Enclosed buoyant convection of a variable-viscosity fluid under time-periodic thermal forcing

Abstract

Finite-volume numerical solutions are obtained for buoyant convection of a fluid with temperature-dependent viscosity in an enclosed space. At one vertical wall the temperature is constant, and at the other vertical wall the temperature is time-periodic. Solutions to the governing Navier-Stokes equations are acquired for a fixed Rayleigh number and over wide ranges of viscosity contrast, which measures the ratio of viscosities at the cold side wall and hot side wall. The effects of variable viscosity on the time-mean value as well as the amplitude of fluctuation of instantaneous heat transfer rate are delineated. The extensive results reveal the existence of resonance and show that resonance becomes more distinctive for large viscosity contrast in the case of the hot-wall temperature oscillation. As the viscosity contrast increases, the upward convective motion is invigorated during the relative heating phase due to the lowered viscosity in the thermal boundary layer near the hot vertical side wall. This is also reflected in the augmentation of the cycle-averaged heat transfer rate. When the temperature oscillation is imposed on the cold wall, the flow is less sensitive to the viscosity variation. Physical interpretations of the overall flow and heat transfer are offered.