A comparative study of porous media models in a differentially heated square cavity using a finite element method

A comparative study is made between different flow models for analysis of natural convection in a differentially heated vertical square cavity filled with a fluid saturated porous medium. The solution is obtained by using a finite element method. The Darcy‐modified Rayleigh number, Ra^*,is varied from 50 to 1000 while the Darcy number, Da, ranges from 5 ×10^–7 to 10^–2. It is generally observed that for small values of Ra^* and Da, all other models converge with the Darcy flow model. However,for large values of Ra^* and Da, the Darcy flow model predicts the highest heat transfer rate, and the Brinkman‐Forchheimer extension yields the lowest heat transfer rate whilst prediction from the Brinkman‐extended model lies in between.