On the influences of the thermal boundary condition at porous-fluid interface upon the Nusselt number in a pipe partially filled by a porous material

Yasser Mahmoudi, University of Cambridge
Nader Karimi, University of Glasgow


This paper examines numerically the heat transfer enhancement in a pipe partially filled with a porous medium under the Local Thermal Non-Equilibrium (LTNE) condition. The flow inside the porous material is modelled using the Darcy-Brinkman-Forchheimer model. The optimum porous thickness (Rr) for heat transfer enhancement is determined under varying parameters. These include the porosity (ε), Darcy number (Da), Reynolds number (Rep), inertia parameter (F), particle diameter (dp), solid-to-fluid conductivity ratio (k) and a reasonable value of the flow pressure drop. The pipe wall is under constant wall temperature boundary condition. Two existing models (models A and B) are considered at the interface between the porous medium and the fluid. The differences between these two models in predicting 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 the porous thickness ratio. However, considerably different values of Nu number are obtained from the two interface models.