a numerical investigation of forced convection in a channel with hot solid block inside a square porous block mounted on a bottom wall was carried out. the lattice boltzmann method was applied for numerical simulations. the fluid flow in the porous media was simulated by brinkman-forchheimer model. the effects of parameters such as porosity and thermal conductivity ratio over flow pattern and t...

In this paper, we study the dimension estimate of global attractor for a 3D Brinkman-Forchheimer equation. Based on differentiability semigroup with respect to initial data, show that strong solution equation has finite Hausdorff and fractal dimensions.

The problems of steady film condensation on a vertical surface embedded in a thin porous medium with anisotropic permeability filled with pure saturated vapour are studied analytically by using the Brinkman-Darcy flow model. The principal axes of anisotropic permeability are oriented in a direction that non-coincident with the gravity force. On the basis of the flow permeability tensor due to t...

This paper is devoted to the homogenizat ion of the Stokes or Navier-Stokes equations with a Dirichlet boundary condit ion in a domain containing many tiny solid obstacles, periodically distributed in each direction of the axes. For obstacles of critical size it was established in Part I that the limit problem is described by a law of Brinkman type. Here we prove that for smaller obstacles, the...

This paper discusses a numerical subgrid resolution approach for solving the Stokes-Brinkman system of equations, which is describing coupled flow in plain and in highly porous media. Various scientific and industrial problems are described by this system, and often the geometry and/or the permeability vary on several scales. A particular target is the process of oil filtration. In many complic...

Many microorganisms swim in a highly heterogeneous environment with obstacles such as fibers or polymers. To better understand how this environment affects microorganism swimming, we study propulsion of a cylinder or filament in a fluid with a sparse, stationary network of obstructions modeled by the Brinkman equation. The mathematical analysis of swimming speeds is investigated by studying an ...

Volume penalization is a subclass of immersed boundary methods for modeling complex geometry flows, which introduces the effects of obstacles by modifying the governing equations. The method presented in this paper encompasses general boundary conditions as an extension of the Brinkman Penalization Method (BPM) [1], which was originally developed for solid, isothermal obstacles in incompressibl...

Traditional heat transfer fluids frequently encounter several limitations in the process, due to lower thermal conductivity process industries, and also has an impact on performance of industrial sectors. In order overcome problem, researchers have currently considered alternative development fluids. Hence, this study will concentrate problem steady combined convective transport. particular, fl...

We present a well-posed model for the Stokes/Brinkman problem with a family of jump embedded boundary conditions (J.E.B.C.) on an immersed interface with weak regularity assumptions. It is issued from a general framework recently proposed for fictitious domain problems. Our model is based on algebraic transmission conditions combining the stress and velocity jumps on the interface S separating ...

We introduce a new finite element method for the approximation of the three-dimensional Brinkman problem formulated in terms of the velocity, vorticity, and pressure fields. The proposed strategy exhibits the advantage that, at the continuous level, a complete decoupling of vorticity and pressure can be established under the assumption of sufficient regularity. The velocity is then obtained as ...