Numerical simulation of laminar forced convection in horizontal pipe partially or completely filled with porous material

Laminar forced convection flow through a pipe partially and completely filled with a porous material is investigated numerically for three different cases. In the first case the porous material has a cylindrical shape placed at the centerline of the pipe, in the second case the porous material has an annular shape and in the third case the porous material has a cylindrical shape placed at zi = 0.05L from the pipe inlet. The momentum equations are used for describing the fluid flow in the clear region. The Darcy-Forcheimer-Brinkman model is adopted to describe the fluid transport in the porous region. The mathematical model for energy transport is based on the one equation model which assumes a local thermal equilibrium between the fluid and the solid phases. The study covers a wide range of the dimensionless outer radius of the porous material 0 ≤ Rpe ≤ 1 and the effect of Darcy number, 2 × 10−4 ≤ Da ≤ 2 × 10−1. The effect of the porous outer radius and Darcy number on the velocity profiles, the local Nusselt number, the average Nusselt number and the pressure drop are studied. Through the study the Prandtl number, Reynolds number, the ratio between pipe length to outer diameter and porosity were kept constant at 0.7, 100, 25 and 0.9 respectively.