Finite element analysis of melting effects on MHD stagnation-point non-Newtonian flow and heat transfer from a stretching/shrinking sheet

A numerical study is presented for boundary layer flow and heat transfer of micropolar (non-Newtonian) fluid from a stretching/shrinking sheet in the presence of melting and viscous heating. In this study the velocity of ambient fluid and stretching/shrinking velocity vary linearly with the distance from the stagnation-point. A uniform magnetic field is applied normal to the sheet and moves with the free stream as encountered in certain magnetic materials processing systems. Using similarity transformations, the governing partial differential equations are transformed into a system of coupled, nonlinear ordinary differential equations. A variational finite element code is implemented to solve the resulting dimensionless boundary value problem. The influence of magnetic body force (M), stretching/shrinking (ε) and melting (Me) parameters on velocity, microrotation, temperature, surface shear stress function (skin-friction) and local Nusselt number are elaborated in detail. Velocity is decreased with a rise in melting parameter, whereas far from the wall microrotation is reduced and furthermore temperatures are depressed. The flow is accelerated, micro-rotation (angular velocity of micro-elements) increased and temperature enhanced with increasing stretching rate (ε > 0) whereas the converse behaviour is observed with increasing shrinking rate (ε < 0). Increasing magnetic parameter is found to both increase temperatures and to accelerate the flow whereas it reduces microrotation near the wall and enhances it further from the wall. Special cases of the present model (with magnetic, dissipative and melting effects negated) are benchmarked with earlier results from the literature and found to be in excellent agreement. Excellent convergence and stability is achieved with the numerical method.