A forth order finite differencce scheme for pennes´ bioheat transfer equation in a three? Dimensional triple-layered skin structure with multilevel bloood vessel

The Pennes´ bioheat transferr equation is a well-known heat conduction equation in which has been used for mathematical representation of the temperature distribution in the tissue because of its simplicity in which the heat transfer between the blood vessels and tissue is assumed to occur mainly across the capillaries where blood velocity is low. In this study, a forth-order compact finite difference scheme for solving Pennes´ bioheat transfer equation is applied to model temperature distribution in a three dimensional skin structure with multilevel blood vessel. Numerical experiments for thermal analysis of a skin composed of epidermis, dermis, and subcutaneous layers are conducted. Basically, blood vessels can be heat sink or heat source. As laser increases the temperature of tissue, blood vessels count as a heat sink. This term is modeled to be proportional to the difference between arterial supply temperature and the local tissue teemperature.