Numerical simulation for nanofluid extravasation from a vertical segment of a cylindrical vessel into the surrounding tissue at the microscale

Abstract

Heat transfer in the biological tissue during/after thermal therapy is dominated by the blood perfusion in the tissue. In this study we introduce a mathematical model to simulate the heat and nanoparticle transport in the tissue in the presence of a vertical vessel at the microscale. This model incorporates the effects of the nanoparticle Brownian motion, nanoparticle transport due to thermophoresis and heat transfer by radiation. We consider the nanoparticles and the interstitial fluid extravasate from the vessel into the surrounding tissue through a uniform distribution of pores at the vessel wall . We introduce similarity transformations to convert the governing equations into a system of ODEs, which we solve numerically using MATLAB. The model predictions show a significant influence of the vessel pore size on the heat transfer in the tissue. On the other hand, the nanoparticle transport across the tissue depends on the thermophoresis parameter. Furthermore, the heat removal from the tissue by the vessel strongly depends on the fluid extravasation velocity and the heat flux across the tissue outer boundary interface.