Temperature field due to conduction heat transfer in thin circular plates, infinitely long cylinders and spheres with discrete heat generation sources using Green's function techniques.

摘要

Green's Function Techniques were used to find the steady state temperature distribution due to conduction heat transfer in thin circular plates (or infinitely long cylinders) and spheres of constant thermal conductivity with discrete heat generation sources, subject to Dirichlet boundary conditions. The Green's Functions were obtained using the method of images. Three cases for thin circular plates with different heating sources in the form of current carrying electric wires were considered: a wire running along the diameter, four equally spaced radial wires and a wire of four sides forming a circular sector. For a solid sphere one case of heating source was considered: an open ring positioned at the center. It is shown that the method used in this work is superior to other methods, yielding elegant analytical or “almost analytical” solutions and involves less computational work for making parametric studies.