The effect of lateral mass flux on the natural convection boundary layers induced by a heated vertical plate embedded in a saturated porous medium with internal heat generation

doi:10.1016/j.ijthermalsci.2006.04.008

International Journal of Thermal Sciences

Volume 46, Issue 2, February 2007, Pages 157-163

https://doi.org/10.1016/j.ijthermalsci.2006.04.008 Get rights and content

Abstract

The effect of suction or injection on the free convection boundary layers induced by a heated vertical plate embedded in a saturated porous medium with an exponential decaying heat generation is studied. Similarity solutions are obtained for the governing steady laminar boundary layer equations using Darcy and Boussinesq approximations. The plate is assumed to have a power law temperature distribution. Three distinct cases of uniform lateral mass flux, uniform surface temperature, and uniform heat flux are studied. The effects of suction/injection parameter $f_{w}$ and temperature exponent λ on the flow of heat transfer are studied. Some exact analytical results are obtained for $λ = 1, - 1 / 3$ . Critical values of the suction/injection parameter are obtained for adiabatic surface as a function of the temperature exponent parameter λ.

References (16)

P. Cheng
The influence of lateral mass flux on free convection boundary layers in a saturated porous medium
Int. J. Heat Mass Transfer
(1977)
C.H. Johnson et al.
Possible similarity solutions for free convection boundary layers adjacent to flat plates in porous media
Int. J. Heat Mass Transfer
(1978)
A. Postelnicu et al.
Similarity solutions of free convection boundary layers over vertical and horizontal surfaces in porous media with internal heat generation
Int. Comm. Heat Mass Transfer
(1999)
A. Postelnicu et al.
Free convection boundary-layer over a vertical permeable flat plate in a porous medium with internal heat generation
Int. Comm. Heat Mass Transfer
(2000)
S. Bagai
Similarity solutions of free convection boundary layers over a body of arbitrary shape in a porous medium with internal heat generation
Int. Comm. Heat Mass Transfer
(2003)
A.D. Nield et al.
Convection in Porous Media
(1999)
D.B. Ingham et al.
Transfer Phenomena in Porous Media
(1998)
P. Cheng et al.
Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike
J. Geophys. Res.
(1977)

There are more references available in the full text version of this article.

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The effect of lateral mass flux on the natural convection boundary layers induced by a heated vertical plate embedded in a saturated porous medium with internal heat generation

Abstract

Int. J. Heat Mass Transfer

Int. J. Heat Mass Transfer

Int. Comm. Heat Mass Transfer

Int. Comm. Heat Mass Transfer

Int. Comm. Heat Mass Transfer

Convection in Porous Media

Transfer Phenomena in Porous Media

Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike

J. Geophys. Res.