Analytical Approach to Solve an Inverse Problem for One-Dimensional Heat Conduction Based on Laplace Transformation : Application to Cylindrical and Spherical Coordinates

An analytical method has been developed to solve an inverse problem for one-dimensional heat conduction in cylindrical and spherical coordinates by using Laplace transformation. This method successfully derives the inverse solution by which the surface temperature and heat flux can be predicted well for any kind of boundary condition with a constant initial condition. The inverse solution obtained by the temperatures at two different measuring points can predict the surface temperature and heat flux with higher accuracy than that at a single measuring point, although the single measuring point is enough for the cylindrical and spherical coordinates to predict them. The same order of accuracy of estimation has been maintained between cylindrical and spherical coordinate.