An HP-Adaptive Finite Element Model for Convective Heat Transfer in an Attic Space

Abstract

An hp-adaptive finite element algorithm is used to simulate heat transfer within attic spaces driven by buoyancy forces. The element size (h-) and shape function order (p-) are dynamically controlled by an a-posteriori error estimator based on the L2 norm. A three-step process is used to solve the system of equations. The hp-adaptive algorithm is validated using natural convection heat transfer within a differentially heated enclosure. Application of the model is used to simulate heat transfer within attic spaces subjected to natural convection for Rayleigh numbers ranging from 7.1×102 to 7.1×105. Attic aspect ratios range from 0.2 to 1.0. Heat transfer rates typical of summer days in Las Vegas are considered: roofs (inclined surfaces) of attics are hot; bases (bottom surfaces) are cold and vertical walls are insulated. Results are compared with data in literature when possible; good agreement is generally observed.