Numerical study of natural convection in square cavities with differentially heated and cooled walls

Abstract

Buoyancy driven natural convection in rectangular or square enclosures is a widely studied heat transfer phenomenon because of its various engineering and industrial applications, such as convection in building elements, liquid filled thermal storage tanks, heat loss from a solar collector, cooling of electronic equipments, convection during growth of crystals and flows in nuclear reactors. The present numerical study explores the nature of unsteady natural convection flow in square cavities with differentially heated and cooled vertical walls and linearly heated / adiabatic horizontal walls. On the vertical walls, heated and cooled portions were assumed to face each other in an opposed manner. The main objective of the study is to determine the influence of Grashof number and the wall temperatures on the heat transfer characteristics by visualizing the flow patterns in the enclosure. Also the effects of angle of inclination in the case of inclined cavity and the role and importance of time dependent boundary conditions on thermally-driven convection in the enclosure are investigated. The study of unsteady natural convective flow in enclosures requires the solution of mass, momentum and energy equations of the flow. In this study, the governing equations of the flow were formulated, non - dimensionlized and reformulated using stream function vorticity approach. Alternating Direction Implicit method was used to solve the coupled equations. The heat transfer was by conduction and convection modes respectively at low and high Grashof number. When Grashof number and amplitude of the temperature oscillations were increased, the strength of the flow increased significantly. Most of the temperature drop existed near the boundary walls. Negative value of the average Nusselt number implied that heat was transferred from the domain to the surroundings. The average Nusselt number was found to behave as a non-linear function of Grashof number. newline newline newline