Effect of metabolic heat generation and blood perfusion on the heat transfer in the tissues with a blood vessel

The heat transfer within a perfused tissue in the presence of a vessel is considered when metabolic heat generation and blood perfusion in the tissue are temperature dependent. The Pennes bio-heat transfer equation is used for the perfused tissue and a lumped capacitance analysis is used for the convection in the vessel with a constant Nusselt number. Approximate analytical solutions are obtained for the case when the arterial temperature of the perfused blood in the bio-heat transfer equation remains constant and is equal to the inlet blood temperature in the vessel. The method of solution is based on the criterion that for any transport problem, the total error over the entire domain of interest which result from introducing an approximate solution into the governing equation must be kept to a minimum. It has been observed that variable metabolic heat generation and variable blood perfusion instead of constant metabolic heat generation and constant blood perfusion in the Pennes equation gives accurate description about the process of the heat transfer inside the tissue.