Unsteady Convective Heat Transfer in Liquid Saturated and Unsaturated Porous Media with Reference to an Energy Storage System

Abstract

Flow and heat transfer in porous media has received much attention due to its importance in various fields of engineering: mechanical, chemical, ground water hydrology, petroleum engineering, soil mechanics and environmental science. The examination of transport in porous media relies on the knowledge gained in studying these phenomena in plain media. The mathematical modeling of convective heat transfer in a porous medium is carried out by volume averaging of governing energy equations for the fluid and the solid phases. The interphase convective heat transfer coefficient hsf couples these two energy equations at the interface. In addition, this model also contains effective thermal conductivity and dispersion tensors and is expected to give reasonably good predictions. This model is called the thermal non-equilibrium model or the 2-equation model. It is advantageous to use this model, as against the thermal equilibrium or 1-equation model, when there is significant heat generation in one of the phases, during sudden heating/cooling of the medium and when the thermal properties of the two phases are distinct. The volume-averaged energy equations based on thermal equilibrium and thermal non-equilibrium between the two phases are developed. The finite difference discretization of the model is carried out by using implicit format for the time derivatives, central difference scheme for second order partial-spatial derivatives and the upwind scheme and QUICK approaches for modeling of convective terms. The resulting algebraic equations are solved by Gauss-Seidel iterations using sufficiently fine grid in space and large number of time-steps. The numerical simulation is first compared with analytical results obtained by neglecting various terms of the mathematical model such as interphase heat transfer and convection. These include 2-D unsteady state conduction, 1-D and 2-D unsteady advection-diffusion in plain flow i.e. no solid phase present in the medium.