zbMATH — the first resource for mathematics

A numerical study of the applicability of the Boussinesq approximation for a fluid-saturated porous medium. (English) Zbl 0575.76089
The regions of applicability of the Boussinesq approximation are investigated for natural convection in a fluid-saturated porous medium. A perturbation method is used to assess the relative importance of individual terms in the differential equations which describe the natural convection process. Specific limits to the validity of the Boussinesq approximation are identified for water and air. For water, it is shown that the restrictions imposed by the classical Boussinesq approximation can be relaxed by allowing for the variation of thermophysical properties with temperature while still retaining the incompressible form of the continuity relation. Results of the analysis are verified through numerical calculations performed for steady natural convection in a planar, water-saturated porous region.

76S05 Flows in porous media; filtration; seepage
76R10 Free convection
76M99 Basic methods in fluid mechanics
Full Text: DOI
[1] Theorie Analytique de la Chaleur, Vol. 2, Gauthier-Villars, Paris, 1903.
[2] Oberbeck, Ann. Phys. Chem. 7 pp 271– (1879)
[3] Gray, Int. J. Heat Mass Transfer 19 pp 545– (1976)
[4] MacGregor, J. Heat Transfer 91 pp 391– (1969) · doi:10.1115/1.3580194
[5] and , ’Laminar natural convection in a rectangular enclosure with moderately large temperature differences’, Proc. Fourth International Heat Transfer Conf., Paper NC 2.10, Paris-Versailles, 1970.
[6] Shaukatullah, Numerical Heat Transfer 2 pp 215– (1979)
[7] and , ’Convective flows in closed cavities with variable fluid properties’, in and (eds), Numerical Methods in Heat Transfer, Wiley, Chichester 1981, pp. 387-412.
[8] Kassoy, Phys. Fluids 18 pp 1649– (1975)
[9] Strauss, J. Geophysical Research 82 pp 325– (1977)
[10] Ribando, J. Heat Transfer 95 pp 42– (1976) · doi:10.1115/1.3450467
[11] Ward, J. Hydraul. Div., ASCE 19 pp 1– (1969)
[12] Dynamics of Fluids in Porous Media, American Elsevier Pub. Co., New York, 1972. · Zbl 1191.76001
[13] and , ’MARIAH–a finite element computer program for incompressible porous flow problems: theoretical background’, SAND79-1622, Sandia National Laboratories, Albuquerque, NM, 1982.
[14] and , ’MARIAH–a finite element computer program for incompressible porous flow problems: user’s manual’, SAND79-1623, Sandia National Laboratories, Albuquerque, NM, 1982.
[15] Hickox, J. Heat Transfer 103 pp 797– (1981)
[16] Hickox, Int. J. Heat and Mass Transfer 28 pp 720– (1985)
[17] Reda, J. Heat Transfer 105 pp 795– (1983)
[18] ’Relaxation from forced downflow to buoyantly driven upflow about a vertical heat source in a liquid-saturated porous medium’, Proc. Fifth Engineering Mech. Div. Conf., ASCE, Laramie, Wyoming, 1984.
[19] Gill, J. Fluid Mech. 26 pp 515– (1966)
[20] ’The effect of conducting divisions on the natural convection of air in a rectangular cavity with heated side walls’, AIAA/ASME 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conf., Paper 82-HT-69, St. Louis, 1982.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.