Numerical Comparison of Laminar Natural Convection Heat Transfer in C-shaped and U-shaped Enclosures

Abstract

This research presents a numerical investigation into the influence of natural convection within C-shaped and U-shaped enclosures, employing air as the enclosed fluid. Both shapes are subjected to uniform boundary conditions, with the hot wall and cold rib of the enclosure kept at constant temperature. The outer C-shaped and U-shaped boundary wall is set to a higher temperature compared to the inner one, while the connecting walls between the cold rib and the hot wall are treated as adiabatic. The study assumes a 2-D problem setup, with varying Rayleigh numbers ranging from 10⁴ to 10⁶, ensuring laminar flow conditions across all scenarios. Various aspect ratios (0.3, 0.5, 0.7), the ratio of the outer length to the inner length of the enclosure, are explored in the simulations. Results are depicted through streamline and temperature contour visualizations, revealing the formation of distinct eddies within the enclosures. The analysis highlights an increase in the Nusselt number with a rising Rayleigh number in both enclosures for specific aspect ratios. Besides, a higher Rayleigh number is associated with the formation of more eddies and pronounced changes in the results, particularly evident at a certain aspect ratio. Moreover, the rate of change in the Nusselt number differs between C-shaped and U-shaped enclosures with increasing Rayleigh numbers. From the viewpoint of natural convection, the formation of eddies can modify the temperature gradients and enhance the Nusselt number by boosting heat transfer from the surface to the adjacent fluid. Notably, the study reveals a heightened presence of eddies which ultimately results in a higher Nusselt number at Ra=10⁶.