[1] This paper presents an approximate analytical solution for non-Darcy flow of a slightly compressible fluid through a fractured reservoir. The analytical solution is obtained using the traditional Warren-Root solution superposed on a dimensionless non-Darcy flow coefficient. The model formulation incorporates the Forchheimer equation into the Warren-Root model for describing non-Darcy flow t...

The equations of fluids in porous media are very useful in designing the rockfill and diversion dams, gabions, breakwaters and ground water reserves. Researches have been showed that the Forchheimer equation is not sufficient for the analysis of hydraulic behavior of free-surface radial flows; because, in these flows, in addition to the hydraulic gradient and velocity, the variable of radius is...

The present analysis investigates non-Darcy forced convective heat transfer in a channel confined by two parallel walls subjected to uniform heat flux in a highly porous medium saturated with a non-Newtonian power-law fluid. Extensive numerical integrations have been carried out utilizing the Brinkman-Forchheimer extension of the Darcy model in order to study the effects of pseudoplasticity, an...

This paper discusses a novel three field formulation for the Darcy-Forchheimer flow with nonlinear viscosity depending on temperature coupled heat equation. We show unique solvability of variational problem by using; Galerkin method, Brouwer’s fixed point and some compactness properties. propose study in detail finite element approximation. A priori error estimate is then derived convergence ob...

Fluid flow through porous media is of great importance for many natural systems, such as transport of groundwater flow, pollution transport and mineral processing. In this paper, we propose and validate a novel finite volume formulation of the lattice Boltzmann method for porous flows, based on the Brinkman–Forchheimer equation. The porous media effect is incorporated as a force term in the lat...

In this paper, Forchheimer equation is used as the constitutive equation for flow through rockfill, and the non-linear two-dimensional governing equation with free surface is solved by a new finite element method in a fixed grid. The model is verified by applying it to different flow conditions. The first scenario, which is assumed to be one-dimensional with analytical solution available for it...

In this paper, Forchheimer equation is used as the constitutive equation for flow through rockfill, and the non-linear two-dimensional governing equation with free surface is solved by a new finite element method in a fixed grid. The model is verified by applying it to different flow conditions. The first scenario, which is assumed to be one-dimensional with analytical solution available for it...

To improve heat and ablation rate modeling of the thermal protection system for reentry vehicles, a material response model with surface ablation and pyrolysis is developed. To accurately model the effects of the pyrolysis gas within the ablator, Darcy’s law is replaced by Forchheimer’s law for flow through porous media. The use of Forchheimer’s law accounts for the inertial effects of the gas ...