Application of the similarity theory including variable property effects to a complex benchmark problem

Abstract

An asymptotic method to account for variable property effects, recently described in this journal, is now applied to a complex benchmark geometry. It is a room which is ventilated by forced convection through inlet and outlet slit nozzles at the top and bottom of the side walls. Four heating elements standing on the ground floor add heat with constant heat flux density of varying strength. CFD solutions with the full coverage of all property temperature dependencies of air and SF6 are compared with asymptotic results (ACFD), applied for these fluids. ACFD results are given as systematic expansions with respect to a heat transfer parameter \({\varepsilon}\) which serves as perturbation parameter. First and second order asymptotic results of the Nuselt number at the surface of the heating elements are shown as well as temperature distributions along the adiabatic walls of the room. Special attention is given to the reference Nuselt numbers of zero order \({(\varepsilon=0)}\) which are those for constant properties only for pure forced convection.