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RESEARCH PAPERS: Porous Media

Combined Influence of Mass and Thermal Stratification on Double-Diffusion Non-Darcian Natural Convection From a Wavy Vertical Wall to Porous Media

[+] Author and Article Information
B. V. Rathish Kumar, Shalini

Parallel Computing Laboratory, Department of Mathematics, Indian Institute of Technology, Kanpur, 208 016, India

J. Heat Transfer 127(6), 637-647 (Jun 06, 2005) (11 pages) doi:10.1115/1.1863258 History: Received March 07, 2004; Revised November 20, 2004; Online June 06, 2005
Copyright © 2005 by ASME
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References

Nield, D. A., and Bejan, A., 1998, Convection in Porous Media, Springer Verlag, New York.
Bejan,  A., and Khair,  K. R., 1985, “Heat and Mass Transfer by Natural Convection in a Porous Medium,” Int. J. Heat Mass Transfer, 28(5), pp. 909–918.
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(12), pp. 2755–2773.
Singh,  P., and Queeny,  O., 1997, “Free Convection Heat and Mass Transfer Along a Vertical Surface in a Porous Medium,” Acta Mech., 123, pp. 69–73.
Nakayama,  A., and Hossain,  M. A., 1995, “An Integral Treatment for Combined Heat and Mass Transfer by Natural Convection in a Porous Medium,” Int. J. Heat Mass Transfer, 38(4), pp. 761–765.
Angirasa,  D., Peterson,  G. P., and Pop,  I., 1997, “Combined Heat and Mass Transfer by Natural Convection in a Saturated Thermally Stratified Porous Medium,” Numer. Heat Transfer, Part A, 31, pp. 255–272.
Rathish Kumar,  B. V., Singh,  P., and Bansod,  V. J., 2002, “Effect of Thermal Stratification on Double-Diffusive Natural Convection in a Vertical Porous Enclosure,” Numer. Heat Transfer, Part A, 41, pp. 421–447.
El-Khatib,  G., and Prasad,  V., 1987, “Effects of Stratification on Thermal Convection in Horizontal Porous Layers With Localized Heating from Below,” ASME J. Heat Transfer, 109, pp. 683–687.
Rathish Kumar,  B. V., and  Shalini, 2004, “Double-Diffusive Natural Convection Induced by a Wavy Surface in a Stratified Porous Medium,” J. Porous Media, 7(4), pp. 31–40.
Takhar,  H. S., and Pop,  I., 1987, “Free Convection From a Vertical Flat Plate to a Thermally Stratified Fluid,” Mech. Res. Commun., 14(2), pp. 81–86.
Tewari,  K., and Singh,  P., 1992, “Natural Convection in a Thermally Stratified Fluid Saturated Porous Medium,” Int. J. Eng. Sci., 8, pp. 1003–1007.
Rees,  D. A. S., and Lage,  J. L., 1997, “The Effect of Thermal Stratification on Natural Convection in a Vertical Porous Insulation Layer,” Int. J. Heat Mass Transfer, 40(1), pp. 111–121.
Rathish Kumar,  B. V., and Singh,  P., 1998, “Effect of Thermal Stratification on Free Convection in a Fluid-Saturated Porous Enclosure,” Numer. Heat Transfer, Part A, 34, pp. 343–356.
Yao,  L. S., 1983, “Natural Convection Along a Vertical Wavy Surface,” ASME J. Heat Transfer, 105, pp. 465–468.
Rees,  D. A. S, and Pop,  I., 1994, “A Note on Free Convection Along a Vertical Wavy Surface in a Porous Medium,” ASME J. Heat Transfer, 116, pp. 505–508.
Cheng,  C. Y., 2000, “Natural Convection Heat and Mass Transfer Near a Vertical Wavy Surface with Constant Wall Temperature and Concentration in a Porous Medium,” Int. Commun. Heat Mass Transfer, 27(8), pp. 1143–1154.
Bejan,  A., and Poulikakos,  D., 1984, “The Non Darcy Regime for Vertical Boundary Layer Natural Convection in a Porous Medium,” Int. J. Heat Mass Transfer, 27(5), pp. 717–722.
Plumb,  O. A., and Huenefeld,  J. C., 1981, “Non-Darcy Natural Convection from Heated Surfaces in Saturated Porous Medium,” Int. J. Heat Mass Transfer, 24(4), pp. 765–768.
Kumari,  M., Pop,  I., and Nath,  G., 1985, “Non-Darcy Natural Convection from a Heated Vertical Plate in Saturated Porous Media with Mass Transfer,” Int. Commun. Heat Mass Transfer, 12, pp. 337–346.
Lai,  F. C., and Kulacki,  F. A., 1987, “Non-Darcy Convection from Horizontal Impermeable Surfaces in Saturated Porous Media,” Int. J. Heat Mass Transfer, 30(10), pp. 2189–2192.
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Figures

Grahic Jump Location
Schematic diagram of the coordinate system with the boundary conditions
Grahic Jump Location
Grid validation tests for various grids: (a) with Gr*=0, (b) with Gr*=1000 and with a=0.2,ϕ=0 deg, B=2,Le=1,ST=0.05, and SC=0.025
Grahic Jump Location
Local Nusselt number plots with (a) varying a, (b) varying Gr*, (c) varying ST and corresponding average Nusselt number plots are in (b), (d) and (f ), respectively.
Grahic Jump Location
f contours for (a) a=0.0, (b) a=0.5 with ϕ=0 deg, B=2,Le=1,Gr*=1,ST=0.05, and SC=0.025, corresponding T and C contours are in (c) and (d) and in (e) and (f ) respectively.
Grahic Jump Location
f-contours for (a) Gr*=0, (b) Gr*=1, (c) Gr*=102 with a=0.2,ϕ=0 deg, B=2,Le=1,ST=0.05, and SC=0.025, corresponding T and C contours are in (d)–(f ) and in (g)–(i) respectively.
Grahic Jump Location
T contours in (a)–(c) and C contours in (d)–(f ) corresponding to ST=0.0, 0.05, 0.1, respectively, with a=0.2,ϕ=0 deg, Gr*=1,B=2,Le=1, and SC=0.025.T contours with varying SC(SC=0.0, 0.025, 0.05) are in (g)–(i) with other parameters fixed as a=0.2,ϕ=0 deg, Gr*=1,B=2,Le=1, and ST=0.05.
Grahic Jump Location
Local Nusselt number plots with (a) varying B, (c) varying Le and corresponding average Nusselt number plots are in (b) and (d), local Sherwood number plots with varying Le in (e) and corresponding average Sherwood number plots in (f ).
Grahic Jump Location
T contours for (a) B=0, (b) B=2, and (c) B=4 with a=0.2,ϕ=0 deg, Gr*=1,Le=1,ST=0.05, and SC=0.025.T contours in (d)–(f ) and C contours in (g)–(i) corresponding to Le=0.05, 1, 5, respectively, with a=0.2,ϕ=0 deg, Gr*=1,B=2,ST=0.05, and SC=0.025.

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