Abstract
This note provides an exact analysis of unsteady free convection flow of viscous fluid past a vertical plate with arbitrary shear stress and ramped wall temperature. The fluid is considered to be electrically conducting and passing through a porous medium. Equations governing the problem are first written in dimensionless form and then solved for the exact solutions using the Laplace transform method. The graphs of velocity, entropy generation, and Bejan number are plotted for various parameters of interest. It is found that velocity and entropy generation decrease with increasing wall shear stress in cases of both ramped and constant wall temperature. It is also observed that Bejan number increases with increasing wall shear stress.