Effects of extended surfaces on heat transfer in buoyancy-driven flow in a square cavity

The finite element method is implemented to determine solutions for buoyancy-driven flow in a square cavity. We consider cases with no extended surface, only one extended surface, and an extended surface on walls opposite and adjacent to the cold wall. An investigation of the Péclet number provides an estimate for the amount of artificial diffusion to be added to the Boussinesq and heat transfer equations for stable numerical solutions to be obtained. The importance of the characteristic length on the flow in the square cavity is investigated in detail. We show grid convergence by computing the grid convergence index (GCI). The impact of the boundary conditions and extended surfaces on the isotherms, velocity streamlines and flux are plotted and discussed. We find that the case with insulated boundary conditions on the sidewalls gives a 31 and 33 percent decrease in the flux when we have two and three extended surfaces, respectively.