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Changes in the porosity and permeability of a porous medium due to melting are modeled. A frozen phase, which initially fills a part of the porous medium, melts and gets dissolved in the injected hot solvent. The amount of melted material, the rate of melting as well as the profiles of temperature, porosity, and concentration are analyzed to understand the nature of this naturally and industrially important phenomenon. Four reference scenarios corresponding to instantaneous thermal equilibrium, no heat transfer to the frozen phase, no-melting, and instantaneous melting conditions are solved analytically and the effects of different parameters are discussed. Numerical simulation results show that the profiles of the fluid temperature, porosity of the medium, and solvent concentration, form three fronts moving at different rates. It is found that for heat transfer coefficients above a certain value, the rate of melting is independent of this parameter and the system can be considered to have reached instantaneous thermal equilibrium. Moreover, slow heat transfer in the medium is shown to increase the rate of melting at long time periods by involving larger areas in the melting process. Heterogeneous scenarios are also analyzed by introducing frozen blocks of different geometries. The ability of the flow to bypass the frozen region involves a new heat transfer mechanism identified as outer-boundary convection. The effects of the geometry of the block along with the other parameters on the melting process are examined. Furthermore a generalizing scheme is proposed to predict the melt production for different block geometries and values of the saturation of the frozen phase. [ABSTRACT FROM AUTHOR]

The unsteady, conjugate, forced convection heat transfer from a porous sphere embedded in another porous medium has been analysed. Both porous media are fluid saturated. Local thermal equilibrium between the two phases is assumed. The fluid flow inside and outside the sphere was considered axisymmetric, steady and incompressible (Darcy and Brinkman flows). The heat balance equations were solved numerically in spherical coordinates system by an implicit alternating direction finite difference method. The influence of the porous media permeability and sphere Peclet numbers on the heat transfer mechanism and rate was analysed for different values of the physical properties ratios (thermal conductivity ratio and heat capacity ratio). [ABSTRACT FROM AUTHOR]

Abstract: In this paper an analytical model was developed to minimize the thermal resistance of an air cooled porous matrix made up of solid spheres with internal heat generation. This was done under the assumption of local thermal equilibrium. The analytical solution of the optimum sphere diameter was found to be independent of the heat generation rate of the solid spheres, but was dependent on the applied pressure drop and fluid properties. The analytical model compared very well to a numerical model found in a computational fluid dynamics code when air and liquid water properties were used for the fluid phase and wood and silica/sand properties were used for the solid phase. [Copyright &y& Elsevier]