Magnetohydrodynamic and radiation effects on the heat transfer of a continuously stretching/shrinking sheet with mass transpiration of the horizontal boundary

The aim of this paper is the investigation of heat transfer regarding the cases of both stretching and shrinking sheets with a sponge-like horizontal wall that allows for mass transpiration. The effects of Prandtl number, radiation and external magnetic field are extensively examined. The Navier-Stokes equations are reduced to partial differential equations, which are eventually become ordinary differential equations and solved analytically. Furthermore, the power-law wall temperature and heat flux boundary conditions are imposed on the boundary layer energy equation for obtaining exact analytical solutions. The results revealed that in both the stretching and shrinking sheet scenarios the thickness of the thermal boundary layer decreases with either increasing of transpiration as well as the Chandrasekhar and Prandtl number numbers or decreasing radiation number. Additionally, the characteristics of the heat transfer regarding a shrinking sheet and those of a stretching sheet are found not to be similar. In fact, a new solution branch appeared which indicates that multiple solutions may emerge under certain circumstances. Finally, by using the present analytical relationships, theoretical guidelines can be given for regulating the procedure.

Automated summary

The paper investigates heat transfer in stretching and shrinking sheets with a sponge-like horizontal wall, considering Prandtl number, radiation, and external magnetic field effects. The Navier-Stokes equations are simplified to partial, and eventually ordinary differential equations, which are analytically solved. Results show that the thickness of the thermal boundary layer decreases with increasing transpiration, Chandrasekhar and Prandtl numbers, or decreasing radiation number, with different heat transfer characteristics between shrinking and stretching sheets.