A numerical study on the effects of radiation and variable thermal conductivity on the flow and heat transfer in the boundary layer of a viscoelastic fluid (Walters’ liquid B’ model) over a stretching porous sheet in the presence of a magnetic field is studied. The momentum differential equation is solved exactly. Two cases of sheet surface conditions are considered — (i) PST case involving prescribed surface temperature and (ii) PHF case involving prescribed heat flux at the surface. The energy equation is solved with the application of the shooting technique using the fourth order Runge-Kutta integration scheme. Numerical results are obtained for various values of non-dimensional parameters — which include among others, the Prandtl number (P), the Eckert number (E) and the Radiation number (N). The significant conclusions are: (1) the momentum boundary layer can be minimized by considering the sheet to be influenced by a continuous suction of the fluid through the porous boundary and by choosing large values for the viscoelastic parameter and the magnetic parameter (2) an ideal combination for faster cooling of the thermal boundary layer would be to consider the suction velocity of the fluid along with a large value for the Prandtl number combined with small values for Radiation and Eckert numbers.

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