Transient natural convection in a square cavity of a fluid with temperature-dependent viscosity

Abstract

A study is made of unsteady natural convection in a square cavity of a fluid with a temperature-dependent viscosity. The flow is driven by instantaneously raising the temperatur at one vertical wall and lowering the other. The viscosity variation is modeled by an exponential form, $\nu/\nu_\o=\exp(-CT)$. Two boundary conditions at the horizontal walls are used: insulating walls and highly conducting walls. Numerical solutions to the governing time-dependent equations at large reference Rayleigh numbers are acquired. The evolutions of the flow patterns and isotherms are presented under various parameter settings. When the viscosity variations are large, convective activities are facilitated in the region of low viscosity and suppressed in the region of high viscosity. The global impact is to enhance the flow and heat transfer in the cavity. A representative time history of the velocities is shown. A heatup time scale is corroborated. The transient behavior of the Nusselt number at the walls is scrutinized. During the transient phase, the effect of a variable viscosity is such that the heat inflow to the cavity exceeds the heat outflow from the cavity. In effect, the cavity acts as a receiver of net heat input during the transient process.