The scope of the present paper is concerned with the numerical prediction of the confined air flow characteristics and thermal convection patterns in sealed attic spaces in roofs with upper inverted V-shapes and horizontal suspended ceilings of conventional houses and buildings. For these isosceles triangular cavities, two relevant cases involve prescribed wall temperatures wherein the bottom base wall is cooled/heated and the upper two inclined walls are symmetrically heated/cooled during the summer and winter seasons. Based on finite element analysis, the COMSOL code is implemented to perform numerical solutions of the two-dimensional system of coupled NavierStokesBoussinesq and energy equations. The computational domain is made coincident with the physical domain to handle potential non-symmetric velocities and non-symmetric temperatures that may occur when exposed to vigorous air flows. The numerical solution via finite elements provides the two velocity fields u (x, y), v (x, y) and the temperature field T (x, y) for the confined air flows. Overall, the target design quantity is the mean wall heat fluxes w q varying with the attic aspect ratio and the temperature difference at two opposing walls. The predicted w q values match the experimental measurements for the two distinct cases related to summer and winter seasons. At the end, comprehensive correlation equations are constructed for the quantification of the mean Nusselt number in terms of the Grashof number and the attic aspect ratio, which could be used in building science research.
A finite element analysis for a thermal convection problem with the
infinite Prandtl number
