STUDY OF NATURAL CONVECTION FLOWS IN A TILTED TRAPEZOIDAL ENCLOSURE WITH ISOFLUX HEATING FROM BELOW

Laminar steady state natural convection in a two-dimensional symmetrical trapezoidal enclosure has been studied using a finite element method. In this investigation, the top wall is considered adiabatic, both inclined sidewalls are maintained at a constant cold temperature and an isoflux heat source is provided at the bottom surface. The pressure-velocity form of the Navier-Stokes equations and energy equation are used to represent the mass, momentum and energy conservations of the fluid medium in the enclosure. Galerkin weighted residual method of finite element formulation with triangular mesh elements is employed. The fluid investigated here is air of Prandtl number fixed at 0.7. The Rayleigh number is varied from 103 to 106 while the sidewall inclination angle is varied from - 15 degrees to 45 degrees. The results are presented in terms of streamline and isotherm plots as well as the variation of average Nusselt number with Rayleigh number for different base wall tilt angles of 0 degrees, 15 degrees, and 30 degrees. The results show that the average Nusselt number increases with the increase of Rayleigh number and the effect of the sidewall inclination angle on heat transfer is significantly reduced at higher Rayleigh number. Effects of sidewall inclination angle on convection heat transfer characteristics decrease with the increase of base wall tilt angle at higher Rayleigh number and Rayleigh number equal to 105 can be considered as a critical limit for the present.