Finite element analysis of natural convection flow in a isosceles triangular enclosure due to uniform and non-uniform heating at the side walls

Abstract

A penalty finite element analysis with bi-quadratic elements is carried out to investigate the effects of uniform and non-uniform heating of inclined walls on natural convection flows within a isosceles triangular enclosure. Two cases of thermal boundary conditions are considered; case I: two inclined walls are uniformly heated while the bottom wall is cold isothermal and case II: two inclined walls are non-uniformly heated while the bottom wall is cold isothermal. The numerical solution of the problem is presented for various Rayleigh numbers ( Ra), ( 10 3 ⩽ Ra ⩽ 10 6 ) and Prandtl numbers ( Pr), ( 0.026 ⩽ Pr ⩽ 1000 ). It has been found that at small Prandtl numbers, geometry does not have much influence on flow structure while at Pr = 1000 , the stream function contours are nearly triangular showing that geometry has considerable effect on the flow pattern. In addition, the presence of multiple circulations are observed for small Pr ( Pr = 0.026 ) which causes wavy distribution of local Nusselt number. It is observed that non-uniform heating produces greater heat transfer rates at the center of the walls than the uniform heating; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominant regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented for specific Prandtl numbers.