Henry Darcy's experimental studies in 1856 of saturated water flowthrough a homogeneous porous medium contained in a vertical column have provided the basis for the quantitative description of fluid flow in a wide variety of both natural and engineered porous medium environmental systems. Extrapolation of Darcy's original observations and conclusions has led to several commonly applied equation...

This paper is concerned with the homogenization of model problems in periodic porous media when important phenomena occur on the boundaries of the pores. To this end, we generalize the notion of two-scale convergence for sequences of functions which are deened on periodic surfaces. We apply our results to two model problems : the rst one is a diiusion equation in a porous medium with a Fourier ...

Evaporation from the surface of a porous medium is a complex process, governed by interplay between (1) coupled liquid and vapor flow in the porous medium, and (2) relative humidity, temperature, and aerodynamic conditions in the surrounding air. In order to avoid the computational expense of explicitly simulating liquid, gas, and heat flow in the porous medium (and the possible further expense...

this work presents the heat transfer characteristics of a new type of porous radiant air heater that operates on the basis of effective energy conversion method between flowing gas enthalpy and thermal radiation. at each layer, the gas and solid phases are considered in non-local thermal equilibrium, and combustion in the porous radiant burner is modeled by considering a non-uniform heat genera...

Abstract This paper is concerned with the homogenization of model problems in periodic porous media when important phenomena occur on the boundaries of the pores. To this end, we generalize the notion of two-scale convergence for sequences of functions which are defined on periodic surfaces. We apply our results to two model problems : the first one is a diffusion equation in a porous medium wi...

steady state natural convection of al2o3-water nanofluid inside a square cavity filled with a porous medium is investigated numerically. the temperatures of the two side walls of the cavity are maintained at th and tc, where tc has been considered as the reference condition. the top and the bottom horizontal walls have been considered to be insulated i.e., non-conducting and impermeable to mass...

In this talk we present a continuum model and numerical results for transient flows over and through porous media. First, we briefly discuss the derivation of the model and present an algorithm for its numerical treatment. Subsequently, we present results from direct numerical simulations for developing flows over porous layers of large porosity. Due to the steep velocity gradients across the i...

We study the asymptotic behavior of compressible isentropic flow through porous medium when the initial mass is finite. The model system is the compressible Euler equation with frictional damping. As t → ∞, the density is conjectured to obey to the well-known porous medium equation and the momentum is expected to be formulated by Darcy’s law. In this paper, we prove that any L∞ weak entropy sol...