Numerical Study of Laminar Natural Convection Heat Transfer in Inclined Trapezoidal Enclosure

In this paper, fluid flow pattern and heat transfer behavior are numerically studied in a trapezoidal enclosure inclined at different tilt angles. The enclosure has isothermally heated cylindrical inner wall and cooled cylindrical outer wall, whereas sidewalls have linearly varying temperature profile. The numerical analysis is performed at different Rayleigh numbers (10³ ≤ Ra ≤10⁶) and Prandtl numbers (0.71 ≤ Pr ≤ 40) assuming steady, incompressible, laminar, Newtonian, and two-dimensional flow. The angle between two nonparallel sidewalls is varied from 10 deg to 90 deg, while the tilt angle is varied from 5 deg to 175 deg. Governing equations along with the Poisson type equation for heatfunctions are solved to obtain fluid flow and direction of heat flow in the trapezoidal enclosure. At low Raleigh number, the isotherms are smooth, indicating the dominance of conduction heat transfer dominates. The streamlines, isotherms, and heatlines in high Prandtl number (Pr = 6.99 ad 40) fluids show a similar pattern as that in the air (Pr = 0.71) at Ra = 10⁶; however, the strength of heatfunctions increases. With the increase in the aspect ratio of the enclosure, thermally stratified region is found to increase in size. Stronger convection is present in the enclosure with a higher angle between two nonparallel sidewalls.