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Thermal ablation of a tumour in the liver with Radio Frequency energy can be accomplished by using a probe inserted into the tissue under the guidance of medical imaging. The extent of ablation can be significantly affected by heat loss due to the high blood perfusion in the liver, especially when the tumour is located close to large vessels. A mathematical model is thus presented here to investigate the heat sinking effects of large vessels, combining a 3D two-equation coupled bio-heat model and a 1D model of convective heat transport across the blood vessel surface. The model simulation is able to recover the experimentally observed different intrahepatic cooling on thermal ablation zones: hepatic veins showed a focal indentation whereas portal veins showed broad flattening of the ablation zones. Moreover, this study also illustrates that this shape derivation can largely be attributed to the temperature variations between the microvascular branches of portal vein as compared with hepatic vein. In contrast, different amount of surface heat convection on the vessel wall between these two types of veins, however, has a minor effect.