The effect of variable thermophysical properties of the working fluid on the processes of natural convection in a closed partially porous cube with a heater

Abstract

The present paper deals with a numerical investigation of natural convection and heat transfer in a closed cubical partially porous cavity with a local heat-generating cubical element at the bottom wall. The working fluid is an incompressible fluid with temperature-dependent viscosity and thermal conductivity. The mathematical model is based on the Boussinesq approximation and a system of equations written in terms of «vector potential - vorticity vector - temperature» variables. The governing equations are solved numerically using the second-order finite difference method and locally one-dimensional Samarskii scheme for time integration. The developed numerical approach is verified by comparing the obtained results with the known solutions of the classical problem of natural convection in a differentially heated cubic cavity. A parametric analysis is carried out to examine the effects of temperature dependence of viscosity and thermal conductivity of the fluid, as well as the height of the porous layer on the flow structure and heat transfer. The results demonstrate that temperature-dependent viscosity causes the intensification of convective motion near the heat source and enhances the general fluid circulation in the cavity. An increase in the parameter of thermal conductivity variation  leads to a more uniform temperature distribution and a reduction of  local thermal gradients. It has been shown that the combined effect of variable viscosity and thermal conductivity changes the average Nusselt number and the thermal regime of the heat-generating element. The hydrodynamics of the process can be significantly improved by introducing a porous layer, which allows decreasing of overheating of the energy source. These findings serve as a basis for selecting coolants with a specified temperature dependence of rheological properties that provide an intensive heat removal near the fuel elements. In particular, the use of fluids with a pronounced decrease of viscosity at heating makes it possible to increase the efficiency of convective heat transfer without changing the geometry of the cooling system.