An analytical derivation of source term dependent, 2-D `generalized Poisson conduction shape factors' (Q2567051)

The authors derive new generalized Poisson conduction shape factors (GPCSFs) including the effects of uniform power deposition and variable temperature conditions. The GPCSFs are derived for a single, circular vessel eccentrically imbedded in a uniformly heated, homogeneous, circular tissue matrix. Results show that when the average temperature of the vessel wall is lower than the average temperature of the tissue boundary, the GPCSFs based on the average tissue matrix temperature (Stm) are much less sensitive to the strength of the source term compared to the GPCSFs based on the average tissue boundary temperature (Stb). Thus, the use of Stm instead of Stb will introduce less error in the estimation of tissue-vessel heat transfer rates when sources are present. Finally, it is shown that the effects of the variable vessel wall and tissue boundary temperatures are significant at large vessel sizes and eccentricities, with vessel size having a larger effect than vessel eccentricity.