An Analytical Derivation of 2-D Conduction Shape Factors

New, improved formulations to evaluate two commonly used 2-D conduction shape factors, standard and average, are presented for a single, circular vessel eccentrically imbedded in a uniformly heated circular tissue matrix in terms of three non-dimensional parameters. The standard conduction shape factor is defined based on the vessel wall temperature and the outer wall temperature. The average conduction shape factor is defined based on the average tissue temperature and the vessel wall temperature. It is shown that both types of 2-D conduction shape factors are functions of the deposited power. The need to use proper expressions to evaluate conduction shape factors to accurately estimate the heat transfer from/to a region of interest when heating is present is stressed.