Analytic and approximate Lie solutions of MHD Casson Fluid flow, heat and mass transfer near a stagnation point over a linearly stretching sheet with constant and variable viscosity and thermal conductivity

Abstract

In this research, the effects of constant and variable viscosity and thermal conductivity on Magneto hydrodynamic (MHD) heat flow and mass transfer in a Casson fluid over a stretching surface are analyzed. Computational techniques are useful tools in solving the partial differential equations involved in this flow. It is desirable to convert these partial differential equations (PDEs) into a system of ordinary differential equations (ODEs). It is because there is no reliable scheme for solving PDEs and approximations used to convert PDEs to ODEs are often so good that ODEs may represent the characteristics of actual system. After obtaining the corresponding system of ODEs with boundary conditions, several computational methods can be employed. The previous study analyzed only coupled system using infinite boundary conditions and it employed Runge and Kutta method (RK-4) for approximating the results. These methods can be computationally expensive and may not represent the flow. In this thesis, Homotopy analysis method (HAM), Homotopy Perturbation Method (HPM) and finite difference method (FDM) are used for obtaining the analytical and approximate solutions of such systems. Moreover, the problem is addressed with both the finite and infinite boundary conditions. Procedures for all these methods are manageable and approximate, usually through codes that are developed for saving time and increasing accuracy. Codes are developed on MAPLE which has built in packages for many mathematical applications. These codes are tested and validated in a rigorous manner. The effect of various parameters on velocity and temperature are studied with the help of graphs and tables using the codes already available and refining them according to the requirement of flow model.