Temperature analysis of a biological tissue during hyperthermia therapy in the thermal non-equilibrium porous model

This study utilizes a porous model to predict the temperature response of a spherical tissue with a heating in its central region. This study considers the blood vessel size is between 8 and 140 μm as well as the velocity is between 0.7 and 34 mm/s, and then calculates the parameter values of porous model in different porosities. Meanwhile, the reasonable Nusselt number of a biological porous model should be less 1.0. By using a software package, the temperatures response of tissues with different vessel diameters, blood velocities, and porosities are calculated. Through a comparison with the results of the well-known Pennes bio-heat transfer equation, the numerical results calculated by the porous model coincide with those calculated by Pennes model when the blood vessel diameter, blood velocity, and porosity are small. Once the vessel diameter and blood velocity increase, the convection effect of blood becomes apparent due to its stronger ability of carrying heat away and induces the temperature distribution of the tissue moving toward the downstream. The results indicate that the Pennes model is suitable for analyzing a tissue when ɛ < 0.05, u ≤ 0.4 cm s−1, and d ≤ 30 μm. Moreover, the application of constant heat transfer coefficient of 170 W m−2 °C−1 on a porous model should be limited in the same condition above, which means a tissue with small vessel distribution, blood velocity, and porosity.