Abstract

Free Convection Flow of dissipative non-Newtonian fluid along a vertical plate in a porous medium

Funmilayo HelenOyelami and Moses SundayDada

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Abstract Transient magnetohydrodynamic free convection flow of non-Newtonian fluids through porous media occurred in a broad range of engineering applications such as transport processes in chemical industry, nuclear waste materials storage, recovery of oil in petroleum reservoirs, food processing, and movement of biological fluids. The viscous behaviour of non-Newtonian fluid is a nonlinear function of deformation rate. This behaviour has been analyzed in existing studies majorly on steady two-dimensional flows and transient one-dimensional flows using Power-law model with assumptions that viscous dissipation and magnetic field are negligible. This study considered the effects of viscous dissipation and magnetic field on transient flow with Prandtl-Eyring non-Newtonian fluid model used to describe the nonlinear relationship between shear stress and rate of deformation. The objectives of the study were to examine the effect of magnetic field, thermal radiation and viscous dissipation on the flow and also to analyze the influence of Prandtl-Eyring parameters on the fluid velocity. The governing equations for the problem were formulated, non-dimensionalised and solved using the implicit finite difference scheme of Crank-Nicolson type. The finite difference equations formed Thomas algorithm tri-diagonal matrix system of equations, which were solved with the help of MATLAB programming package. The results revealed that increasing magnetic field retarded velocity distribution and accelerated the temperature and concentration of the fluid, an increase in viscous dissipation caused a decrease in velocity and temperature distributions while increasing thermal radiation reduced the velocity and temperature of the fluid. The study concluded that magnetic field and viscous dissipation effects are important in analyzing the viscous behaviour of non-Newtonian fluids using Prandtl-Eyring model. It was recommended that viscous dissipation and magnetic field should be given attention when considering transient magnetohydrodynamic flow of non-Newtonian fluids. Keywords: Magnetohydrodynamic; viscous dissipation; magnetic field; thermal radiation; Prandtl-Eyring fluid; non-Newtonian.

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