Natural Convection of Variable Viscosity Fluid in a Partially Porous Cube Having Heat-generating Element Under Local Thermal Non-Equilibrium Model

A mathematical modeling of natural convective energy transport inside partially porous cube with thermally producing element and porous layer has been performed. The viscosity of working medium is considered as temperature dependent with the exponential law. The local thermal non-equilibrium conditions have been used for description of heat transfer inside porous structure. The mathematical model has been formulated employing dimensionless vector potential functions, vorticity vector and temperature. The finite difference technique has been employed to solve the differential equations. The influence of key parameters such as the Nield number, Darcy number, viscosity variation characteristic, thickness of porous zone and time on the fluid flow structure and energy transport inside the cube has been scrutinized. The outcomes have shown that the introduction of a porous zone and an increase in its height lead to more uniform energy removal from the heated unit. In addition, the mean Nusselt number at the energy element surface and the mean temperature within the source are increased with a growing of the interfacial heat transfer coefficient (Nield number) for large permeability of the porous material (Darcy number) while for the intensity of the flow within the chamber the opposite effect can be observed.