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Mixed convection boundary-layer flow of a micro polar fluid towards a heated shrinking sheet by homotopy analysis method

Rashidi Mohammad Mehdi (Mechanical Engineering Department, Engineering Faculty of Bu-Ali Sina University, Hamedan, Iran + University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai, Peoples Republic of China)
Ashraf Muhammad (Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakariya University, Multan, Pakistan)
Rostami Behnam (Young Researchers & Elites Club, Hamedan Branch, Islamic Azad University, Hamedan, Iran)
Rastegari Taher Mohammad (Mechanical Engineering Department, Engineering Faculty of Bu-Ali Sina University, Hamedan, Iran)
Bashir Sumra (Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakariya University, Multan, Pakistan)

A comprehensive study of two dimensional stagnation flow of an incompressible micro polar fluid with heat transfer characteristics towards a heated shrinking sheet is analyzed analytically. The main goal of this paper is to find the analytic solutions using a powerful technique namely the Homotopy Analysis Method (HAM) for the velocity and the temperature distributions and to study the steady mixed convection in two-dimensional stagnation flows of a micro polar fluid around a vertical shrinking sheet. The governing equations of motion together with the associated boundary conditions are first reduced to a set of self-similar nonlinear ordinary differential equations using a similarity transformation and are then solved by the HAM. Some important features of the flow and heat transfer for the different values of the governing parameters are analyzed, discussed and presented through tables and graphs. The heat transfer from the sheet to the fluid decreases with an increase in the shrinking rate. Micro polar fluids exhibit a reduction in shear stresses and heat transfer rate as compared to Newtonian fluids, which may be beneficial in flow and thermal control of polymeric processing.

Keywords: stagnation flow, heat transfer, micro polar fluid, shrinking sheet