An analysis is performed to study radiation effects on magnetohydrodynamic (MHD) unsteady free-convection flow past a semi-infinite vertical plate with variable surface temperature in the presence of transversal uniform magnetic field. The boundary layer equations are transformed into a linear algebraic system by an implicit finite-difference method. A parametric study is performed to illustrate the influence of radiation parameter, magnetic parameter, and Prandtl number on the velocity and temperature profiles. The numerical results reveal that the radiation has significant influences on the velocity and temperature profiles, skin friction, and Nusselt number. The results indicate that the velocity, temperature, and local and average skin friction increase as the radiation parameter increases, while the local and average Nusselt numbers decrease as the radiation parameter increases.

We consider the quasistatic Signorini′s contact problem with damage for elastic-viscoplastic bodies. The mechanical damage of the material, caused by excessive stress or strain, is described by a damage function whose evolution is modeled by an inclusion of parabolic type. We provide a variational formulation for the mechanical problem and sketch a proof of the existence of a unique weak solution of the model. We then introduce and study a fully discrete scheme for the numerical solutions of the problem. An optimal order error estimate is derived for the approximate solutions under suitable solution regularity. Numerical examples are presented to show the performance of the method.