Application of the UNIFAES discretization scheme to mixed convection in a porous layer with a cavity, using the Darcy model

Journal of Porous Media

Volumn 3, Issue 2, 2000, Pages 139-154

  Llagostera, Jorge ^a   Figueiredo, José R ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000684547     PISSN: 1091028X     EISSN: None     Source Type: Journal    
DOI: 10.1615/jpormedia.v3.i2.40     Document Type: Article

References (30)

1. Allen, D.N. de G. and Southwell, R.V., Relaxation methods applied to determine the motion, in two dimensions, of a viscous flow past a fixed cylinder, Q. J. Mech. Appl. Math., vol. 8, pp. 129-145, 1955.
2. Bejan, A., Convection Heat Transfer, 2nd ed., John Wiley & Sons, New York, 1995.
3. Brouwers, H.J.H., Heat-transfer between a fluid saturated porous-medium and a permeable wall with fluid injection or withdrawal, Int. J. Heat Mass Transfer, vol. 37, pp. 989-996, 1994.
4. Cheng, P., Similarity solutions for mixed convection from horizontal impermeable surfaces in saturated porous media, Int. J. Heat Mass Transfer, vol. 20, pp. 893-898, 1977.
5. Cheng, P., Heat transfer in geothermal systems, Adv. Heat Transfer, vol. 14, pp. 1-105, 1978.
6. nd Symposium on Development and use of Geothermal Resources, United Nations, vol. 3, pp. 1591-1598, 1977.
7. Combarnous, M.A. and Bia, P., Combined free and forced convection in porous media, Soc. Petrol. Eng. J., vol. 11, pp. 399-405, 1971.
8. Dufour, F. and Neel, M.C., Numerical study of instability in a horizontal porous channel with bottom heating and forced horizontal flow, Phys. Fluids, vol. 10, pp. 2198-2207, 1998.
9. Figueiredo, J.R., Unified finite approach exponential-type scheme for convective-diffusive fluid transport equations. In Current Developments in Numerical Simulation of Heat and Mass Transfer, ASME-HTD-339, pp. 55-64, 1997.
10. Figueiredo, J.R. and Llagostera, J., Comparative study of the unified finite approach exponential-type scheme (UNIFAES) and its application to natural convection in porous cavity, Numer. Heat Transfer B Fund., vol. 35, pp. 347-367, 1999.
11. Hasnaoui, M., Bilgen, E., and Vasseur, P., Natural-convection above an array of open cavities heated from below, Numer. Heat Transfer A Appl., vol. 18, pp. 463-482, 1990.
12. Horton, C.W. and Rogers, R.T., Convection currents in a porous medium, J. Appl. Phys., vol. 16, pp. 367-370, 1945.
13. Lai, F.C. and Kulacki, F.A., Experimental study of free and mixed convection in horizontal porous layers locally heated from below, Int. J. Heat Mass Transfer, vol. 34, pp. 525-541, 1991a.
14. Lai, F.C. and Kulacki, F.A., Oscillatory mixed convection in horizontal porous layers locally heated from below, Int. J. Heat Mass Transfer, vol. 34, pp. 887-890, 1991b.
15. Lapwood, E.R., Convection of a fluid in a porous medium, Proc. Cambridge Philos. Soc., vol. 44, pp. 508-521, 1948.
16. Leonard, B.P. and Drummond, J.E., Why you should not use 'hybrid', 'power-law' or related exponential schemes for convective modelling - there are much better alternatives. Int. J. Numer. Methods Fluids, vol. 20, pp. 421-442, 1995.
17. Llagostera, J. Mixed Convection Past an Open Cavity, State University at Campinas, Campinas, Brazil, 1990 (Doctoral thesis, in Portuguese).
18. Llagostera, J., Natural convection in an irregular porous cavity: effects of thermal boundary conditions, Heat Transfer 1994, vol. 7, pp. 103-108, Taylor & Francis, 1994.
19. Manole, D.M., Lage, J.L., and Nield, D.A., Convection induced by inclined thermal and solutal gradients, with horizontal mass-flow, in a shallow horizontal layer of a porous medium, Int. J. Heat Mass Transfer, vol. 37, pp. 2047-2057, 1994.
20. Nield, D.A., Correlation formulas for mixed convection heat-transfer in saturated porous-media, Int. J. Heat Fluid Flow, vol. 14, pp. 206-206, 1993.
21. Nield, D.A. and Bejan, A., Convection in Porous Media, Springer-Verlag, New York, 1992.
22. Patankar, S.V., Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980.
23. Prasad, V., Lai, F.C., and Kulacki, F.A., Mixed convection in horizontal porous layers heated from below, J. Heat Transfer, vol. 110, pp. 395-402, 1988.
24. Rivas, E.K. de, On the use of non-uniform grids in finite-difference equations, J. Comput. Phys., vol. 10, pp. 202-210, 1972.
25. Robillard, L., Wang, C.H., and Vasseur, P., Multiple steady states in a confined porous medium with localized heating from below, Numer. Heat Transfer, vol. 13, pp. 91-110, 1988.
26. Schrock, V.E. and Laird, A.D.K., Physical modeling of combined forced and natural convection in wet geothermal formations, J. Heat Transfer, vol. 98, pp. 213-220, 1976.
27. Spalding, D.B., A novel finite difference formulation for differential expressions involving both first and second derivatives, Int. J. Numer. Methods Eng., vol. 4, pp. 551-559, 1972.
28. Varejão, L.M.C., Flux-Spline Method for Heat and Momentum Transfer, Ph.D. Thesis, University of Minnesota, Minneapolis, 1979.
29. Vynnycky, M. and Pop, I., Mixed convection due to a finite horizontal flat plate embedded in a porous medium, J. Fluid Mech., vol. 351, pp. 359-378, 1997.
30. Wong, H.H. and Raithby, G.D., Improved finite-difference methods based on a critical evaluation of the approximation errors, Numer. Heat Transfer, vol. 2, pp. 139-163, 1979.