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.
Highlights
The topic of boundary layer fluid flow on the stretching surfaces is widely investigated for single solution cases
We discuss the numerical results of Equations (8) and (9) with their boundary conditions (10). These equations are highly non‐linear third order ordinary differential equations (ODEs), there is the possibility of the presence of multiple solutions
These equations are highly non-linear third order ODEs, there is the possibility of the presence of multiple solutions
Summary
The topic of boundary layer fluid flow on the stretching surfaces is widely investigated for single solution cases. The qualities of final products in such processes largely depend upon the cooling rate in the process of heat exchange. A magnetohydrodynamic parameter is an important parameter to use, such that the rate of the cooling might be controlled so that the desired products with quality can be obtained. Crane [1] gave the method of solution for the incompressible steady-state 2D boundary layer flow in the case of viscous fluid on the stretching surface. The problem examined by Crane has been studied more by extending it into many diverse aspects–some of its recent important directions over the stretching flows were considered by Mabood et al, [2], Rana et al, [3], Hamad [4], Hassan et al [5] and Haq et al, [6]. Hamad and Ferdows [7]
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