Thermal Convection in a Nanofluid Layer with Thermorheological Effect

Abstract

Thermorheological effect on the onset of convection in a horizontal nanofluid layer heated from below is studied for rigid-rigid, free-free and rigid-free boundaries by incorporating the effects of Brownian motion and thermophoresis. The viscosity of nanofluid is allowed to vary exponentially with temperature. The boundaries are considered to be isothermal and the normal flux of nanoparticle volume fraction is taken to be zero on the boundaries. The resulting eigenvalue problem is solved numerically by the Galerkin method and observed that the instability sets in only as stationary convection irrespective of the velocity boundary conditions. The stability characteristics of the system are strongly dependent on the viscosity parameter. At low values of the viscosity parameter, the variation in the critical Rayleigh number is found to be nominal but increases with increasing viscosity parameter, reaches a maximum and then decreases. Results also indicate that increase in the modified diffusivity ratio, concentration Rayleigh number, and Lewis number is to hasten the convection while the modified particle density increment has no observable effect on the onset of convection.