論文ID: 23-00235
An Excel program that uses tri-diagonal matrix algorithm (TDMA) is proposed to calculate one dimensional steady heat conduction. The program gives analytical exact solutions to calculate multi-layered symmetric flat plate, solid cylinder, sphere, double-sided flat plate, hollow cylinder, and spherical shell geometries. Three different boundary conditions and arbitrary heat generation rates can be applied. Most existing numerical analysis methods use the finite difference approximation. When the thickness and physical properties of adjacent layers are extremely different in the vicinity layers, accurate values cannot be obtained without a very large number of calculation meshes. A large number of meshes increases calculation time, even for simple geometries. However, the analytical method described in this paper does not affect the accuracy of the analysis even if the adjacent media have extremely different thicknesses, because an exact solution is obtained. The effectiveness of the program is demonstrated by solving an example using this Excel program. Furthermore, the method is applied various engineering problems to show how to make simplified heat transfer models to the realistic engineering problems. By using this program to perform heat transfer calculation examples described in JIS, laws and regulations, it was easy to confirm the validity of the regulations and standard settings. The excel program is open to the public for engineering design.
