Thermal boundary layer in stagnation-point flow past a permeable shrinking sheet with variable surface temperature

An investigation is made to study the heat transfer in boundary layer stagnation-point flow over a non-isothermal permeable shrinking sheet with suction/injection. In this study, power-law variation of sheet temperature is considered. By similarity transformation, the governing equations with the boundary conditions are transformed to self-similar nonlinear ordinary differential equations and then those are solved numerically by shooting method. In presence of variable sheet temperature, the variation of temperature is analysed. For larger shrinking rate compared to that of straining rate, dual solutions for velocity and temperature are obtained. It is found that for positive value of power-law exponent of variable sheet temperature heat transfer at the sheet as well as heat absorption at the sheet with temperature overshoot near the sheet occur and for negative value heat transfer from the sheet occurs though there is overshoot away from the sheet. With increasing positive power-law exponent heat transfer reduces for first solution and heat absorption enhances for second solution. Whereas, with increasing magnitude of negative power-law exponent heat transfer increases for second solution and for first solution the heat transfer increases for larger shrinking rate and it decreases for smaller shrinking rate. Due to suction heat transfer/absorption increases in all cases and for injection heat transfer/absorption increases for first solution and decreases for second solution. Also, interesting effects of suction/injection and Prandtl number on temperature distribution are observed when the sheet temperature varies (directly/inversely) along the sheet.