MHD stagnation-point flow and heat transfer past a non-isothermal shrinking/stretching sheet in porous medium with heat sink or source effect

The MHD stagnation-point flow of electrically conducting fluid and heat transfer past a non-isothermal shrinking/stretching sheet in a porous medium in presence of heat sink or source are investigated. The governing equations are transformed by similarity transformation technique and the converted equations are solved numerically by shooting method. Computed results are presented in some figures. It is obtained that the boundary layer solutions of steady flow exist with higher shrinking rate for the presence of magnetic field. Also, similar fact is observed when the porous parameter increases. The similarity solutions for some cases of shrinking sheet are of dual nature; it means that there exists two solutions for higher shrinking rate and the solution is unique for all stretching sheet cases. The impact of variable wall temperature along the sheet is massive on the thermal flow and the temperature field. For direct variation of wall temperature along the sheet heat absorption is noted for first solution in shrinking sheet case and it increases with the introduction of heat source; but, the presence of heat sink controls the heat absorption and it helps to return back to normal heat transfer process. Whereas, smooth zik-zak nature of temperature profiles is found for the inverse variation of wall temperature for shrinking sheet case with heat transfer from the surface to the ambient fluid layer. On the other hand, for stretching sheet case normally heat transfer occurs, but for higher values of heat source parameter and for larger magnitudes of power-law exponent of inverse variation of wall temperature heat absorption is also noticed. (C) 2017 Elsevier Ltd. All rights reserved.