Studying the natural convection problem in a square cavity by a new vorticity-stream-function approach

Abstract

In this study, a benchmark natural convection problem is studied under a Gay-Lussac type approximation incorporating centrifugal effects in the context of a new vorticity-streamfunction approach. This approximation differs from the classic Boussinesq approximation in that density variations are considered in the advection term as well as the gravity term in the momentum equations. Such a treatment invokes Froude number as a non-Boussinesq parameter deviating results from the classic Boussinesq approximation. Numerical simulations of the natural convection in square cavity are performed up to = 10 6 and = 0.3 at = 0.71 via proposed formulation and results are compared against the conventional Boussinesq approximation in terms of the average and local Nusselt number and entropy generation. Comparing results indicate that, up to = 10 5 , mentioned approaches are showing almost identical performance, but as the Rayleigh number exceeds 10 5 , formed thermal boundary layer under Gay-Lussac type approximation is slightly thicker compared to the Boussinesq approximation accompanied by a stronger velocity gradient.

Natural convection and entropy generation in square and skew cavities due to large temperature differences: A Gay–Lussac‐type vorticity stream‐function approach

“…Iterative solution procedure is stopped as soon as the maximum difference of scalar values during two successive iterations becomes less than 10 −7 . Accurate performance of the CVFEM solver is already tested in previous works [37][38][39][40][41][42][43][44][45] but here in 2). The present simulations recover published values very well, with discrepancies lower than 0.41%.…”