Buoyant convective heat transfer of a realistic viscous fluid in a confined space

Abstract

A numerical and analytical study is conducted on the buoyant convection of an incompressible fluid in a rectangular cavity. Realistic viscous fluids, such as Newtonian fluids with a temperature-dependent viscosity or purely viscous non-Newtonian power-law fluids, are selected as a working fluid. The properly-defined overall Rayleigh number is very large so that a boundary-layer flow pattern prevails. A scale analysis is performed to obtain a rudimentary understanding of the flow and the heat transfer characteristics. Comprehensive numerical solutions are obtained to the well-established governing equations. The major emphasis is placed on the distinguishing features of the convective heat transfer of realistic viscous fluids considered here, compared with those of a conventional Newtonian fluid. First, finite-volume numerical solutions are obtained for buoyant convection of a Newtonian 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 sidewall and hot sidewall. 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 sidewall. 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 i...