Thermophoresis
particle
deposition
617
International Journal of Numerical
Methods for Heat & Fluid Flow
Vol. 19 No. 5, 2009
pp. 617-632
# Emerald Group Publishing Limited
0961-5539
DOI 10.1108/09615530910963553
Received 7 September 2007
Revised 6 May 2008
Accepted 29 May 2008
Thermophoresis particle
deposition – thermal radiation
interaction on natural convection
heat and mass transfer from
vertical permeable surfaces
H.M. Duwairi
Mechanical Engineering Department, Faculty of Engineering and Technology,
The University of Jordan, Amman, Jordan, and
Rebhi. A. Damseh
Mechanical Department, Al-Husun University College,
Albalqa Applied University, Irbid, Jordan
Abstract
Purpose – The purpose of this paper is to study thermophoresis particle deposition and thermal
radiation interaction on natural convection heat and mass transfer by steady boundary layer flow
over an isothermal vertical flat plate embedded in a fluid saturated porous medium.
Design/methodology/approach – The governing partial differential equations are transformed
into non-similar form by using special transformation and then the resulting partial differential
equations are solved numerically by using an implicit finite difference method.
Findings – Different results are obtained and displaced graphically to explain the effect of various
physical parameters on the wall thermophoresis deposition velocity and concentration profiles. It is
found that the increasing of thermal radiation parameter or dimensionless temperature ratio heats the
fluid and decreases temperature gradients near permeable wall, which increases local Nusselt
numbers and decreases wall thermophoresis velocities. It is also found that the effect of power indices
of either temperatures or concentration enhances both local Nusselt numbers and wall
thermophoresis velocities. Comparison with previously published work in the limits shows
excellent agreement.
Originality/value – The paper presents useful conclusions based on graphical results obtained
from studying numerical solutions for thermophoresis-thermal radiation heat and mass transfer
interaction by steady, laminar boundary layer over a vertical flat plate embedded in a porous medium.
Keywords Heat transfer, Mass transfer, Convection, Porous materials
Paper type Research paper
Nomenclature
C ¼ species concentration
C
F
¼ Forcheimer coefficient
C
f
¼ local skin friction factor
c
p
¼ specific heat capacity
D ¼ Brownian diffusion coefficient
Da
x
¼ local Darcy number, K=x
2
f ¼ dimensionless stream function
g ¼ gravitational acceleration
h ¼ local heat transfer coefficient
K ¼ permeability
k ¼ thermal conductivity
k
t
¼ thermophoresis coefficient
Le ¼ Lewis number,
m
=D
p ¼ constant defined in
Equation (6)
M
w
ðxÞ¼local surface mass flux
N ¼ buoyancy ratio,
½
C
ðC
w
ÀC
1
Þ=
T
ðT
w
ÀT
1
Þ
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