Magnetic Control of Nanofluid Transport in Porous Media under Variable Viscosity and Thermal Conductivity

Abstract

The objective of this research is to determine how a magnetic field influences nanofluid transport within a porous medium due to both the variations of fluid
viscosity and thermal conductivity. A two dimensional steady state flow model was developed to examine the magnetohydrodynamic effects, Darcy resistance and
the temperature dependence of the fluids' properties. The governing nonlinear equations for momentum (velocity), energy (temperature) and concentration
(nanoparticles) were reduced from partial differential to ordinary differential equations using similar variables. The Homotopy Perturbation Method was then used
to find an analytical solution of these coupled ODEs which would provide closed form solutions for the velocity, temperature and concentration fields. A detailed
examination was performed on the effect of several significant physical parameters including the magnetic parameter, the Prandtl number, the Eckert number, the
thermal conductivity variation, thermophoresis and the Lewis number. It was demonstrated that the magnetic field has a large impact on reducing the motion of
the fluid; while varying the thermal conductivity and viscous dissipation have a positive impact on increasing thermal transport. Thermophoresis and mass
diffusivity also greatly affect the distribution of nanoparticles. The analytical results of the present model show good agreement with the previous models and
therefore confirm that the current model is accurate and physically relevant.