Finite Element Analysis of Fin Effect on Buoyancy Convection of Air Enclosed in a Complex Square Cavity

By using a second order Euler-Taylor-Galerkin (ETG) finite element method of fractional steps developed by the authors, a two-dimensional numerical solution for natural convection in a square cavity with a fin is presented in this paper. Code validation and the mesh resolution effect are studied firstly for buoyancy convection of air enclosed in a simple square cavity at Ra=10⁴ and 10⁵. Ten sets of finite element meshes are generated to analyze the mesh resolution effect. As the results shown, the maximum relative error of the averaged Nu is lower than 4% with that provided by Davis. Considering the mesh resolution effect, 100×100 elements or grids with the same elements density are then decided to be used in the whole computation. Calculations are then carried out to study the fin effect at Ra=10⁴. It is observed that the change on the characteristic of each fin makes great effect on heat transfer. Moreover, flow field and temperature distribution strongly affected from the fin characteristic. In order to understand the fin effect more clearly, evolution curves of the averaged Nu with H/B or W/B are also fitted.