Mixed radiation-convection boundary layer flow of an optically dense fluid along a vertical flat plate in a non-Darcy porous medium

Takhar, Harmindar S., Bég, O. Anwar, Chamkha, Ali J., Filip, D. and Pop, Ioan (2003) Mixed radiation-convection boundary layer flow of an optically dense fluid along a vertical flat plate in a non-Darcy porous medium. International journal of applied mechanics and engineering, 8 (3). pp. 483-496. ISSN 1734-4492

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Abstract

The combined effects of thermal radiation flux, thermal conductivity, Reynolds number and non-Darcian (Forcheimmer drag and Brinkman boundary resistance) body forces on steady laminar boundary layer flow along a vertical surface in an idealized geological porous medium are investigated. The classical Rosseland one-dimensional diffusion approximation is implemented in the energy equation to avoid solving the general integro-differential equation for radiative transfer. Pseudo-similarity transformations are invoked and the resulting highly coupled and non-linear set of ordinary differential equations for momentum and energy equations are solved numerically using a well-tested and highly accurate shooting Runge-Kutta quadrature with a Merson-Gill algorithm. It is shown that the dimensionless velocity functions generally increase with rising radiation parameter and the Prandtl number, and the dimensionless temperature functions decrease as the non-Darcian body forces decrease. It is also shown that the dimensionless temperature functions rise in magnitude with rising radiation parameter and the Prandtl number but are depressed by lowered non-Darcian resistance parameter and rising Reynolds number. Generally radiation is seen to substantially boost the overall heat transfer.