In this paper, we study the effects of nonlinear convection and thermophoresis in steady boundary layer flow over a vertical impermeable wall in a non-Darcy porous medium. Both the fluid temperature and the solute concentration are assumed to be nonlinear while at the wall, both the temperature and concentration are maintained at a constant value. A similarity transformation was used to obtain a system of nonlinear ordinary differential equations, which were then solved numerically using the Matlab bvp4c solver. A comparison of the numerical results with previously published results for special cases shows a good agreement. The effects of the nonlinear temperature and concentration parameters on the velocity and heat and mass transfer are shown graphically. A representative sample of the results is presented showing the effects of thermophoresis on the fluid velocity and heat and mass transfer rates. It is found among other results, that the concentration profiles decreased with increasing values of the thermophoretic parameter.
Issue Section:
Porous Media
References
1.
Bejan
, A.
, and Khair
, K. R.
, 1985
, “Heat and Mass Transfer by Natural Convection in a Porous Medium
,” Int. J. Heat Mass Transfer
, 28
, pp. 909
–918
.10.1016/0017-9310(85)90272-82.
Lai
, F. C.
, and Kulacki
, F. A.
, 1991
, “Coupled Heat and Mass Transfer by Natural Convection From Vertical Surfaces in Porous Media
,” Int. J. Heat Mass Transfer
, 34
, pp. 1189
–1194
.10.1016/0017-9310(91)90027-C3.
Lai
, F. C.
, and Kulacki
, F. A.
, 1991
, “Non-Darcy Mixed Convection Along a Vertical Wall in a Saturated Porous Medium
,” ASME J. Heat Transfer
, 113
, pp. 252
–255
.10.1115/1.29105374.
Lai
, F. C.
, 1991
, “Coupled Heat and Mass Transfer by Mixed Convection From a Vertical Plate in a Saturated Porous Medium
,” Int. Commun. Heat Mass Transfer
, 18
, pp. 93
–106
.10.1016/0735-1933(91)90011-R5.
Angirasa
, D.
, Peterson
, G. P.
, and Pop
, I.
, 1997
, “Combined Heat and Mass Transfer by Natural Convection With Opposing Buoyancy Effects in a Fluid Saturated Porous Medium
,” Int. J. Heat Mass Transfer
, 40
, pp. 2755
–2773
.10.1016/S0017-9310(96)00354-76.
Latour
, J.
, Spiegel
, E. A.
, Toomre
, J.
, and Zahn
, J. P.
, 1976
, “Stellar Convection Theory. I. The Anelastic Modal Equations
,” J. Astrophys.
, 207
, pp. 233
–243
.10.1086/1544877.
Toomre
, J.
, Zahn
, J. P.
, Latour
, J.
, and Spiegel
, E. A.
, 1976
, “Stellar Convection Theory. II. Single-Mode Study of the Second Convection Zone in an A-Type Star
,” J. Astrophys.
, 207
, pp. 545
–563
.10.1086/1545228.
Van der Borght
, R.
, 1975
, “Finite-Amplitude Convection in a Compressible Medium and Its Application to Solar Granulation
,” Mon. Not. R. Astron. Soc.
, 173
, pp. 85
–95
.9.
Van der Borght
, R.
, 1980
, “A Numerical Study of Non-Linear Convection in a Compressible Medium
,” J. Comput. Appl. Math.
, 6
, pp. 283
–294
.10.1016/0771-050X(80)90038-810.
Partha
, M. K.
, 2010
, “Nonlinear Convection in a Non-Darcy Porous Medium
,” Appl. Math. Mech.
, 31
, pp. 565
–574
.10.1007/s10483-010-0504-611.
Kremer
, D. M.
, Davis
, R. W.
, Moore
, E. F.
, Maslar
, J. E.
, Burgess
, D. R.
, Jr., and Ehrman
, S. H.
, 2003
, “An Investigation of Particle Dynamics in a Rotating Disk Chemical Vapor Deposition Reactor
,” J. Electrochem. Soc.
, 150
, pp. 918
–922
.10.1149/1.153618012.
Eckert
, E. R. G.
, and Drake
, R. M.
, 1972
, Analysis of Heat and Mass Transfer
, McGraw-Hill
, New York
,13.
Fuchs
, N. A.
, 1964
, The Mechanics of Aerosols, The Macmillan Co.
, New York
.14.
Epstein
, M.
, Hauser
, G. M.
, and Henry
, R. E.
, 1985
, “Thermophoretic Deposition of Particles in Natural Convection Flow From a Vertical Plate
,” ASME. J. Heat Transfer
, 107
, pp. 272
–276
.10.1115/1.324741015.
Chamkha
, A. J.
, and Pop
, I.
, 2004
, “Effect of Thermophoresis Particle Deposition in Free Convection Boundary Layer From a Vertical Flat Plate Embedded in a Porous Medium
,” Int. Commun. Heat Mass Transfer
, 31
, pp. 421
–430
.10.1016/j.icheatmasstransfer.2004.02.01216.
Goren
, S. L.
, 1977
, “Thermophoresis of Aerosol Particles in the Laminar Boundary Layer on a Flat Plate
,” J. Colloid Interface Sci.
, 61
, pp. 77
–85
.10.1016/0021-9797(77)90416-717.
Ferdows
, M.
, Nazmul
, and Masahiro
, O. T. A.
, 2011
, “Thermophoresis and Chemical Reaction Effects on MHD Natural Convective Heat and Mass Transfer Flow in a Rotating Fluid Considering Heat and Mass Fluxes
,” Can. J. Sci. Eng. Math.
, 2
, pp. 114
–139
.18.
Chamkha
, A. J.
, and Issa
, C.
, 2000
, “Effects of Heat Generation/Absorption and Thermophoresis on Hydromagnetic Flow With Heat and Mass Transfer Over a Flat Surface
,” Int. J. Numer. Methods Heat Fluid Flow.
, 10
, pp. 432
–449
.10.1108/0961553001032740419.
Partha
, M. K.
, 2009
, “Suction/Injection Effects on Thermophoresis Particle Deposition in a Non-Darcy Porous Medium Under the Influence of Soret, Dufour Effects
,” Int. J. Heat Mass Transfer
, 52
, pp. 1971
–1979
.10.1016/j.ijheatmasstransfer.2008.07.05520.
Partha
, M. K.
, 2008
, “Thermophoresis Particle Deposition in a Non-Darcy Porous Medium Under the Influence of Soret, Dufour Effects
,” Heat Mass Transfer
, 44
, pp. 969
–977
.10.1007/s00231-007-0330-z21.
Muhaimin
, I.
, Kandasamy
, R.
, Khamis
, A. B.
, and Roslan
, R.
, 2013
, “Effect of Thermophoresis Particle Deposition and Chemical Reaction on Unsteady MHD Mixed Convective Flow Over a Porous Wedge in the Presence of Temperature-Dependent Viscosity
,” Nucl. Eng. Des.
, 261
, pp. 95
–106
.10.1016/j.nucengdes.2013.03.01522.
Murthy
, P. V. S. N.
, 2000
, “Effect of Double Dispersion on Mixed Convection Heat and Mass Transfer in Non-Darcy Porous Medium
,” ASME J. Heat Transfer
, 122
, pp. 476
–484
.10.1115/1.128699523.
Telles
, R. S.
, and Trevisan
, O. V.
, 1993
, “Dispersion in Heat and Mass Transfer Natural Convection Along Vertical Boundaries in Porous Media
,” Int. J. Heat Mass Transfer
, 36
, pp. 1357
–1365
.10.1016/S0017-9310(05)80103-624.
Cheng
, P.
, 1981
, “Thermal Dispersion Effects in Non-Darcian Convective Flows in a Saturated Porous Medium
,” Lett. Heat Mass Transfer
, 8
, pp. 267
–270
.10.1016/0094-4548(81)90041-225.
Plumb
, O. A.
, 1983
, “The Effect of Thermal Dispersion on Heat Transfer in Packed Bed Boundary Layers
,” ASME/JSME Thermal Engineering Joint Conference
, Vol. 2
, pp. 17
–21
.26.
Hong
, J. T.
, and Tien
, C. L.
, 1987
, “Analysis of Thermal Dispersion Effect on Vertical-Plate Natural Convection in Porous Media
,” Int. J. Heat Mass Transfer
, 30
, pp. 143
–150
.10.1016/0017-9310(87)90067-627.
Lai
, F. C.
, and Kulacki
, F. A.
, 1989
, “Thermal Dispersion Effects on Non-Darcy Convection Over Horizontal Surfaces in Saturated Porous Media
,” Int. J. Heat Mass Transfer
, 32
, pp. 971
–976
.10.1016/0017-9310(89)90246-928.
Murthy
, P. V. S. N.
, and Singh
, P.
, 1997
, “Thermal Dispersion Effects on Non-Darcy Natural Convection With Lateral Mass Flux
,” Heat Mass Transfer
, 33
, pp. 1
–5
.10.1007/s002310050155Copyright © 2014 by ASME
You do not currently have access to this content.
