Blasius flow and heat transfer of fourth-grade fluid with slip

This investigation deals with the effects of slip, magnetic field and non-Newtonian flow parameters on flow and heat transfer of an incompressible, electrically conducting fourth grade fluid past an infinite porous plate subject to suction and blowing, known as the Blasius flow problem. The heat transfer analysis has been carried out for two heating processes, namely, when the plate is assumed to be at higher temperature than the fluid, and in the second case, the plate is assumed to be insulated. The order of the resulting differential equations exceeds the available adherence boundary conditions due to the presence of the higher order material derivatives of the strain tensor in the constitutive relation for the fourth grade fluid. The system of highly non-linear differential equations is solved using a fourth order Runge-Kutta method along with a shooting method for moderate values of the flow and heat transfer parameters. The effective Broyden’s technique has been adopted in order to improve the initial guesses and to satisfy the boundary conditions at infinity. The combined effects of the non-Newtonian flow parameters and slip on the momentum and thermal boundary layers have been discussed in details. An exceptional crossovers is obtained in the velocity profile in presence of slip. The fourth grade fluid parameter is found to increase the momentum boundary layer thickness, whereas the slip parameter substantially decreases it. Similarly, the non-Newtonian fourth grade fluid parameters and the slip have opposite effects on the thermal boundary layer thickness.