Convective Effect on Magnetohydrodynamic (MHD) Stagnation Point Flow of Casson Fluid over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions

Abstract

In the current study, the characteristics of heat transfer of a steady, two-dimensional, stagnation point, and magnetohydrodynamic (MHD) flow of shear thickening Casson fluid on an exponentially vertical shrinking/stretching surface are examined in attendance of convective boundary conditions. The impact of the suction parameter is also considered. The system of governing partial differential equations (PDEs) and boundary conditions is converted into ordinary differential equations (ODEs) with the suitable exponential similarity variables of transformations and then solved using the shooting method with the fourth order Runge–Kutta method. Similarity transformation is an important class of phenomena in which scale symmetry allows one to reduce the number of independent variables of the problem. It should be noted that solutions of the ODEs show the symmetrical behavior of the PDES for the profiles of velocity and temperature. Similarity solutions are obtained for the case of stretching/shrinking and suction parameters. It is revealed that there exist two ranges of the solutions in the specific ranges of the physical parameters, three solutions depend on the opposing flow case where stagnation point (A) should be equal to 0.1, two solutions exist when λ1 = 0 where λ1 is a mixed convection parameter and A > 0.1, and a single solution exists when λ1 > 0. Moreover, the effects of numerous applied parameters on velocity, temperature distributions, skin friction, and local Nusselt number are examined and given through tables and graphs for both shrinking and stretching surfaces.