Influence of Wall Conductivites on a Fully Developed Mixed-Convection Magnetohydrodynamic Nanofluid Flow in a Vertical Channel

A fully developed mixed-convection nanofluid flow in a vertical channel with variable thermal and electrical wall conductivities in the presence of a uniform transverse magnetic field is studied. The working fluid is a homogeneous mixture of a base fluid (water) and metallic nanoparticles of three different kinds, namely, copper, alumina, and titanium dioxide. The fluid is also electrically conducting in the presence of an applied magnetic field. The flow is characterized by a moderate magnetic Reynolds number. An induced magnetic field is present. The effects of the pertinent parameters on the nanofluid temperature, velocity, and induced magnetic field strength, as well as on the shear stress and heat transfer rate at the channel wall, are shown. In the case of a negative vertical temperature gradient (heating from below), there exists a critical Rayleigh number at which the fluid becomes unstable. This number is also found as a function of the wall conductivities.