Unsteady free convective viscoelastic boundary layer flow past a vertical porous plate with internal heat generation/absorption

Abstract

Unsteady boundary layer free convection flow of an incompressible electrically conducting viscoelastic second-order fluid over a vertically permeable flat plate is considered, where temperature and concentration differences are responsible for the convective buoyancy current. The flow is affected by a constant suction of fluid through the permeable wall in the presence of a temperature-dependent heat source/sink and applied transfer magnetic field. This intricate mathematical problem has been solved analytically. The analysis has been carried out for small values of the viscoelastic parameter and the results are presented in table and graphical form. The effect of various nondimensional physical parameters, such as the viscoelastic parameter, Grashof number Gr, modified Grashof number Gm, source/sink parameter, frequency parameter, time dependency parameter, Prandtl number, Schmidt number, permeability parameter, and magnetic parameter, on the boundary layer velocity and skin-friction coefficient are investigated. Some of the several important findings of the results are: (i) the increase of the velocity in the boundary layer with the increase of viscoelastic parameter is significant for higher values of the Grashof number; (ii) the combined effect of increasing the values of viscoelastic parameter, modified Grashof number, and permeability parameter is to enhance the horizontal velocity profile largely in the boundary layer; (iii) the effect of increasing the value of the Prandtl number is to decrease the skin-friction coefficient for smaller values of viscoelastic parameter, and its effect is to increase the skin-friction parameter for higher values of viscoelastic parameter in the presence of convective current generated by cooling of the boundary wall and concentration gradient (both Gr and Gm positive); (iv) the limiting value of viscoelastic parameter for which separation of boundary layer takes place is higher for higher values of permeability parameter and Hartmann number, and lower values of Prandtl number; (v) the effect of temperature-dependent heat source is to enhance the reverse flow in the negative x direction near the boundary wall more significantly in the case of a viscoelastic fluid than a viscous fluid. © 2006 Begell House, Inc.