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

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....

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Bibliographic Details
Published inFluids (Basel) Vol. 4; no. 2; p. 95
Main Authors Rees, D. Andrew S., Bassom, Andrew P.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.06.2019
Subjects
Bingham fluid
Boundary conditions
channel flow
convection
Convective flow
Heat
Heat generation
Heating
Parameters
porous media
Temperature
Temperature profiles
Viscosity
Yield stress
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Summary: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.
ISSN:2311-5521
2311-5521
DOI:10.3390/fluids4020095