Natural convection in tilted square cavities with triangular shaped top cold wall

Abstract

A numerical study of natural convection in a tilted square cavity with heated horizontal base and cold upper wall is presented. The present study is based in such a configuration where the top triangular wall of two different shapes is maintained at a constant low temperature. A constant heat flux source whose length is 20% of the total length of the cavity is discretely embedded at the left corner of the bottom wall. The remaining part of the bottom wall and the two sidewalls are considered to be adiabatic. The study includes computations for inclination angles of the cavity from 0° to 45°, where the Grashof number, Gr varies from 10³ to 10⁶. The Penalty finite element method has been used to see the effects of inclination angles and Grashof number on heat transfer process in the cavity. Results are presented in the form of streamline and isotherm plots as well as the variation of the average Nusselt number. Observation shows the significant effect of different triangular top surface on the heat transfer characteristics at the higher Grashof number and inclination angle.

Keywords: Natural convection, Penalty finite element, Nusselt number, Isoflux heating.

doi:10.3329/jme.v39i1.1831

Journal of Mechanical Engineering, vol. ME39, No. 1, June 2008 30-39