Application of the Control Volume Method using the Voronoi polygons for numerical modeling of bio-heat transfer processes

In the paper, the problem concerning the numerical modeling of thermal processes in the domain of a biological tissue being in thermal contact with the environment is discussed. The changing ambient temperature causes that the non-steady heat transfer process is considered. The cross-section of the forearm (2D problem) is treated as a non-homogeneous domain in which the sub-domains of skin tissue, fat, muscle and bone are distinguished. From the mathematical point of view, the boundary-initial problem described by the system of energy equations (the Pennes equations), boundary conditions on the external surface of the system, boundary conditions on the surfaces limiting the successive sub-domains and the initial condition is analyzed. At the stage of numerical computations, the Control Volume Method using the Voronoi polygons is applied. In the final part of the paper, examples of computations are shown.