Analytic Series Solution for Unsteady Mixed Convection Boundary Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium

This paper deals with the asymptotic analysis of similarity solutions of the two-dimensional mixed convection boundary-layer flow over a vertical surface with a power law temperature. It is shown that the extended governing equations can be reduced, using a coordinate transform, to the case of the boundary-layer development of large time solutions for the unsteady mixed convection near the stagnation point on a vertical surface in a porous medium. The perturbation solutions for small and large values of the mixed convection parameter are obtained. The asymptotic behavior of the solution was examined for different values of the power law exponent parameter.

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Mixed Convection Boundary-layer Flow Past a Vertical Surface Embedded in a Porous Medium: Exponential Case

Transport in Porous Media ◽

10.1007/s11242-014-0408-2 ◽

2014 ◽

Vol 106 (2) ◽

pp. 425-438 ◽

Cited By ~ 1

Author(s):

Norshafira Ramli ◽

J. H. Merkin ◽

I. Pop

Keyword(s):

Boundary Layer ◽

Porous Medium ◽

Mixed Convection ◽

Boundary Layer Flow ◽

Vertical Surface ◽

Convection Boundary Layer ◽

Flow Past ◽

Convection Boundary ◽

Exponential Case ◽

Layer Flow

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Unsteady mixed convection boundary layer flow along a symmetric wedge with variable surface temperature embedded in a saturated porous medium

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-03-2014-0077 ◽

2015 ◽

Vol 25 (5) ◽

pp. 1162-1175

Author(s):

Saleh M. Al-Harbi ◽

F. S. Ibrahim

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Porous Medium ◽

Mixed Convection ◽

Boundary Layer Flow ◽

Convection Boundary Layer ◽

Content Type ◽

Unsteady Mixed Convection ◽

Convection Boundary ◽

Layer Flow

Purpose – The purpose of this paper is to study laminar two-dimensional unsteady mixed-convection boundary-layer flow of a viscous incompressible fluid past a symmetric wedge embedded in a porous medium in the presence of the first and second orders resistances. Design/methodology/approach – The governing boundary-layer equations along with the boundary conditions are first converted into dimensionless form by a non-similar transformation, and then resulting system of coupled non-linear partial differential equations were solved by perturbation solutions for small dimensionless time until the second order. Numerical solutions of the governing equations are obtained employing the implicit finite-difference scheme in combination with the quasi-linearization technique. The obtained results will be compared with earlier papers on special cases of the problem to examine validity of the method of solution. Findings – The effects of various parameters on the fluid velocity and fluid temperature as well as the wall heat transfer rate and skin-friction coefficient are presented graphically and in tabulated form. Originality/value – The study of heat transfer in porous media has been attracted the attention of many researchers in recent times due to the utmost importance in many different applications, including physical, geophysical and chemical applications. Also in different areas of engineering and modern purposes as oil refining, pollution of the air with poison gas, the process of mineral extraction, the design water tanks and study volcanic activity. Also has many uses in medicine, modern science, food products, textiles and ion exchange.

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