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Loosening local equilibrium assumptions in two-phase flow in porous media gives rise to new, unknown variables. More specifically, when loosening the local thermal equilibrium assumption, one has to describe the heat transfer between multiple phases, present at the same mathematical point. In this paper, we calibrate a macro-scale mathematical model which is free of local equilibrium assumptions to experimental observations. We emphasize the correct determination and upscaling of necessary input parameters from the experimental data achieved by image analysis. By choosing an appropriate scaling parameter, we are able to reproduce experimental measurements satisfactorily. This is a first step towards quantifying heat transfer in two-phase flow in porous media. Ultimately, our aim is to find the limits of the applicability of local equilibrium assumptions in two-phase flow in porous media. [ABSTRACT FROM AUTHOR]

The steady natural convection in a two-dimensional porous square cavity filled with a nanofluid and including internal heat generation is presented in this paper. The mathematical model considered consists of the Darcy equation for the momentum, while a new model is proposed for the energy and nanoparticles’ concentration equations. The system of partial differential equations is written in terms of a dimensionless stream function, temperature and concentration of the nanoparticles and is solved numerically using the finite difference method. The effects of the governing parameters, such as: Rayleigh number Ra , the Lewis number Le and the dimensionless ratio between the thermophoretic and Brownian coefficients N BT on the velocity, temperature and nanoparticles’ concentration, Nusselt and Sherwood numbers are studied. It is found that the addition of the nanoparticles into the fluid saturated porous medium reduces the temperature and enhances the heat transfer when the value of the thermal conductivity of the nanoparticles is much higher than the thermal conductivity of the solid structure of the porous medium. This addition has almost no effect on the flow and heat transfer characteristics when the values of the thermal conductivity of the nanoparticles and the thermal conductivity of the solid structure of the porous medium have close values. [ABSTRACT FROM AUTHOR]