Comparative analysis of analytical and numerical approximations for the flow and heat transfer in mixed convection stagnation point flow of Casson fluid

Abstract

A mathematical description of non-Newtonian mixed convective Casson fluid stagnation point flow and transfer of heat exists in terms of partial differential equations. We considered the same to study it further under the effects of unsteadiness and varied film thickness parameters. For inclusion of these parameters in the flow model study we modified the available similarity transformations. The governing equations with three independent variables are converted into ordinary differential equations by employing the modified invertible transformations. For the mass and heat transfer in the mixed convection stagnation point unsteady flow of Casson fluid over a stretching sheet, a detailed comparative analysis is carried out in this paper, of the analytical and numerical approximation techniques. The Homotopy Analysis Method is applied for the analytical solutions while the Runge-Kutta with a Shooting Method (RKF45) and Finite Difference Method are used for obtaining the numerical solutions. With these solution schemes we present an analysis of velocity and temperature profiles under the effects of embedded parameters such as the Casson fluid parameter, unsteadiness parameter, mixed convection parameter, Prandtl number, Eckert number, and stretching ratio. The results are presented in both graphical and tabulated forms and they illustrate the dependence of mass and heat transfer characteristics of Casson fluid upon the embedded parameters. Further, we have shown an agreement between the analytical and the approximate solutions for the considered flow and heat transfer which reflects a validation of the results presented here.