Comparative Analysis of Analytical and Numerical Approximations for the Mass and Heat Transfer in Mixed Convection Stagnation Point Flow of Casson Fluid Over the Stretching Sheet Considering Unsteadiness Parameter

Abstract

The mathematical formulation is presented for a Non-Newtonian Casson fluid model with unsteadiness and variable fluid film thickness factors in terms of partial differential equations (PDEs). With the help of available similarity transformations, the governing PDEs are converted into ordinary differential equations (ODEs). For the mass and heat transfer in the mixed convection stagnation point flow of Casson fluid over an unsteady stretching sheet, a detailed comparative analysis is carried out in this paper of the analytical and numerical approximation techniques. The Homotopy Analysis Method (HAM) is applied for the analytical solution while the RK4 with the Shooting Method (RKF45) and Finite Difference Method (FDM) are used for the numerical solutions. The velocity and temperature profiles are analyzed 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 upon the embedded parameters for the mass and heat transfer characteristics of Casson fluid. The MAPLES codes for these analytical and numerical approximation schemes are created and successfully tested for validation. The limitations of analytical and numerical methods, accuracy, and computational times are presented as well in the end sections. The final results obtained through these analytical and numerical methods provide very valuable insights into the behavior of fluid flow and assist in the design and optimization of various fluid engineering and mechanical industrial systems. Moreover, this study will contribute by providing more solvable classes of the mixed convection stagnation point flow of Non-Newtonian Casson fluid problems.