Solving bio-heat transfer multi-layer equation using Green’s Functions method

Abstract

An analytical method using Green’s Functions for obtaining solutions in bio-heat transfer problems, modeled by Pennes’ Equation, is presented. Mathematical background on how treating Pennes’ equation and its μ2T term is shown, and two contributions to the classical numbering system in heat conduction are proposed: inclusion of terms to specify the presence of the fin term, μ2T, and identify the biological heat transfer problem. The presentation of the solution is made for a general multi-layer domain, deriving and showing general approaches and Green’s Functions for such n number of layers. Numerical examples are presented to simplify human skin as a two-layer domain: dermis and epidermis, accounting metabolism as a heat source, and blood perfusion only at the dermis. Time-independent summations in the series-solution are written in closed forms, leading to better convergence along the boundaries. Details on obtaining the two-layer solution and its eigenvalues are presented for boundary conditions of prescribed temperature inside the body and convection at the surface, such as its intrinsic verification.