In this paper, we investigate the influence of melting on mixed convection heat and mass transfer from vertical flat plate in a non-Newtonian fluid-saturated non-Darcy porous medium including the prominent Soret effect. The wall and the ambient medium are maintained at constant but different levels of temperature and concentration such that the heat and mass transfer occurs from the wall to the medium. The Ostwald–de Waele power law model is used to characterize the non-Newtonian fluid behavior. A similarity solution for the transformed governing equations is obtained. The numerical computation is carried out for various values of the nondimensional physical parameters. The variation of temperature, concentration, and heat and mass transfer coefficients with the power law index, mixed convection parameter, inertia parameter, melting parameter, Soret number, buoyancy ratio, and Lewis number is discussed for a wide range of values of these parameters.
References
1.
Epstein
, M.
, and Cho
, D. H.
, 1976, “Melting Heat Transfer in Steady Laminar Flow Over a Flat Plate
,” ASME J. Heat Transfer
, 98
, pp. 531
–533
.2.
Kazmierczak
, M.
, Poulikakos
, D.
, and Pop
, I.
, 1986 “Melting from a Flat Plate Embedded in a Porous Medium in the Presence of Steady Convection
,” Numer. Heat Transfer
, 10
, pp. 571
–581
.3.
Kazmierczak
, M.
, Poulikakos
, D.
, and Sadowski
, D.
, 1987, “Melting of a Vertical Plate in Porous Medium Controlled by Forced Convection of a Dissimilar Fluid
,” Int. Commun. Heat Mass Transfer
, 14
, pp. 507
–517
.4.
Pozvonkov
, F. M.
, Shurgalskii
, E. F.
, and Akselrod
, L. S.
, 1970, “Heat Transfer at a Melting Flat Surface Under Conditions of Forced Convection and Laminar Boundary Layer
,” Int. J. Heat Mass Transfer
, 13
, pp. 957
–962
.5.
Bakier
, A. Y.
, 1997, “Aiding and Opposing Mixed Convection Flow in Melting from a Vertical Flat Plate Embedded in a Porous Medium
,” Transp. Porous Media
, 29
, pp. 127
–139
.6.
Gorla
, R. S. R.
, Mansour
, M. A.
, Hassanien
, I. A.
, and Bakier
, A. Y.
, 1999, “Mixed Convection Effect on Melting from a Vertical Plate in a Porous Medium
,” Transp. Porous Media
, 36
, pp. 245
–254
.7.
Tashtoush
, B.
, 2005, “Magnetic and Buoyancy Effects on Melting from a Vertical Plate Embedded in a Saturated Porous Media
,” Energy Convers. Manage.
, 46
, pp. 2566
–2577
.8.
Cheng
, W. T.
, and Lin
, C. H.
, 2006, “Transient Mixed Convective Heat Transfer with Melting Effect from the Vertical Plate in a Liquid Saturated Porous Medium
,” Int. J. Eng. Sci.
, 44
, pp. 1023
–1036
.9.
Cheng
, W. T.
, and Lin
, C. H.
, 2007, “Melting Effect on Mixed Convective Heat Transfer with Aiding and Opposing External Flows from the Vertical Plate in a Liquid-Saturated Porous Medium
,” Int. J.Heat Mass Transfer
, 50
, pp. 3026
–3034
.10.
Cheng
, W. T.
, and Lin
, C. H.
, 2008, “Unsteady Mass Transfer in Mixed Convective Heat Flow from a Vertical Plate Embedded in a Liquid Saturated Porous Medium with Melting Effect
,” Int. Commun. Heat Mass Transfer
, 35
, pp. 1350
–1354
.11.
Poulikakos
, D.
, and Spatz
, T. L.
, 1988, “Non-Newtonian Natural Convection at a Melting Front in a Permeable Solid Matrix
,” Int. Commun. Heat Mass Transfer
, 15
, pp. 593
–603
.12.
Chen
, H. T.
, and Chen
, C. K.
, 1988, “Natural Convection of Non-Newtonian Fluids along a Vertical Plate Embedded in a Porous Medium
,” ASME J. Heat Transfer
, 110
, pp. 257
–260
.13.
Chen
, H. T.
, and Chen
, C. K.
, 1988, “Natural Convection of a Non-Newtonian Fluid about a Horizontal Cylinder and Sphere in a Porous Medium
,” Int. Commun. Heat Mass Transfer
, 15
, pp. 605
–614
.14.
Nakayama
, A.
, and Koyama
, H.
, 1991, “Buoyancy Induced Flow of Non-Newtonian Fluids over a Non-Isothermal Body of Arbitrary Shape in a Fluid-Saturated Porous Medium
,” Appl. Sci. Res.
, 48
, pp. 55
–70
.15.
Shenoy
, A. V.
, 1994, Non-Newtonian Fluid Heat Transfer in Porous Media
, Advances in Heat Transfer
, Vol. 24
, Academic Press
, New York
, pp. 101
–190
.16.
Nakayama
, A.
, and Shenoy
, A. V.
, 1992, “A Unified Similarity Transformation for Darcy and Non-Darcy Forced, Free, and Mixed Convection Heat Transfer in Non-Newtonian Inelastic Fluid-Saturated Porous Media
,” Chem. Eng. J.
, 50
, pp. 33
–45
.17.
Shenoy
, A. V.
, 1993, “Darcy-Forchheimer Natural, Forced and Mixed Convection Heat Transfer in Non-Newtonian Power-Law Fluid Saturated Porous Media
,” Transp. Porous Media
, 11
, pp. 219
–241
.18.
Hooper
, W.B.
, Chen
, T. S.
, and Armaly
, B. F.
, 1993, “Mixed Convection from a Vertical Plate in Porous Media with Surface Injection or Suction
,” Numer. Heat Transfer
, 25
, pp. 317
–329
.19.
Ibrahim
, F. S.
, Abdel-Gaid
, S. M.
, and Gorla
, R. S. R.
, 2000, “Non-Darcy Mixed Convection Flow along a Vertical Plate Embedded in a Non-Newtonian Fluid Saturated Porous Medium with Surface Mass Transfer
,” Int. J. Numer. Methods Heat Fluid Flow
, 10
, pp. 397
–408
.20.
Chamkha
, A. J.
, and Al-Humoud
, J. M.
, 2007, “Mixed Convection Heat and Mass Transfer of Non-Newtonian Fluids from a Permeable Surface Embedded in Porous Medium
,” Int. J. Numer. Methods Heat Fluid Flow
, 17
, pp. 95
–212
.21.
Alam
, M. S.
, and Rahman
, M. M.
, 2005, “Dufour and Soret Effects on MHD Free Convection Heat and Mass Transfer Flow Past a Vertical Flat Plate Embedded in a Porous Medium
,” J. Nav. Archit. Mar. Eng.
, 2
, pp. 55
–65
.22.
Postelnicu
, A.
, 2007, “The Influence of Chemical Reaction on Heat and Mass Transfer by Natural Convection from Vertical Surfaces in Porous Media Considering Soret Dufour Effects
,” Heat Mass Transfer
, 43
, pp. 595
–602
.23.
Narayana
, P. A. L.
, Murthy
, P. V. S. N.
, and Gorla
, R. S. R.
, 2008, “Soret-Driven Thermo-Solutal Convection Induced by Inclined Thermal and Solutal Gradients in a Shallow Horizontal Layer of a Porous Medium
,” J. Fluid Mech.
, 612
, pp. 1
–19
.24.
Kairi
, R. R.
, and Murthy
, P. V. S. N.
, 2009, “The Effect of Melting and Thermo-Diffusion on Natural Convection Heat Mass Transfer In A Non-Newtonian Fluid Saturated Non-Darcy Porous Medium
,” Open Transp. Phenom. J.
, 1
, pp. 7
–14
.25.
Christopher
, R. H.
, and Middleman
, S.
, 1965, “Power Law Fluid Flow Through a Packed Tube
,” Ind. Eng. Chem. Fundam.
, 4
, pp. 422
–426
.26.
Dharmadhikari
, R. V.
, and Kale
, D. D.
, 1985, “The Flow of Non-Newtonian Fluids Through Porous Media
,” Chem. Eng. Sci.
, 40
, pp. 527
–529
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