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Transient convection in a porous medium

  • J. W. Elder (a1)
Abstract

Laboratory and numerical experiments on non-steady convective flows in a porous medium are reported. The main objective is to note the detailed comparison found between the time-dependent solutions and the time-like development of the iterative solutions of the steady equations originally pointed out by Garabedian (1956) and others.

Two flows are chosen for study. The first is the flow which develops when a blob of hot fluid is released at the base of a porous slab. The second is the flow which develops when a portion of the base of a porous slab is suddenly heated. The former flow is very simple and ideally suited for establishing the numerical scheme. The latter flow, however, produces several unexpected features. The gross features of the time development, when the motion is strongly non-linear, show an alternation between periods of slow gradual adjustment and periods of rapid change.

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References
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Courant, R., Friedrichs, K. O. & Lewy, H. 1928 Math. Ann. 100, 32.
Elder, J. W. 1966a J. Fluid Mech. 24, 823.
Elder, J. W. 1966b J. Fluid Mech. 27, 29.
Elder, J. W. 1966c In: The Mantles of the Earth and the Terrestrial Planets (ed. S. K. Runcorn). New York: Wiley. (in the Press).
Fox, L. 1962 Numerical Solutions of Ordinary and Partial Differential Equations. London: Pergamon Press.
Garabedian, P. R. 1956 Math. Tables Aids Comput. 10, 183.
HELE-SHAW, H. S. J. 1898 Trans. Inst. Nav. Arch. 40, 21.
Lapwood, E. R. 1948 Proc. Camb. Phil. Soc. 44, 508.
Malkus, W. V. R. 1954 Proc. Roy. Soc. A, 225, 185.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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