Abstract
This is a numerical study of turbulent natural convection flow in a rectangular enclosure. The flow of heat is one form of Newtonian motion. We consider natural convection in a three dimensional rectangular enclosure in the form of a room with heaters placed on opposite walls and two windows each on the adjacent opposite walls. The study of free convection in the past five decades focused mainly on two different simple geometries, first the single isothermal or constant flux vertical plate in isothermal stagnant surrounding, secondly, the enclosed rectangular cavity with heated floor and cooled walls. There has also been much emphasis on Reyleigh number as opposed to the Reynolds number used in this study. To analyze the flow and heat transfer rates, a complete set of non-dimensionalized equations governing Newtonian fluid and boundary conditions are recast into vector potential to eliminate the need for solving the continuity equations. A Boussinesq fluid motion in a three dimensional cavity is considered. The governing equations with the boundary conditions are descritized using three point central difference approximations for a non-uniform mesh. The resulting finite difference equations are solved using Matlab simulation software. The solutions are presented at the Reynolds number 5500, with Prandtl number 0.71. The results are presented on graphs to show velocity profiles and temperature distribution in the room. The room is divided into a number of regions with those near the heaters having high temperatures as those near the windows have low temperatures. Convective currents caused by buoyancy forces play a major role in determining the velocity profiles in the room. Keywords—Heat Convection in an Enclosure; Heat Transfer; Natural Convection in a Rectangular Enclosure.
Highlights
A fluid is a substance whose constituent particles continuously change their positions relative to one another when subjected to energy change or force
If the Reynolds number of the system is small, the viscous force is predominant and the effects of viscosity are important, while if it is large, the inertia force is predominant and the viscous effects are only important in the narrow layer near the solid boundary
In this study we investigate temperature distribution and velocity profiles in an enclosure brought about by heat transfer
Summary
A fluid is a substance whose constituent particles continuously change their positions relative to one another when subjected to energy change or force. Convection could be shown by movement of air due to buoyancy up and around the room subject to differential heating encountered in many practically important engineering problems. They include thermal insulation of buildings, heat transfer through open windows, refrigeration, etc. High Reynolds number natural convection has been identified as one of the main subjects for future research, extension to three dimensional calculations for practical and real life situations is considered of prime importance
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