BEM SOLUTION TO TRANSIENT FREE CONVECTIVE HEAT TRANSFER IN A VISCOUS, ELECTRICALLY CONDUCTING, AND HEAT GENERATING FLUID

Abstract

The nonlinear partial differential equations for the transient free convective heat transfer in a viscous, electrically conducting, and heat-generating fluid past a vertical porous plate in the presence of free stream oscillations are solved by the boundary element method (BEM). Time-dependent fundamental solutions are employed in a time marching scheme to resolve the field variables. Numerical results are compared with previously reported analytical solutions in order to validate the developed BEM algorithm. These previous studies reported results for simpler versions of our problem, in which the convective effects in the momentum and energy equations were neglected in order to obtain analytical numerical solutions. Our BEM results are shown to be in close agreement with the reported data. The effects of convection currents, the temperature-dependent heat sources (or sinks), the magnetic currents, and the viscous dissipation on the flow and heat transfer characteristics are assessed in a parametric study, which considers a variety of the dimensionless parameters Gr, Ec, Pr, M, and γ. It is observed that γ plays an important role in delaying the fluid flow reversal, present in the case of air, and acts to enhance the effect of Gr in augmenting the rate of heat transfer at the wall. The skin friction is observed to be an increasing function of Gr, Ec, and γ and a decreasing function of M and Pr. However, the rate of heat transfer (in an absolute sense) is an increasing function of M, γ, Gr, and Ec and a decreasing function of Pr, Of all the parameters, the Prandtl number has the strongest effect on the flow and heat transfer characteristics.

Notes

Address correspondence to Dr. Kuppalapalle Vajravelu, Department of Mathematics, University of Central Florida, P.O. Box 161364, Orlando, FL 32816-1364, USA.