Unsteady natural convection heat transfer of nanofluid in an annulus with a sinusoidally heated source

We study the unsteady natural convection of nanofluid between the outer and inner surfaces of a concentric annulus. The inner surface is heated sinusoidally with time about a fixed mean temperature but the outer boundary is kept at a constant temperature. The effects of Brownian motion and thermophoresis are taken into account. Numerical solutions are presented using the continuous finite-element method. Results indicate that the heat and mass transfer rates are significantly influenced by inner wall temperature oscillation, which presents periodic triangle fluctuation for the considered parameters of amplitude A, inner circle radius R, and frequency F.