Hydromagnetic Jeffery-Hamel Unsteady Flow of a Dissipative Non-Newtonian Fluid with Nonlinear Viscosity and Skin Friction

Abstract

In this paper, the unsteady two-dimensional Jeffery-Hamel flow of an incompressible non-Newtonian fluid, with nonlinear viscosity and skin friction, flowing through a divergent conduit in the presence of a constant applied magnetic field in the direction perpendicular to the fluid motion is studied. The resulting nonlinear partial differential equations governing this flow problem are reduced into a system of nonlinear ordinary differential equations using similarity transformation. The resulting boundary value problem is solved numerically using the collocation method and implemented in MATLAB using the bvp4c inbuilt function to obtain the numerical solution. The effect of varying Reynolds number Re, Hartmann number Ha, Prandtl number Pr, Eckert number Ec, and unsteadiness parameter λ on the fluid velocity, fluid temperature, skin-friction, and heat transfer rate are presented in form of graphs and tables; and are discussed. From the results, it is noted that there aresignificant effects of pertinent parameters on the flow variables. This study provides useful information for engineering, technological, and industrial applications such as in hydromagnetic power generators.