Generalized dual-phase lag bioheat equations based on nonequilibrium heat transfer in living biological tissues

Based on a nonequilibrium heat transfer model in the living tissue obtained by performing volume average to the local instantaneous energy equations for blood and tissues, the dual-phase lag bioheat equations with blood or tissue temperature as sole unknown temperature are obtained by eliminating the tissue or blood temperature from the nonequilibrium model. The present dual-phase model successfully overcame the drawbacks of the existing dual-phase lag bioheat equation obtained by simply modifying the classical Pennes bioheat equation. Under the dual-phase model developed in this work, the phase lag times are expressed in terms of the properties of blood and tissue and the interphase convective heat transfer coefficient and blood perfusion rate. The phase lag times for heat flux and temperature gradient for the living tissue are estimated using the available properties from the literature. It is found that the phase lag times for heat flux and temperature gradient for the living tissue are very close to each other.