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Importance of Darcy or Brinkman laws upon resonance in thermal convection

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Abstract

Thermal convection is analysed in a layer of Brinkman or Darcy porous material when the buoyancy force is quadratic in the temperature field and there is also present a constant heat source. In this situation resonance may occur in the sense that convective motion may commence simultaneously in two separate layers in the porous medium. It is shown that whether resonance occurs or not depends crucially on whether a Brinkman or Darcy law holds and this indicates how important it is to understand the model for flow in porous media.

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Authors and Affiliations

  1. Department of Mathematics, University of Durham, Durham, DH1 3LE, UK

    B. Straughan

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  1. B. Straughan
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Correspondence to B. Straughan.

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Communicated by Salvatore Rionero.

Results contained in the present paper have been presented at WASCOM 2015.

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Straughan, B. Importance of Darcy or Brinkman laws upon resonance in thermal convection. Ricerche mat 65, 349–362 (2016). https://doi.org/10.1007/s11587-015-0250-z

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  • DOI: https://doi.org/10.1007/s11587-015-0250-z

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