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Non-isothermal hydromagnetic convection in a porous medium with heat sink: hypergeometric function solutions

Bég, O. Anwar and Takhar, Harmindar S. and Bég, Tasveer A. and Singh, Ashok K. (2007) Non-isothermal hydromagnetic convection in a porous medium with heat sink: hypergeometric function solutions. International journal of applied mechanics and engineering, 12 (2). pp. 337-351. ISSN 1734-4492

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Abstract

The present paper deals with the free convection laminar boundary layer flow and heat transfer of an incompressible, electrically conducting, viscous fluid through a porous medium caused by stretching a porous wall in the presence of a heat source and under the influence of uniform magnetic field. Exact solutions of the basic equations of momentu m and energy ar e obtained after reducing them i n to non-linear ordinary differential equations and using confluent hypergeometric functions. The variations in the velocity field and temperature distribution with the Prandtl number (Pr), hydromagnetic parameter (M), permeability param eter (K), suction parameter (N), wall temperature parameler (S), and the heat sink parameter (Q) are obtained and depicted graphically. The skin-friction at the wall is also derived, and the numerical values for various physical parameters are also tabulaled. Magnetic field (M) is seen to reduce both longitudinal and translational velocities and also lower temperalures, aiding in controlling momentum and heat transfer during materiaIs processing. Suction (N) posivitely influences the transverse velocity but depresses the longitudinal velocity magnitudes as we II as decreasing tempcratures. Suction therefore also assists in controlling heat transfer in Ihe boundary layer. Increasing permeability parameter (K) depresses the longitudinal velocity but elevates transverse velocities and increases the skin friction at the wall. Both rising temperature (non-isothermal wall) parameter (S) and heat sink parameter (Q) decrease temperature values. The model finds applications in nucIear engineering control systems and MHD energy systems.

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