FreeFEM analysis of thermally induced higher-grade Darcy-Forchheimer flow through heated semi-circular cylinders

Abstract In this article, a higher grade Darcy-Forchheimer porous model is derived by using the concepts of tensor calculus. The model presented is accounting for non-linear flow behavior at highly permeable media where the flow is induced by temperature boundary conditions. To this end, a square geometry with two semi-circular heating cylinders mounted at its bottom wall is considered for the analysis of thermal flow dynamics. To solve the obtained coupled system of highly nonlinear partial differential equations the finite element procedure is adopted. Weak formulation of the problem is calculated via the application of variational calculus. The numerical algorithm is implemented through the open source code FreeFEM++. Obtained solutions are validated by reduced model with exact solutions. Mesh independence of the solution is shown through mesh independence analysis test. Results are computed for varying physical parameters with some interesting new observations. Moreover, streamline plots for the velocities and isotherms are shown and discussed. It is found that the Nusselt number increases with increasing Grashhoff and Frochheimer numbers, but decreases with increasing medium porosity.