One dimensional heat conduction analysis by tri-diagonal matrix algorithm (TDMA) applicable to Excel program. Unified analysis of implicit unsteady heat conduction for flat plates, cylinders, and spheres

An Excel program that uses tri-diagonal matrix algorithm (TDMA) is proposed to calculate one dimensional unsteady heat conduction using implicit method. The program is unified analysis method to calculate 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. The unsteady numerical analysis is compared with the exact solution to verify the accuracy. Furthermore, the effectiveness of the program is demonstrated by solving various engineering examples using this Excel program. (author)