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Natural convection flow of a viscous incompressible fluid in a rectangular porous cavity heated from below with cold sidewalls

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Abstract

We consider the flow, which is induced by differential heating on the boundaries of a porous cavity heated from below. In particular we allow the sidewalls to have the same cold temperature as the upper surface, and thus the problem is a variant of the Darcy-Bénard convection problem, but one where there is flow at all non-zero Grashof numbers. Attention is focused on how the flow and heat transfer is affected by variations in the cavity aspect ratio, the Grashof number and the Darcy number. The flow becomes weaker as the Darcy number decreases from the pure fluid limit towards the Darcy-flow limit. In addition the number of cells which form in the cavity varies primarily with the aspect ratio and is always even due to the symmetry imposed by the cold sidewalls.

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Acknowledgements

The authors are acknowledging with gratitude to the Ministry of Science & Technology, Peoples’ Republic of Bangladesh, for providing fund to perform this work (Grant No. BPM/Sec-9/B/Gr 2000-2001/463.)

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Authors and Affiliations

  1. Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh, Bangladesh

    M. A. Hossain

  2. Department of Mechanical Engineering, University of Bath, Bath BA7 2AY, U.K. (e-mail: ensdasr@bath.ac.uk), UK

    D. A. S. Rees

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  1. M. A. Hossain
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  2. D. A. S. Rees
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Correspondence to M. A. Hossain.

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Hossain, M.A., Rees, D.A.S. Natural convection flow of a viscous incompressible fluid in a rectangular porous cavity heated from below with cold sidewalls. Heat and Mass Transfer 39, 657–663 (2003). https://doi.org/10.1007/s00231-003-0455-7

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