Three-dimensional natural convection of fluid with temperature-dependent viscosity within a porous cube having local heater

A numerical simulation is conducted on the convective heat transfer of liquid having variable viscosity in a closed porous 3D enclosure under an influence of isothermal or heat-generating solid body. Two vertical surfaces of the chamber are considered at fixed low temperature while other surfaces are thermally insulated. The local energy source is placed on the lower surface of the chamber. The control equations are written using non-dimensional variables "vector potential functions - vorticity vector - temperature". The finite difference technique of the second order accuracy is used to work out the differential equations. The effect of control parameters including the Rayleigh number, Ostrogradsky number, Darcy number, viscosity variation parameter and time on the liquid flow structure and heat transfer inside the cavity has been studied. The obtained data show that the porous material and variable viscosity working fluid can be considered as good conditions for the heat removal from the heated element in a closed chamber. A comparison of 2D and 3D models for natural convection of fluid having temperature-dependent viscosity in chambers with local heaters of various types has shown the features of different spatial approaches and boundary conditions for heated elements.