In present study based on porous media approach, heat transfer model of living tissue is developed using volume averaging method. In the first section, the energy equations of porous media are derived considering classic Fourier’s law for heat conduction. After volume averaging of these equations, the appeared integral terms are interpreted and simplified. Next some modification are suggested among which the correction of interfacial heat transfer coefficient between blood and tissue is most (more) important. In the second section, non-Fourier thermal behavior of porous media is investigated. At first, for dual-phase lag heat conduction the temperature and heat flux lag times between tissue and blood are estimated and because of their considerable differences with experiments on similar media a hyperbolic two-step model is developed. Then for magnetic nanoparticle hyperthermia process, the probability of thermal non-equilibrium between tissue and nanoparticles is studied which leads to development of a hyperbolic three-step model. More significant than above two models and for resolving the inconsistency of energy conservation in DPL conduction equation, an unprecedented (innovative) parabolic three-step model is established. To evaluated and assessment of these modifications a tissue-like vascular medium is introduced with some anatomical similarities and dissimilarities to real living tissue and its governing energy equations are derived. With the aim of numerical solution validation, three-equation local thermal non-equilibrium model in 1D and steady-state condition is solved analytically. Results show that the correction of averaging limits as well as the correction of interfacial heat transfer coefficient lead to prediction of lower temperature during interstitial hyperthermia treatment. Furthermore, the assumption of dual-phase-lag for tissue heat conduction involves some errors in energy conservation especially for large heat flux lag time. Although the parabolic three-step model eliminates this imperfection, the oscillation behavior of temperature in this model is questionable and needs more research and development. Key words: Living tissue, Porous media, Volume averaging, Dual-phase-lag, Hyperbolic two-step model, Parabolic three-step model.
