Laminar natural convection in a rectangular cavity
Thoya, Patrick Kitsao
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This project is basically a numerical study of the structure of the flow and heat transfer rates due to collision of opposed laminar natural convection boundary layer in an enclosure. Natural convection plays an important role in the flow and heat transfer in a wide range of technological applications. A fluid motion of a Boussinesq fluid in a three dimension rectangular cavity has been considered. To enable the analysis of flow and heat transfer rates, a complete set of non-dimensional equations governing newtonian fluids and boundary conditions were recast into vorticity/vector potential to eliminate the need for solving the continuity equation. The governing equations with the boundary conditions were discretised using a three-point central difference approximation for a non-uniform mesh. The resulting finite difference equations were then solved using the method of false transients and the Samarskii-Andreyev. A powerful computer code was used to generate the current results. The non-uniform mesh has been implemented in the project to allow for efficient use of computer time and storage. This enables placement of more nodes in regions of high velocity gradients and fewer nodes in other regions so that the total number of nodes used is minimized. This mesh type does not compromise the accuracy of the solution as it is demonstrated that order of (h2) accuracy may be maintained, where h is the spatial step size. The Rayleigh number used to obtain the current results was between 5 x 105 and 5 x 106. The study revealed that at higher Rayleigh number, there is substantial increasing exchange of hot air from the lower region to the upper region and vice versa. Temperature tends to decrease as the flow moves away from the 'active wall'.