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Bounds for heat transport in a porous layer

Published online by Cambridge University Press:  29 March 2006

F. H. Busse  and
D. D. Joseph
F. H. Busse
Affiliation:
Department of Planetary and Space Sciences, University of California, Los Angeles
D. D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota
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Abstract

Bounds on the heat transport in a porous layer are derived using the variational method of Howard (1963) and Busse (1969b). The relatively simple structure of the variational problem in the case of porous convection allows one to formulate the theory more simply and to investigate some of the mathematical questions posed by the earlier work. A precise characterization of the solution with N wavenumbers is given. The variational problem is solved exactly among functions with a single overall wavenumber and this solution is in good agreement with a nonlinear perturbation solution of the governing equations and with experiments. An N-wavenumber solution is constructed for large Nusselt numbers by boundary-layer methods. The asymptotic solution is compared with a numerical solution of the problem for N = 2. The comparison supports the boundary-layer assumptions introduced in the asymptotic analysis.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 54 , Issue 3 , 8 August 1972 , pp. 521 - 543
Copyright
© 1972 Cambridge University Press

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References

Busse, F. H. 1969a Z. angew. Math. Phys. 20, 1–14.
Busse, F. H. 1969b On Howard's upper bound for heat transport in turbulent convection J. Fluid Mech. 37, 457–477.Google Scholar
Combarnous, M. & LeFur, B. 1969 Transfert de chaleur par convection naturelle dans une couche poreuse horizontale Comptes Rendus, 269, 1009–102.Google Scholar
Elder, J. W. 1967 Steady free convection in a porous medium heated from below J. Fluid Mech. 27, 29–48.Google Scholar
Hancock, H. 1958 Elliptic Integrals. Dover.
Howard, L. N. 1963 Heat transport in turbulent convection J. Fluid Mech. 17, 405–432.Google Scholar
Irmay, S. 1958 On the theoretical derivation of Darcy and Forcheimer formulae Trans. Am. Geophys. Union, 39, 702–707.Google Scholar
Katto, Y. & Masuoka, T. 1967 Criterion for the onset of convective flow in a fluid in a porous medium Int. J. Heat Mass Transfer, 10, 297–309.Google Scholar
Lapwood, E. R. 1948 Convection of a fluid in a porous medium Proc. Comb. Phil. Soc. 44, 508–21.Google Scholar
Schneider, K. J. 1963 Investigation of the influence of free thermal convection on heat transfer through granular material. 11th Int. Cong. of Refrigeration (Munich), paper 11–4.Google Scholar
Westbrook, D. R. 1969 The stability of convective flow in a porous medium Phys. Fluids, 12, 1547.Google Scholar