 16 suggested ratio of formation of CO and CO . Å ã CO −3300 rc = = 12 exp (6) Wood-surface temperature. The wood-surface tempera- CO T 2 char ° ° ture varies from 300C to 500C during the total combus- Å Å ã ã 1 M CO tion period and changes along the surface and with time ˙ ˙ m = m × 2 1 − (7) CO,char char Φ M char . The char-combustion and volatile-oxidation pro- ÅÅ ã ã cesses govern the temperature of the wood surface. To 2 M CO ˙ ˙ m = m × − 1 (8) CO ,char char include both processes in one equation, it is assumed Φ M char that the volatile phase typically occupies 40% of the time Å ã 1 M O and char-burning occupies 60% . Taking these factors ˙ ˙ m = − m × (9) O ,char char Φ M char into account, Date in 1988 postulated the average wood- burning rate as : Å Å ã Volatile combustion. Volatile combustion includes the oxida- ˙ m (1 − f) fuel ρ D −E wood wood vol = 0.4 x υ exp vol vol tion of CO, H and hydrocarbon. In order to properly char - A 8 R T 2 wood vol Å ãã acterize the oxidation process of hydrocarbons, the model −E char + 0.6 (1 − x ) υ exp vol char uses reactions presented by Hautman . These overall R T char (21) reactions would describe the breakdown of the hydro- Sharma and Pukalla show that the density of wood (ρ ) carbon into the intermediate olefins, the oxidation of the wood found in Nepal generally varies from 452 to 960 kg/m intermediate olefins to CO and the oxidation of CO to CO: . The values of different constants (E, ν , E ν ) vol vol char, char C H → 7/2C H + H 7 16 2 4 2 are functions of the wood diameter and are based on the curve-fitting of data provided by Tinney et al. . C H + O → 2CO + 2H 2 4 2 2 CO + 1/ O → CO 2 2 2 2.2.2 Fluid-flow model In naturally driven wood-burning stoves, the buoyancy H + 1/ O → H O 2 2 2 2 force drives the airflow against the flow resistance. The reaction rates for the consumption () Rof four react- The mass-flow rate of air for a natural-draught stove ants are shown below: is primarily calculated using the general stack equa- Å ã x a a b c tion . The equation balances the pressure force and R = −10 exp − [C H ] [O ] [C H ](10) C H 7 16 2 2 4 7 16 R T buoyancy force: Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 292 | Clean Energy, 2019, Vol. 3, No. 4 The heat-transfer coefficient (h) is a function of the Å ã Nusselt (Nu) number. In the case of natural-draught flue ˙ (22) m = C × A × ρ × 2gH − 1 air d flue T cookstoves, the Nusselt number can be evaluated from amb the relation [3536 , ]: Agenbroad used the general stack equation in its most basic form . Kshirsagar et al. calculated the coeffi- 0.25 (28) Nu = 0.53 × (Gr × Pr) cient of discharge (C) incorporating major and minor 3 2 losses . A similar approach of pressure balance g × B × T × l × ρ Gr = (29) incorporating losses is used in this model to determine 2 the airflow rate. (30) Pr = μ × 2.2.3 Heat-transfer model where μ, C , k, and ρ are the dynamic viscosity, specific heat The operation of the stove consists of two distinct phases: p capacity, thermal conductivity and density of the fluid, the initial transient state and the operational steady state. respectively. Heat-transfer phenomena in both phases are unique. Although the cookstove generally should be designed for Transient model. As heat is absorbed by the wall of the the operational steady stage, the mud cookstove needs cookstove, its temperature increases with time and the a considerable amount of time to reach the steady state. heat is conducted towards the outer wall. Similarly, pot Thus, a transient heat-transfer model is essential for mud and water temperatures vary with time. The general heat- stoves. conduction equation for ‘homogenous material’ with no internal heat generation and ‘unsteady-state one- Conduction. The heat transfer through conduction can be dimension heat flow’ is given below : calculated using the Fourier Conduction Law: d T ρ C dT 1 dT − kAdT p ˙ (31) (23) = = Q = dx k dt α dt dx where α is the thermal diffusivity of the wall material. Using where k is the thermal conductivity of the material. The an explicit, finite-difference approximation, Equation (31) major regions of interest from the viewpoint of conduction is solved and incorporated into this model. are (i) transfer of heat from the pot to the content of the pot, (ii) loss of heat through the stove wall and (iii) transfer of heat to the interior of the wood. 2.3 Model assumption Radiation. The rate of radiation heat transfer is given by the Some assumptions are made for simplification of the Stefan-Boltzmann law: model, as listed below: (24) Q = εσ AT (i) The fluid motion and heat transfer are one-dimen- sional processes. The emissivity (ε) depends upon the temperature (T) and (ii) The fluid is Newtonian and the flow is laminar. the characteristic length (). L Sigel and Howell have pro- (iii) The temperature, pressure and density are constant vided the following empirical relation for the calculation for a particular zone and particular time. of emissivity : (iv) A continuous fuel-feed rate is assumed. ¶Ä ä −4 ε = exp 0.848 + 9.02 × 10 × T (v) The thermal resistance of the pot material is Ä ä © −6 neglected. + 0.9589 + 4.8 × 10 × T × ln (0.2 × L ) (25) (vi) The heat lost by the water through evaporation during sensible heating is neglected. Volume L = 3.6 × (26) b (vii) The heat required for pyrolysis of the fuel is supplied Surface Area from the fuel bed (char) only. In a cookstove, the regions of interest from the radiation (viii) Only the heat-transfer process is analysed as a tran- point of view are the radiation emitted by the flame; the sient process. radiation exchange between the inner walls, pot and fire The validity of the one-dimensional assumption for fire bed; and the radiation loss to the atmosphere through the simulation may be questioned, for two reasons: three- door opening, the stove wall and pots. dimensional characteristics and turbulent character - istics. However, considerable insight into the fluid flow Convection. The convective heat transfer is estimated using and heat transfer can be gained without introducing the the relation: complexity that turbulent three-dimensional motion (27) Q = hA ΔT possesses. Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 Parajuli et al. | 293 2.4 Mathematical-model formulation C = 0.9362 + 0.0002 × T (kJ/kgK) (37) p,vol vol 2.4.1 Analysis of zone 1 The heat transfer from the char to the door, first pot and The fuel-feed rate is a constant input parameter based on inner wall involves solving the interconnected radiation which volatile and char release rates are evaluated. The calculations. Assuming the first zone to be of a cylindrical combustion of char releases heat equivalent to the product shape, the view factor (F) between two parallel plates of of the mass of the char and its calorific value (CV): cylinder can be evaluated as : Q = m × CV char char char (32) Ä ä 2 2 2 (38) F = Y − Y − 4B C The heat produced from the char will be transferred to the char−pot1 2B door, inner wall, pot and wood for moisture evaporation 0.5 D and pyrolysis. pot1 (39) B = 2H ˙ ˙ ˙ ˙ ˙ Q = Q + Q + Q + Q char wood char−pot1 char−door char−wall1 (33) pot1 The burning of wood is an exothermic process as a whole. C = (40) 2H However, heat is required for pyrolysis and moisture evap- oration. The production of volatiles is vigorous, in the range 2 2 (41) Y = 1 + B + C of 350–400 C . Thus, the model assumes that a certain Other view factors can be calculated using view-factor amount of energy is required to heat the wood from am- algebra: bient temperature to 400 C, its latent heat for pyrolysis; ° F = 1 − F (42) char−cyl char−pot1 to increase the temperature of volatiles from 400 C to the wood-surface temperature; and for moisture evaporation: A F = A F + A F char char−cyl char char−door char char−wall1(43) ˙ To simplify the radiation calculation, the electrical analogy Q = m (1 − f) C (673 − T ) wood fuel p wood amb has been presented in Fig. 2. + LH + C (T − 673) wood p vol wood + m ˙ × f C (T − T ) In an electrical analogous circuit, points 1, 2, 3, 4 and 5 de- fuel p water boil amb + LH + C (T − T ) water p steam wood boil note char, pot 1, wood, wall 1 and door, respectively. Applying (34) nodal analysis at point ‘a’ and point ‘b’ of Fig. 3 gives: Å ã Å ã 0.1031 + 0.003867 × T + 4.19f 1 1 1 1 E E b2 b4 C = p.wood J + E − − − = − − b0 1 + f R R R + Z R R + Z R 01 01 02 2 04 02 2 04 +(0.02355T − 1.32f − 6.191) f (44) (35) Å ã Å ã 1 1 1 1 E E b1 b5 J − − − + E = − − + Q 1 b0 wood J Z R R R Z R 1 01 15 01 1 15 LH = 10467.5 (49 × D + 38) ; D is in meters wood wood wood kg (45) (36) Then, Equation (33) becomes, b4 b5 1 Z Z R 2 E 1 12 b2 b1 1a b 2 b3 Fig. 2 Electrical analogy of radiation heat transfer in zone 1 R R 17 15 4 Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 294 | Clean Energy, 2019, Vol. 3, No. 4 b4 b5 1 Z E Z 2 b2 b1 1 1a b b3 Fig. 3 Simplified star connection Table 2 Parameters in the electrical analogous circuit Resistance Values Resistance Values Heat transfer Values 1− ε J -E 1 char _ 1 b5 R Z Q char -door 12 1 ε .A R F .A 15 char -pot1 char char char 1 1− ε _ E -E pot1 b0 b2 R Z Q char -pot1 15 F .A 2 R +Z char -door char ε .A o2 2 pot1 pot1 1− ε E -E 1 wall _ b0 b4 R Z char -wall 14 4 F .A ε .A R +Z char -wall char wall wall o4 4 1 _ _ Q Q char -wood wood F .A wall -pot1 char ˙ ˙ ˙ ˙ J − E J − E J − E 1 b5 1 b2 1 b4 Q = Q + Q + Q(50) ˙ ˙ vol vol−pot1 vol−wall1 flue1 Q = + + + Q(46) char wood R R + Z R + Z 15 02 2 04 4 The heat transfer from the volatiles to pot 1 takes place Equations (44), (45) and (46) are unknowns in J, E and E . 1 b0 b1 through radiation and convection: These equations can be solved for the heat transfer from Ä ä the char to wall 1, char to pot 1 and char to door, and char 4 4 Q = σ A ε T − α T pot1 pot1 pot1 vol−pot1 flue1 flame temperature. + h A T − T 1 pot1 flame pot1 The mass fraction of species j leaving fuel bed (ω )is j,bed (51) given by: The flame temperature varies with the height of the flame. m˙ × ω + m˙ + m˙ + m˙ air j,air j,vol j,char j,moisture Dupuy et al. have provided a correlation for the vertical ω = (47) j,bed flue flame temperature profile that is used to calculate the flame temperature striking the pot . ˙ ˙ ˙ ˙ ˙ m = m + m + m + m (48) flue air vol char moisture The heat transfer to wall 1 takes place by radiation as The species now enter the volatile combustion zone. The well as convection : rate of heat production from volatile combustion is: Ä ä 4 4 Q = σ A ε T − α T vol−wall1 wall1 flue1 1 wall1 iwall1 Q = R × ΔH (49) vol j,net f ,j + h A (T − T ) 1side wall1 1 iwall1 (52) where ∆H is the heat of formation, which is corrected for f,j Ç å temperature. The heat produced from volatile combustion 1/6 0.6 + 0.387 × (Gr × Pr) is transferred to the first pot, the wall of zone 1 and the re- h = k (53) 1side 0.559 1 + 9/16 Pr maining is taken by the flue gas: 4 Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 Parajuli et al. | 295 The temperature of the flue gas rises from ambient tem- 2.4.4 Analysis of the flue flow perature to the temperature of zone 1: The mass-flow rate of air is calculated based on the pres- sure difference assuming one-dimensional flow in all Q = m × C × (T − T )(54) flue1 flue p1 1 amb three zones: Equations (49), (50), (51), (52) and (54) can be solved for T, 2 2 k + k ρ V ρ V k ρ V amb in ent amb in bend1 exp1 1 1 P − P = − + + the heat gained by pot 1 and wall 1. Similarly, the mass 1 0 2 2 2 fraction of species j leaving the volatile combustion zone (1 + k ) ρ V cont1 2 2 can be calculated as: (63) m × ω + R × M flue j,bed j,net j 2 2 2 ω = (55) j,exit ρ V k ρ V 1 + k ρ V 2 2 2 2 exp2 3 3 ˙ bend2 (64) flue P − P = − + + 2 1 2 2 2 2 2 2 2 ρ V k ρ V λ H ρ V k ρ V 2.4.2 Analysis of zone 2 3 3 bend3 3 3 chim 3 3 exit 3 3 P − P = − + + + 3 2 2 2 2 D 2 chim The heat carried by the flue gas from the first zone is trans- (65) ferred to pot 2 and wall 2, and the remainder is carried out P − P =(ρ − ρ ) × g × H (66) by the flue gas to the third zone: 3 0 amb 3 chim where P, V and k denote the pressure, velocity and loss ˙ ˙ ˙ ˙ Q = Q + Q + Q(56) flue1 flue2−pot2 flue2−wall2 flue2 coefficients, respectively. Converting all velocity vari- ables into mass-flow rates and denoting the ratio of The temperature of this zone is T. The heat transfer from the mass-flow rate of flue gas to air by ψ , P – P will be 3 0 the flue gas to pot 2 is: equivalent to: Ä ä 4 4 Q = σ A ε T − α T + h A T − T flue2−pot2 pot2 flue2 2 pot2 pot2 2 pot2 2 pot2 Å ã 2 2 m ˙ −1 + K K + K ψ (57) ent bend1 exp1 air Ä ä 2ρ 1 A amb (A Ar) pot1 Similarly, the heat lost through the wall is given by: door amb Å ã Ä ä K + K ψ 4 4 ˙ cont1 bend2 Q = σ A ε T − α T flue2−wall2 wall2 flue2 2 wall2 iwall2 + Ä ä hole amb + h A (T − T ) 2side wall2 2 iwall2 Å ã (58) λ H chim 2 K + K + + 1 bend3 exp2 ψ chim Ä ä Due to the heat transfer to pot 2 and wall 2, the tempera- chim amb ture of the flue gas changes from T to T So, using the 1 2. (67) energy balance: Equations (66) and (67) can be equated and solved for mass-flow rate of air. The loss coefficient can be calculated ˙ ˙ ˙ (59) m × C × (T − T )= Q + Q flue p2 1 2 flue2−pot2 flue2−wall2 using Table 3. Equations (57), (58) and (59) can be solved to calculate the temperature of zone 2. 2.4.5 Analysis of transient heat transfer The one-dimensional transient heat-transfer problem 2.4.3 Analysis of zone 3 is solved using an explicit, finite-difference approxima- The heat carried by the flue gas from the second zone is tion. The initial wall and pot temperatures are known and transferred to the chimney walls and the remainder is car - the following equations (described here for zone 1 only) ried out by the flue gas to the atmosphere: are used to calculate respective temperature at the next time step: ˙ ˙ ˙ Q = Q + Q (60) flue2 flue3−chim loss Ä ä i+1 i i T = T + T for 0 ≤ i ≤ j and 0 ≤ m ≤ n m m+1 m−1 The temperature of this zone is T. The heat transfer from (68) the flue gas to the chimney walls is: Ä ä 4 4 Q = σ A ε T − α T flue3−chim chim flue3 3 chim ichim Table 3 Minor loss coefficients + h A (T − T ) 3side chim 3 ichim Loss coefficient  Value (61) Due to heat transfer to the chimney wall, the temperature Entrance (k ) 0.5 ent of the flue gas changes from T to T So, using the energy Exit (k ) 1 2 3. exit balance: Bending (k ) 0.9 (assume all bends of similar types) bend Ä ä large Expansion (k ) exp − 1 Q = m ˙ × C × (T − T )(62) A small flue3−chim flue p3 2 3 Contraction (k ) 1 A small cont 1 − 2 A large Equations (61) and (62) can be solved to calculate the tem- Friction Factor (λ) 64/Re perature of zone 3. Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 296 | Clean Energy, 2019, Vol. 3, No. 4 where j = analysis time/time_step_size (Δt) and n = thick- 2.4.6 Post-processing parameters ness of wall/spatial_step_size (Δx). The following post-processing parameters are evaluated to Using the boundary conditions for the outer wall with define the cookstove performance: energy conservation: m ˙ air Ä ä Air Fuel Ratio (AFR)= (74) i i ˙ i+1 i Ä ä fuel kA T − T 1 0 ρ A Δx T − T i i 0 0 h A T − T + = C 0 amb 0 p Δx 2 Δt AFR − AFRs (69) (75) Excess Air Ratio (EAR)= AFRs The above equation can be solved for the outer-wall tem- i+1 AFRs is the stoichiometric air-to-fuel ratio and is calculated perature (T ) using ∆x = : to be 6.62 based on a generic wood formula suggested by Ä ä h Δx i+1 i 0 i Tillman . The amount of heat that shall be liberated by (70) T = T − T − T 0 1 0 amb burning fuel in the assumed rate is: Using the boundary condition for the inner wall with en- P = m × CV (76) fuel wood ergy conservation: The CV of wood with moisture content f is : i+1 i Ä ä kA ρ A Δx T − T i i n n ˙ (71) Q + T − T = C n−1 n p CV = LHV (1 − f) − f (4.186 (T − T )+ 2257)(77) wall wood boil amb Δx 2 Δt Since heat transfer is a transient problem, an average value The above equation can be solved for the inner-wall tem- i+1 of the heat gained by the pot per unit time is evaluated and perature (T ) using Δx = 2αΔt : is further used in the calculation of efficiencies: ˙ i Δx Q i+1 i wall Q + Q (72) char vol T = T + n n−1 (78) η = comb k A This concept has been used for the transient heat transfer Q + Q pot1 pot2 through the walls of all zones. Similarly, the temperat- η = (79) thermal Q + Q char vol ures of the pots also vary with time. Some portion of heat gained by the pot is lost through its side wall. The re- η = η + η (80) overall comb thermal maining heat is used to increase the temperatures of the water and the pot: 2.4.7 Mathematical-model integration In this work, the model is integrated into MATLAB . Fig. 4 Ä ä i+1 i T − T pot pot shows the basic flow of the program. The assumption i i ˙ ˙ Q − Q = m C + m C pot water p,water pot p,pot potloss Δt of one-dimensional heat transfer allows conversion of (73) Input parameters • Calculation of Heat Generation Combustion model • Calculation of Species Fraction calculation Heat transfer model • Solve steady heat transfer problem for one time step Zone1 Transient • Record temperature, heat loop Zone2 transfer rate at that time step • Solve for next Zone3 time step • Calculation of mass flow rate of Flue flow fresh air entering the cookstove No Is ΔT<0.1°C Yes Output parameters Fig. 4 Basic flowchart of mathematical model Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 Parajuli et al. | 297 the complex equations into simple algebraic forms. All To compare the mathematical model with experimental equations were compiled in MATLAB and an iterative results, stoves were fabricated with varying chimney procedure-based solver was developed. The basic numer - heights and combustion-chamber heights. All cookstoves ical methods were used to solve these equations. The in- were fabricated by a stove master, who has the eminence puts into the program are stove geometry and operational of crafting hundreds of two-pot mud ICSs. WBT 4.2.3 was parameters, as shown in Table 4. The iteration ends for con- performed in the Stove Testing Lab at Pulchowk Campus vergence of temperature less than 0.1 C and the program . Thermal efficiency and temperatures (flame, char, generally converges in 8–20 iterations. The program ter - wall and water) were studied to describe the performance minates with an insignificant amount of error in approxi- of the cookstove. mation. Thus, the model can be used to vary important Equipment used while testing solicits paramount con- input parameters to evaluate cookstove-performance cern. The temperatures of both pots were continuously parameters. noted down at intervals of 2 minutes. Two different digital thermometers were used. One was a multi-stem therm- ometer with an external sensing probe with a resolution of 0.1 C. The thermometer measured the temperature 3 Technical evaluation of the cookstove ° ° in 1-second intervals and in the range of –50 C to 200C. The purpose of designing and developing improved Another was a multipurpose thermocouple thermometer cookstoves is to achieve clean combustion and higher that could accept seven types of thermocouples. A K-type efficiency to meet the cooking requirements. Although thermocouple of lower range (up to 300 C) was used to field measurements (controlled cooking test and kitchen- measure the second-pot temperature whereas another performance test) are able to provide representative and K-type thermocouple of higher range (up to 900 C) was reliable results, they require a relatively high labour in- used to measure the flame temperature. A moisture meter tensity, high cost and are usually time-consuming . designed to measure the wood-moisture content with Laboratory testing is intended to be reproducible and po- range of 8–60%, accuracy of 2% and resolution of 0.1% was tentially suitable to compare the performance of different used. A digital weight-measuring instrument that could cookstoves . Thus, a water-boiling test (WBT) under measure weights up to 30 kg with a resolution of 2 grams lab conditions is used to assess the performance of the was used to measure the weight during the test. The wall cookstove. It is intended to measure how efficiently a stove temperature was measured using an infrared thermom- ° ° uses fuel to heat water in a cooking pot and the quantity of eter with a temperature range of –30 C to 650C. The ac- emissions produced while cooking. Institutions like GACC curacy of the instrument is up to 1% of reading and the and Aprovecho have set benchmarks and standards for repeatability is 0.8%. The wood used for experimentation WBTs . was Sal (i.e. ‘Sorea Robusta’) and was sun-dried before Table 4 Reference input conditions Particulars Values Particulars Values Cookstove material (mud)  Water Thermal conductivity (k) 0.65 W/mK Mass of water in first pot (m ) 5 kg water Density (ρ) 2400 kg/m Mass of water in the second pot (m ) 5 kg water Specific heat (C ) 1381 J/kgK Char  Emissivity (ε) 0.68 Calorific value (CV ) 29 500 kJ/kg char Pot Emissivity (ε ) 0.85 char Specific heat (C ) 400 J/kgK Stove dimensions p pot Emissivity (ε ) 0.95 Door diameter 0.15 m pot Mass of first pot (m ) 0.8 kg Hole diameter 0.075 m pot2 Diameter of first pot (D ) 0.18 m Height of combustion chamber 0.40 m pot1 Height of first pot (H ) 0.20 m Length of combustion chamber 0.40 m pot1 Mass of second pot (m ) 0.5 kg Length of second chamber 0.35 m pot2 Diameter of second pot (D ) 0.15 m Height of chimney 0.99 m pot2 Height of second pot (H ) 0.20 m Length of chimney 0.13 m pot2 Wood  Chimney diameter 0.075 m Lower Heating Value (LHV) 19 500 kJ/kg Operational parameters Moisture content by weight (f) 10% Fuel-feed rate 0.3 g/s Volatile content by weight (x) 80% Inlet-area ratio (Ar) 0.7 vol Density (ρ ) 880 kg/m wo Diameter (D ) 0.025 m wo Length (L ) 0.05 m wo Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 Outer Wall Temp (K) 298 | Clean Energy, 2019, Vol. 3, No. 4 testing. The experimentation was conducted in a closed on which the model is based can be assumed to be realis- lab with no wind conditions and tests were performed at tically representing the physical phenomena. the rate of one test per day to reduce the background con- centration and to allow the cookstove to cool before the 4.2 Model-predicted reference-condition result beginning of the cold-start test. 4.2.1 Important parameters Table 4 shows the specification of the reference stove. The unsteady-state analysis of 1 hour has been done and 4 Results and discussions important performance parameters are evaluated. The 4.1 Comparison between model and experiment efficiency, EAR, temperature of zones and pots, time to boil water in both pots, etc. are presented in Table 5. The Experimental results from the WBT test are compared with thermal efficiency of 20% suggests that heat transfer to the the model-predicted results. The experimentally meas- pots is low. The combustion efficiency is below 100% even ured efficiency is 18.13%, which agrees with the model- for 200% excess air. The overall efficiency is predicted to be predicted value of 17.35%. The wood-surface temperature ~17.1%. Experience suggests the efficiency of the two-pot measured during the test was 693 K and was close to the mud ICS to be in the range of 16–20%. For a wood-burning 1-hour time-averaged value of 683 K predicted by the rate of 0.3 g/s, the airflow rate is 5.83 g/s in this stove; model. Pandit et al. showed that, over 1 hour of combus- 197.32% excess air is supplied due to the natural draft of tion, the time-average value of the wood-surface tempera- the chimney. This high quantity of air quenches the flame, ture was 723 K . During char-burning, the measured thereby decreasing the flame temperature and thermal ef- char-surface temperature of 1108 K was consistent with ficiency. The temperature of the char is ~860C, which is the model-predicted value of 1136 K. in accordance with the value assumed by Kshirsagar et al. The inner- and outer-wall temperatures predicted by the . After 1 hour, the first-pot temperature reaches 100 C, model and the measured experimental values plotted whereas the second-pot temperature reaches 66 C. Single- against time show a similar trend in Fig. 5. The tempera- pot enclosed cookstoves would not be able to capture the ture of the outer wall measured during experimentation energy absorbed by the second pot. after 1 hour was 49C, which is in accordance with the model-predicted value of 52C. The variation of chimney height and the efficiency are plotted in Fig. 6. The trend of 4.2.2 Emission the efficiency measured during the experiment is in ac- Air from the atmosphere is assumed to have only oxygen cordance with the model prediction. Fig. 7 shows the vari- and nitrogen in certain proportions, as listed in Table 6. In ation of efficiency with combustion-chamber height. The the fuel bed, char-burning, pyrolysis and wood-moisture experiment was done by dipping the pot by ~4 cm into the evaporation occur simultaneously. Some of the oxygen is combustion chamber. There was a 2% increase in the effi- consumed by the char-burning process, producing CO and ciency as suggested by the model and the result from the CO . The Hautman reaction predicts the consumption and experimentation is also similar. production of different species in a wood-burning process. From the above compared data, it can be observed that the temperature at various locations and the efficiency at 4.2.3 Heat balance varied chimney and combustion-chamber heights are in The components of the heat balance are shown in accordance with model-predicted data. Thus, the process Figure 8. The char-burning releases 1115 W (21.5%) and 700 330 650 325 600 320 550 315 Inner Actual Inner Predicted Outer Actual Outer Predicted 0 500 1000 1500 2000 2500 3000 3500 4000 Time (sec) Fig. 5 Variation of inner- and outer-wall temperatures with time Inner Wall Temp (K) Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 Parajuli et al. | 299 80 cm 100 cm 120 cm 21.8 21.1 20.7 20.3 19.4 18.4 18.1 18.1 17.4 17.0 16.3 15.6 Cold Start Hot Start Simmer Model Fig. 6: Variation of efficiency with chimney height 23.01 21.75 21.37 20.28 19.38 19.32 18.13 17.35 Cold StartHot Start Simmer Mathematical Model 40 cm 36 cm Fig. 7 Variation of efficiency with combustion-chamber height Around 4.7% of the heat is utilized by the second pot, Table 5 Reference-condition result whereas 2.7% of the heat is lost through wall 2. The re- Temperatures maining heat is carried by the flue gas and 8% of the heat Efficiencies (%) (Kelvin) is lost through the chimney wall in zone 3. Around 40% of the heat is carried away by the flue gas exiting from the Thermal efficiency (η ) 19.86 Pot 1 (T ) 373 therm pot1 chimney, which is a great amount. Some researchers have Combustion efficiency (η ) 86.12 Pot 2 (T ) 339.45 comb pot2 Overall efficiency (η ) 17.10 Zone 1 (T ) 728 utilized this heat to run a fan, which will create a forced overall 1 Mass-flow rate of air 5.83 g/s Zone 2 (T ) 679 draught in the cookstove. Around 14% of the heat is lost Excess air ratio (EAR) 1.9732 Zone 3 (T ) 618 3 due to the incomplete combustion of the fuelwood. Thus, Time to boil water, pot 1 2586.4 s Flame (T ) 807 flame there exists an opportunity for the cookstove designer to Time to boil water, pot 2 – Char (T ) 1136 char reduce the heat taken by flue gas to the atmosphere. Fig. 9 shows rate of heat stored and lost by walls in dif- volatile-burning releases 3359 W (64.6%) of heat. Heat lost ferent zones. It is clear from the figure that a significant through the door (3.5%) is high due to the large opening amount of heat is stored by the wall of zone 1.This is be- area. A small amount (5.5%) of heat is transferred from the cause of the high thermal mass of mud. Heat stored and char to the first pot and the wall of zone 1. Around 6.8% lost through wall 2 is small compared to the chimney and of the heat is required for the pyrolysis process. Some wall 1 due to the shorter time and smaller contact area portion of the heat released from volatile combustion is of the flue gas with wall 2. A high quantity of heat is lost gained by pot 1 (7.5%) and lost through wall 1 (1.6%). Heat through chimney walls because of the large surface area transfer to the wall is minimal due to the high tempera- exposed to the atmosphere. Thus, alternate materials like ture of the inner wall. The remaining heat is carried by the vermiculate, fire bricks, composite materials, etc. may be flue gas to the secondary zone, where no heat is produced. evaluated to enhance the efficiency of the cookstove. Efficiency Efficiency Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 300 | Clean Energy, 2019, Vol. 3, No. 4 Table 6 Emission fraction of different species (%) Particulars O N CO CO H H O C H C H 2 2 2 2 2 7 16 2 4 Atmosphere 23.3 76.7 – – – – – – Bed 20.9 73.1 1.4 1.9 0.020 1.6 1.1 – Zone 1 20.1 73.1 1.1 2.9 0.018 1.9 0.9 0.03 Exit 16.7 73.1 – 6.9 – 3.1 – 0.18 40.2 13.9 12.8 8.0 7.1 6.8 4.7 3.9 2.7 Fig. 8 Heat-transfer components (%) Loss Store 124.5 327.9 288.9 112.2 41.3 29.5 Wall1 Wall2 Chimney Fig. 9 Heat stored and lost through the walls of different zones 4.2.4 Transient behaviour Some parameters, such as the inlet-area ratio and the door Generally, with elapsed time, the rate of energy stored by (opening) diameter, chimney height and diameter, etc. are a wall slowly decreases because of its increasing tempera- coupled and studied. ture, thus reducing the energy-curve slope. But, for the (i) Variation of the inlet-area ratio and diameter of the time period of 1-hour duration, the energy stored by the door: The variation of the door diameter alters the wall of zone 1 does not change its slope and is shown to area through which fresh air enters the stove. A factor be strongly represented by a straight line, as shown by the called the inlet-area ratio (Ar) is used, which is the dotted line in Fig. 10. It suggests that the stove is nowhere ratio of the area unoccupied by fuel in the door to near the steady-state region. This is because of the high the total door area. Fig. 11 shows that the quantity of thermal mass of the mud. Therefore, the mud stove cannot air entering the cookstove increases with increases be modelled as a steady-state heat-transfer problem. in the door diameter and inlet-area ratio. The excess air saturates at around 200% because of the capacity 4.3 Model-predicted results of the input- of the chimney (99 cm height, 7.5 cm diameter). The parameter variation increase in the air quantity enhances the combus- The result of the variation of one parameter at a time while tion but quenches the flame. So, it was noted from keeping all others constant is discussed in this section. the model that the combustion efficiency is increased Door Pot 1 Wall 1 Pyrolysis Pot 2 Wall 2 Chimney Exit Incombustion Heat Flux (W) Heat Transfer (%) Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 Parajuli et al. | 301 160 0000 y = 405.6x + 60704 140 0000 R = 0.9964 120 0000 100 0000 800 000 600 000 400 000 200 000 0 500 1000 1500 2000 2500 3000 3500 4000 Time (Sec) Fig. 10 Energy stored by walls of zone 1 2.1 1.9 Ar=0.5 Ar=0.6 Ar=0.7 Ar=0.8 1.8 1.7 1.6 1.5 10 12 14 16 18 20 Door Diameter (cm) Fig. 11 Variation of excess air ratio with door diameter whereas the thermal efficiency is decreased. However, combustion-chamber height results in a reduction in as the EAR saturates with increases in the door diam- the thermal efficiency, as shown in Fig. 13. The stove eter and inlet-area ratio, the efficiency also saturates. being evaluated has a combustion-chamber height of 25 cm. Thus, the height can be reduced as much as The overall efficiency shown in Fig. 12 indicates the designer wishes but decreasing the combustion- hardly any increase beyond a door diameter of 15 cm. chamber height to <20 cm may significantly alter the Moreover, increasing the door diameter raises the flame development. Thus, a combustion-chamber question of the strength of the cookstove, which is not height of 20 cm is suggested. A simple modification can part of this analysis. The inlet-area ratio is an oper - be made in the current stove by dropping the pot inside ational factor and is beyond the scope of the designer. the combustion chamber by 5 cm. The variation of the inlet-area ratio for door diameters >15 cm results in insignificant changes. Therefore, it (iii) Variation of combustion-chamber wall thickness: As the is recommended that the door (opening) diameter be thickness of the combustion chamber is varied, the effi- kept at 15 cm. ciency of the stove was observed to vary insignificantly by 0.7%. The small amount of increase noted with the in- (ii) Variation of height of combustion chamber: As the crease in wall thickness is due to the reduction of the height of the combustion chamber is increased, a de- heat lost to the surroundings and increase in the inner- crease in the temperature of the flame striking the wall temperature. No new modification is suggested for bottom of the pot was noticed in the model. Apart wall thickness from the model evaluation. The designer from the reduction in the flame temperature, the wall surface area also increases, thereby reducing the en- can choose the thickness of the mud wall depending on ergy received by the pot. Therefore, an increase in the the strength of the wall required. Energy Stored by Wall1 (Joules) Excess Air Ratio Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 302 | Clean Energy, 2019, Vol. 3, No. 4 17.5 16.5 Ar=0.5 Ar=0.6 Ar=0.7 Ar=0.8 15.5 10 12 14 16 18 20 Door Diameter (cm) Fig. 12 Variation of efficiency with door diameter Thermal Overall 10 15 20 25 30 35 40 Height of Combustion Chamber (cm) Fig. 13 Variation of efficiency with combustion-chamber height 12 14 16 18 20 22 24 Diameter of Pot1 (cm) Fig. 14 Variation of overall efficiency with pot 1 diameter (iv) Variation of first-pot and second-pot diameters: It is to parameter is guided by the site-specific requirement. be noted that the pot diameter and the combustion- With an increase in the first-pot diameter, the area chamber diameter are used interchangeably in the art- available for heat transfer increases, which results in icle, as the local design of the cookstove is based on an increase in thermal efficiency. However, because the diameter of the utensil available. Therefore, the of the increased volume for combustion, the rate of Heat Received by Pot1 (W) Efficiency Efficiency Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 Parajuli et al. | 303 reaction decreases, reducing the combustion efficiency. hence these materials can be used for space-heating Thus, the overall efficiency as plotted in Fig. 14 repre - purposes. The lowest amount of heat transfer to the sents a bell-shaped curve and indicates the optimum wall is for vermiculate. The decrease in heat transfer first-pot diameter as 16.5 cm. to the wall results in an increase in heat transfer to Increasing the second-pot diameter increases the heat- the pot, thus increasing the thermal efficiency. Fig. 15 transfer area, thus enhancing the thermal efficiency. It shows that the use of mild steel and stainless steel is assumed that combustion does not take place in the reduces thermal efficiency, whereas firebrick and ver - second zone. So, combustion efficiency does not alter miculate increase it. Similarly, the outer-wall temper - with the second-pot diameter variation. Thus, overall ature was also noted in the model and it was observed efficiency gradually increases. The similar trend was that firebrick has the lowest outer-wall temperature, noted from the model-predicted output. Therefore, it making it safer for operation. Vermiculate, although is recommended to keep the second-pot diameter as it has the most promising efficiency, has a higher large as practically possible. wall temperature compared to the mud cookstove. Mild steel and stainless steel have an outer temper - (v) Variation of stove material: The effect on cookstove ature of around 160C, which is not safe for operation. performance with a variation of five materials as Accidents resulting in burning of skin may happen listed in Table 7 is analysed. The heat lost and stored when using such materials. The study of five different by walls of different materials is tabulated in Table 8. stove materials shows that a material of low conduc- When mud is used as the stove material, a high quan- tivity and low specific heat capacity should be used. tity of heat is stored by the walls and a small quan- tity is lost through the walls. This is due to the larger (vi) Variation of chimney diameter and height: It is thermal mass and lower thermal conductivity of mud. noted from the stack equation that an increase in The maximum amount of heat lost through stove the chimney diameter and height increases the air - walls is for mild steel and is similar for stainless steel, flow rate. An increase in the airflow rate increases the Table 7 Properties of different cookstove materials  Materials Mud Stainless steel Mild steel Vermiculate Firebrick Density (ρ) 2400 7900 7870 90 1280 Conductivity (k) 0.65 14.9 80.2 0.06 0.30 Specific heat capacity (Cp) 1381 477 447 960 1000 Table 8 Heat stored and lost, and temperatures for different materials Materials Mud Stainless steel Mild steel Vermiculate Firebrick Heat stored by walls (W) 565 433 464 339 125 Heat lost through walls (W) 359 869 818 271 173 Outer-wall temperature (°C) 52 170 154 42 84 Thermal Overall 25.0 22.7 21.7 19.9 19.6 17.1 16.7 16.5 14.2 14.2 Mud Mild Steel Stainless Steel Firebrick Vermiculate Fig. 15 Variation of efficiency with material Efficiency Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 304 | Clean Energy, 2019, Vol. 3, No. 4 7.5 cm 9 cm 10 cm 11 cm 11.5 cm 50 60 70 80 90 100 110 120 130 Chimney Height (cm) Fig. 16 Variation of efficiency with chimney height and diameter Moisture Fraction (%) Fig. 17 Variation of heat release with moisture content combustion efficiency; however, it also reduces the released from volatile combustion rapidly decreases. thermal efficiency due to flame quenching. Chimney Also, the heat required for wood-moisture evapor - height and its diameter were found to be strongly ation gradually increases, which reduces thermal effi- coupled, as shown in Fig. 16. For each chimney height, ciency. Wood with a moisture content above this value we can find a value of chimney diameter where the should not be used directly in cookstoves, but can be overall efficiency is optimal. And, for each of the cases first subjected to sun-drying before being used in the considered, the optimum efficiency is calculated to be cookstove. 18.6%. It is recommended that these two parameters be analysed together while designing/fabricating the cookstove. 5 Conclusion A novel transient heat-transfer model integrating com- (vii) Variation of moisture content of wood: With an bustion and flue-gas flow has been successfully developed increase in the moisture content of the wood, the dry for a specific enclosed mud cookstove. The study demon- weight and heat released decrease. Further, heat is strates that mathematical models can be fruitfully used to required for moisture evaporation. However, with an determine the optimum values for design and operational increase in the moisture content, the rate of volatile parameters. combustion increases. This enhances the combus- The major takeaways of this study, which are general to tion efficiency. Thus, the heat released from the vol- all cookstoves, are: atiles is almost constant with up to 20% moisture content. Increasing the moisture content beyond 20% (i) Mud cookstoves cannot be modelled assuming steady- saturates the combustion efficiency. Hence, the heat state heat transfer. Efficiency Heat Release from Volatile (W) Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 Parajuli et al. | 305 (ii) Materials of low thermal conductivity and low specific (i) Around 40% of the heat is carried by the flue gas and heat capacity are suitable for cookstoves. lost to the atmosphere. (iii) The amount of air drawn into the stove is a function (ii) The door-opening diameter should be 15 cm, for which of the chimney height and diameter, and depends to a variation in the inlet-area ratio has no impact. limited extent on other openings. (iii) The height of the combustion chamber should be (iv) The chimney diameter and height are strongly reduced by 5 cm from the existing dimension. correlated and should be analysed together. (iv) The wall thickness of the combustion chamber of (v) Wood with a moisture content beyond 20% is the current cookstove is acceptable and no change is recommended to be sun-dried before use. suggested. (v) The optimum diameter of the first pot is 16.5 cm and Further, the key findings of this research particular to the the second-pot diameter should be kept as large as improved two-pot enclosed mud cookstove are: practically possible. Nomenclature A Area Ru Universal gas constant AFR Air-fuel ratio T Temperature AFRs Stoichiometric air-fuel ratio t Time Ar Inlet-area ratio V Velocity Cd Discharge coefficient Z Resistance Cp Specific heat capacity Subscripts CV Calorific value 1, 2, 3 Zone 1, zone 2, zone 3 D Diameter j Species EAR Excess air ratio vol Volatile E Black body radiation amb Ambient f Moisture content by weight (%) i Inner F View factor o Outer g Acceleration due to gravity cont Contraction Gr Grasshoff number exp Expansion H Height chim Chimney h Convective heat-transfer coefficient comb Combustion H Heat of formation Superscripts J Radiosity i Time step k Thermal conductivity/loss coefficient Greek letters L Length α Thermal diffusivity/absorptivity L Characteristics length ε Emissivity LH Latent heat η Efficiency LHV Lower heating value λ Friction factor M Molecular weight μ Dynamic viscosity m Mass ρ Density ˙ Mass-flow rate rc Ratio of CO to CO Nu Nusselt number σ Stephen Boltzmann constant P Pressure/power Φ Stoichiometric air requirement Pr Prandtl number ω Mass fraction of species Heat-transfer rate Re Reynolds number R Reaction rate/resistance Downloaded from https://academic.oup.com/ce/article-abstract/3/4/288/5581952 by DeepDyve user on 10 December 2019 306 | Clean Energy, 2019, Vol. 3, No. 4  Gogoi B, Baruah DC. 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Clean Energy – Oxford University Press
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