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ISSN: 1091-028X Print
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Pages: 108
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Free Convection from a Horizontal Surface in a Porous Medium with Newtonian Heating
Daniel Lesnic
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
Derek B. Ingham
Department of Applied Mathematical Studies, The University of Leeds, Leeds, LS2 9JT, UK
Ioan Pop
Faculty of Mathematics, University of Cluj, R3400 Cluj, CP253, Romania
ABSTRACT
A very effective solution method is proposed to solve the steady free convection boundary-layer flow on a horizontal surface embedded in a porous medium in which the flow is generated by Newtonian heating. Asymptotic solutions, which are valid for small and large values of x, the coordinate along the plate, as well as a very accurate numerical solution of the full governing equations that matches the asymptotic solutions have been obtained It is found that for small values of x the first-order flow is driven by a constant heat flux from the surface, and the higher order terms are then perturbations of the standard uniform heat flux solution, which is the same behavior seen in the corresponding conjugate problem. However, there is an essential difference between the present situation and the conjugate problem when the solution far downstream is considered. For the conjugate problem, the flow far downstream approaches the standard isothermal wall solution, whereas in the present situation, the flow far downstream at large values of x gives rise to a new similarity solution in which the wall fluid velocity and temperature are almost linear and quadratic functions of x, respectively.
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