Explicit Solutions of MHD Flow and Heat Transfer of Casson Fluid over an Exponentially Shrinking Sheet with Suction

Abstract

In this study, the magnetohydrodynamic (MHD) flow and heat transfer of a Casson fluid over an exponentially shrinking sheet with suction is investigated using the homotopy analysis method (HAM). Different from previous numerical methods and analytical techniques, we have obtained an explicit formula solution to the presented nonlinear problem. The explicit solutions of f(η) and θ(η) are obtained and are valid in the whole domain. The changes in velocity and temperature profiles are studied in cases of different Casson fluid parameter γ, magnetic interaction parameter M, suction parameter s, and Prandtl number Pr. The convergent solutions are verified by comparison with the numerical results. In addition, the skin friction coefficient Cf and local Nusselt number Nux are analyzed using the analytic formulas of f″(0) and θ′(0), respectively. The analytical formulas help us intuitively analyze the influence of various parameters at the theoretical level. The effects of different physical quantities on Cf and Nux are thoroughly investigated.