Heat Conduction Solutions Using Gauss-Siedel Method

-, Avinder Singh (2020) Heat Conduction Solutions Using Gauss-Siedel Method. Final Year Project (Bachelor), Tunku Abdul Rahman University College.

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Abstract

The research focus onto heat conduction problems encountered in the studies of heat transfer. To obtain solution for rate of heat transfer of heat conduction problems, one must be able to obtain the thermal conductivity of the material, the area perpendicular to heat flow, the length of which heat is conducted through and the temperature gradient within the object. The temperature gradient is always the tricky part as temperatures are distributed and varies within different point of the object. The research explores the numerical approach to obtain the temperature distribution within an object via the Gauss-Seidel method. Three geometries were chosen being flat plate with bottom fins, projectile geometry and single rectangular fin to compute temperature distribution via Gauss-Seidel method by discretizing the geometry into a system of grids and nodes to be represented in the form of a matrix in MATLAB. In addition to that, investigation upon different guess values and its effects on the final solution as well as number of iterations required to arrive at convergence is also performed showing that regardless of guess values, the calculation will always converge at the same final solution with the difference being the number of iteration required to arrive convergence. The Gauss-Seidel method was then contended against the Jacobi method to demonstrate the advantage in terms of computation speed over Jacobi method. The results obtained for all three geometries are highly in agreement to the respective reference paper that utilizes other methods to obtain solution with low percentage differences; hence, allowing the Gauss-Seidel method to be a viable alternative method to solve for heat conduction problems.