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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]

Abstract: This paper examines numerically the heat transfer enhancement in a pipe partially filled with a porous medium under local thermal non-equilibrium (LTNE) condition. The flow inside the porous material is modelled using the Darcy–Brinkman–Forchheimer model. The effect of different parameters such as, inertia (F), Darcy number (Da), conductivity ratio, porosity and particle diameter on the validity of local thermal equilibrium (LTE) are studied. The optimum porous thickness for heat transfer enhancement under varying F and with reasonable pressure drop is determined. The pipe wall is under constant wall temperature boundary condition. Two models are considered at the interface between the porous medium and the fluid. The differences between these models in predicting the temperature of the fluid and solid phases as well as the Nusselt (Nu) number for different pertinent parameters are discussed. In general, the two interface models result in similar trends of Nu number variation versus porous thickness ratio. However, considerably different values of Nu number are obtained from the two interface models. The effects of inertia term on the Nu number and pressure drop are further studied. For a given model and for Da<10−3, the Nu number is found independent of F. However, for Da>10−3 as F increases the computed Nu number increases. [Copyright &y& Elsevier]

Abstract: This paper examines the steady natural convection in a partially opened enclosure filled with porous media using the Brinkman–Forchheimer model. Whilst the part of the left vertical wall of the cavity is heated, the other walls are adiabatic or thermally insulated Based upon numerical predictions, the effects of pertinent parameters such as Grashof number, Darcy number, porosity, length of the heated wall and the location center of the opened cavity are examined. It is found that as the Grashof number increases, due to strengthening buoyancy driven flows, the local Nusselt number from partially heated vertical wall, at a given position on this wall increases. This, in turn, increases the temperature of the heated wall. The results of this study can be used in the design of an effective cooling system for electronic components to help ensure effective and safe operational conditions. [Copyright &y& Elsevier]

Abstract: This paper developed a mathematical model for the coupled heat and mass transfer in porous media based on the fractal characters of the pore size distribution. According to Darcy’s law and Hagen–Poiseuille’s law for liquid flows, the diffusion coefficient of the liquid water, a function of fractal dimension, is obtained theoretically. The liquid flow affected by the surface tension and the gravity, the water vapor sorption/desorption by fibers, the diffusion of the water vapor and the phase changes are all taken into account in this model. With specification of initial and boundary conditions, distributions of water vapor concentration in void spaces, volume fraction of liquid water, distribution of water molecular content in fibers and temperature changes in porous fibrous media are obtained numerically. Effects of porosity of porous fibrous media on heat and mass transfer are analyzed. The theoretical predictions are compared with experimental data and good agreement is observed between the two, indicating that the fractal model is satisfactory. [ABSTRACT FROM AUTHOR]

Abstract: This paper focuses on the investigation of the 3D mathematical model to simulate the coupled heat and liquid moisture transfer in hygroscopic porous fibrous media. The flow of the liquid moisture, the water vapor sorption/desorption by fibers and the diffusion of the water vapor are taken into account in this 3D model. Prediction-corrector method is used to solve the 3D governing equations. A series of computational results of the coupled heat and moisture transfer are obtained with the specific initial conditions and boundary conditions. The distribution of the water vapor concentration in the void spaces, the volume fraction of the liquid water in the void spaces, the distribution of the water content in fibers and the changes of the temperature in porous fibrous media are computed. It is shown that the effects of the gravity and capillary actions are significant in hygroscopic porous fibrous media. The comparison with the experimental measurements shows the reasonable agreement between the two. The results illustrate that the 3D model of the coupled heat and liquid moisture transfer in hygroscopic porous fibrous media is satisfactory. [Copyright &y& Elsevier]

Abstract: The Herschel–Bulkley (HB) fluid is the representative fluid which may be reduced to the power-law fluid, Bingham and Newtonian fluids in appropriate conditions. In this paper, fractal models for velocity and the starting pressure gradient for HB fluid in porous media are derived based on fractal characteristics of porous media and capillary model. The proposed models are expressed as a function of fractal dimensions, porosity, maximum pore size and representative length of porous media. Every parameter in the proposed expressions has clear physical meaning, and the proposed models relate the flow characteristics of HB fluid to the structural parameters of porous media. The variation trends of fractal velocity and starting pressure gradient versus different impact factors are shown, and the analytical expressions reveal the physical principles for flow velocity and starting pressure gradient in porous media. [Copyright &y& Elsevier]

Abstract: In this paper, laminar and turbulent flows in channels are considered. The primary interest for industrial purpose is a macroscale description of mean flow quantities derived from the microscopic details of the flow in each subchannel. A double averaging procedure has been used to derive balance equations for mean flow variables within laminar and turbulent regimes. This up-scaling procedure results in additional contributions, amongst which dispersion predominates. Thermal dispersion might be seen as the sum of a first contribution, hereafter denoted “passive”, due to velocity heterogeneities, and a second one, called “active”, due to wall heat transfer. The aim of the present work is to propose practical models for thermal dispersion that account for laminar and turbulent regimes. Embedded in CFD code, they are validated against RANS simulations. Our results illustrate the importance of thermal dispersion for heated flows in the presence of nonuniform wall heat flux or temperature jumps. [Copyright &y& Elsevier]