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The Effect of Internal and External Heating on the Free Convective Flow of a Bingham Fluid in a Vertical Porous Channel

1
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK
2
School of Natural Sciences, University of Tasmania, Hobart TAS 7001, Australia
*
Author to whom correspondence should be addressed.
Fluids 2019, 4(2), 95; https://doi.org/10.3390/fluids4020095
Received: 14 April 2019 / Revised: 10 May 2019 / Accepted: 16 May 2019 / Published: 24 May 2019
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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Abstract

We study the steady free convective flow of a Bingham fluid in a porous channel where heat is supplied by both differential heating of the sidewalls and by means of a uniform internal heat generation. The detailed temperature profile is governing by an external and an internal Darcy-Rayleigh number. The presence of the Bingham fluid is characterised by means of a body force threshold as given by the Rees-Bingham number. The resulting flow field may then exhibit between two and four yield surfaces depending on the balance of magnitudes of the three nondimensional parameters. Some indication is given of how the locations of the yield surfaces evolve with the relative strength of the Darcy-Rayleigh numbers and the Rees-Bingham number. Finally, parameter space is delimited into those regions within which the different types of flow and stagnation patterns arise. View Full-Text
Keywords: porous media; convection; Bingham fluid; yield stress; channel flow porous media; convection; Bingham fluid; yield stress; channel flow
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Rees, D.A.S.; Bassom, A.P. The Effect of Internal and External Heating on the Free Convective Flow of a Bingham Fluid in a Vertical Porous Channel. Fluids 2019, 4, 95.

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