Heat transfer in enclosures having a fixed amount of solid material simulated with heterogeneous and homogeneous models

This work compares two different approaches for obtaining numerical solutions for laminar and turbulent natural convection within a cavity filled by a fixed amount of a solid conducting material. In the first model, a porous-continuum, homogeneous or macroscopic approach is considered based on the assumption that the solid and the fluid phases are observed as a single medium, over which volume-averaged transport equations apply. Secondly, a continuum, heterogeneous or microscopic model is considered to solve the momentum equations for the fluid phase resulting in a conjugate heat transfer problem in both the solid and the void space. In the continuum model, the solid phase is composed of square obstacles, equally spaced within the cavity. In both models, governing equations are numerically solved using the finite volume method. The average Nusselt number at the hot wall, obtained from the porous-continuum, homogeneous or macroscopic model, for several Darcy numbers, are compared with those obtained with the second approach, namely the continuum model, with different number of obstacles. When comparing the two methodologies, this study shows that the average Nusselt number calculated for each approach for the same Ram differs from each other and that this discrepancy increases as the Darcy number decreases, in the porous-continuum model, or the number of blocks increases, in the continuum model. Inclusion of turbulent transfer raises Nusselt for both the continuum and the porous-continuum models. A correlation is suggested to modify the macroscopic Rayleigh number in order to match the average Nusselt numbers calculated by the two models for Ram = const = 104 and Da ranging from 1.2060 × 10−4 to 1.