Effect of Wall Conductivity on Mixed Convection Magnetohydrodynamic Nanofluid Flow with Thermal Non-Equilibrium Approach in Vertical Channel

This present work reports the fully developed hydromagnetic mixed-convection nanofluid flow in a vertical channel teeming by porous media with variable thermal and electrical wall conductivities and thermal non-equilibrium condition is taken into account. The fluid is assumed electrically conducted and taking as a mixture of base fluid (water) and three different metallic nanoparticles copper, alumina and titanium dioxide. The non-Darcy-Brinkman-Forchheimer extended model has been contemplated and solved governed differential equation by analytically as well as by numerically. Special attention is given to understand the effect of solid volume friction of the nanofluid (psi) and wall thermal conductivity (tau) parameters for both buoyancy assisted as well as opposed cases when the interval of inter-phase heat transfer coefficient H is taken from [1, 500]. It is observed that the point of inflection and flow separation are appeared in the velocity profile for both cases and disappeared slowly from the profile as both parameters psi and tau increases and it stabilize the system. There exists a minimum value H (0) of H for both case when tau <= 0.5 the heat transfer rate Nu (nf) of the fluid increases at the wall. Further, for tau > 0.5 Nu (nf) suddenly decreases and converge asymptotically in the case of buoyancy assisted flow. It is also observed that there exist two type interval of H in the buoyancy opposed for different value of tau. In first interval [0, H (0)], when tau <= 0.5 profile is same as in buoyancy assisted case but as soon as tau increases heat transfer rate first decreases upto a threshold value of H and after that in increases rapidly. Over all for both the cases system become stable and non thermal equilibrium condition convert into thermal equilibrium when H, tau and Phi increases.