Microwave ablation (MWA) is a process that uses the heat from microwave energy to kill cancer cells without damaging the surrounding tissue. The effectiveness of this technique is related to the temperature achieved during the process, as well as the input microwave power and heating time of treatment. The modeling of heat transport within biological tissues are key issues and have been used extensively in medical thermal therapeutic applications, for instance MWA treatment for predicting the temperature distribution during process. In this work, the interstitial MWA in porous liver by single slot microwave coaxial antenna (MCA) is carried out. A mathematical model of MWA of the porous media approach is proposed, which uses transient energy equation coupled with electromagnetic wave propagation equation to describe the temperature distribution within porous liver under local thermal non-equilibrium (LTNE) assumption. The LTNE assumption is taken into account by solving the two energy equations for tissue and blood phases. The thermal model considers the tissue with its blood vessel distribution as a porous medium and employs both the interfacial convective heat transfer and blood perfusion rate terms in the transient energy equations for both tissue and blood phases. The coupled nonlinear set of these equations is solved using the axisymmetric finite element method (FEM). The influences of blood velocities, porosities, input microwave powers and positions within the porous liver (distance from a MCA) on the tissue and blood temperature distributions have been investigated. Furthermore, the tissue and blood temperatures of LTNE model are compared with the tissue temperature of Pennes model and Klinger model. Through an accuracy comparison, the temperature results of the one-energy equation under local thermal equilibrium (LTE) model and Pennes model are compared with the experimental results from previous work in order to show the validity of the numerical results. The results show that the LTE assumption is found to be suitable for predicting the temperature distribution when the blood velocities to be 0.4 cm/s and 2 cm/s in all porosities, whilst, in case of blood velocities to be 3 cm/s and 3.4 cm/s the LTNE assumption for heat transfer analysis needs to be utilized. In addition, the LTE model is suitable for predicting a distribution of temperature when the high porosity for this model. This investigation provides the essential aspects for a fundamental understanding of heat transport within biological tissues while experiencing an applied electromagnetic field such as applications in the thermal ablation. (C) 2013 Elsevier Ltd. All rights reserved.