Role of the inclination of an inverted‐V upper plate on the heat and flow behavior of trapped gases in a modified Rayleigh–Bénard cavity

Thermal buoyant air inside a modified Rayleigh–Bénard (RB) cavity bounded by a lower flat plate and an inverted‐V upper plate has been investigated numerically using the finite‐volume method. The second‐order‐accurate QUICK and SIMPLE schemes were used for the discretization of the convective terms and the pressure–velocity coupling in the set of conservation equations, respectively. The problem under study is controlled by two parameters: (1) the Rayleigh number ranging from 10³ to 10⁶ and (2) the relative height of the vertical sidewalls d. In reference to the latter, it varies from one limiting case corresponding to the standard RB cavity (a rectangle with d = 1) to another limiting case represented by an isosceles triangular cavity where d = 0. The numerical results for the velocity and temperature fields are presented in terms of streamlines, isotherms, local and mean heat fluxes. An additional effort was devoted to determine the critical Ra values characterizing the transition from symmetrical to asymmetrical buoyant airflow responsive to incremental changes in Ra. For purposes of engineering design, a general correlation equation for the Nusselt number in terms of the pertinent Ra and d was constructed using nonlinear multiple regression theory. Copyright © 2007 John Wiley & Sons, Ltd.