Free convection flow of visco-elastic fluid past an infinitive vertical porous plate

Abstract

This work provides a comprehensive theoretical analysis of a two-dimensional unsteady free convection flow of an incompressible, visco-elastic fluid past an infinite vertical porous plate. Solutions for the zero~.orderperturbation velocity profile, the ,~.fi~t ~order perturbation velocity profile and temperature profile in closed form are obtained with the help of Laplace transform technique. It covers the area of boundary layer flow of viscous, incompressible and electrically conducting fluid in the presence of strong magnetic field along a heated vertical flat plate. The ensuing boundary layer flows considered here are governed by a non-similar set of parabolic equations. Local non-similarity method is employed to investigate the solutions of boundary layer equations representing the flow and temperature fields. The numerical solutions are carried out for Prandtl's number, 0.1, 0.72,1.0,1.5 and 2.0 which arc appropriate for ditIerent types of liquid metals and for different values of magnetic field parameter, M. Finally, a problem on free convection boundary layer flow of visco-elastic incompressible and electrically conducting fluid past an infinite vertical porous plate along an isothermal vertical surface are studied in the presence of a transverse magnetic field. The results thus obtained have a graphical illustration for different values of the magnetic field parameter M, transpiration parameter a, Grashofnumber Gr, Visco-elasticity parameter s and the Prandtl number Pro