FINITE ELEMENT ANALYSIS OF LAMINAR MIXED CONVECTION IN A LID-DRIVEN TRAPEZOIDAL CAVITY CONTAINING FOUR INCLINED OBSTACLES

Abstract

Mixed convection in enclosures with internal obstacles is relevant to the thermal management of electronic, energy, and process equipment, yet results for trapezoidal lid-driven cavities with several inclined obstacles are scarce. This study examines steady, laminar, two-dimensional mixed convection of an incompressible Newtonian fluid in a trapezoidal cavity (base 4L, lid 2L, height 3L) with a heated base, a cold moving lid, adiabatic inclined side walls, and four inclined rectangular obstacles. The Boussinesq-approximated equations were non-dimensionalised and solved with a penalty-formulated Galerkin finite element method in COMSOL Multiphysics on a mesh of 5,208 elements. Eight cases were examined: Grashof number Gr = 3,000–500,000 at Reynolds number Re = 1, and Re = 0.1–1.0 at Gr = 1,000. Every case showed two counter-rotating cells on either side of a central jet. Raising Gr from 3,000 to 500,000 increased the peak dimensionless speed from 2.19 to 254.7 and drew a narrow finger of cold fluid from the lid towards the heated base; the local power-law exponent of peak speed fell from 1.47 to 0.59. At Gr = 1,000, raising Re from 0.1 to 1.0 reduced the peak speed from 104.37 to 1.17, produced smoother, more stratified isotherms, broke the flow symmetry, and increased the reported temperature gradient from 0.316 to 0.771. The Richardson number, Ri = Gr/Re2, organised the flow morphology. Because mesh-independence and benchmark validation were not reported and Nusselt numbers were not computed, the findings are qualitative.