Open AccessSolving bio-heat transfer multi-layer equation using Green’s Functions method
Author(s) -
de Oliveira Eduardo Peixoto,
Gilmar Guimarães
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2090/1/012150
Subject(s) - heat transfer , thermal conduction , eigenvalues and eigenvectors , convergence (economics) , boundary value problem , mathematics , mathematical analysis , materials science , physics , mechanics , thermodynamics , quantum mechanics , economics , economic growth
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 μ 2 T 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, μ 2 T, 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.