Heat Conduction in Unsteady, Periodic, and Steady States in Laminated Composites

1980 ◽  
Vol 102 (4) ◽  
pp. 742-748 ◽  
Author(s):  
S. C. Huang ◽  
Y. P. Chang
Keyword(s):  
Heat Conduction ◽  
Analytical Solutions ◽  
Green's Functions ◽  
Green’S Functions ◽  
Laminated Composites ◽  
Steady States ◽  
Number Of Layers

This paper provides analytical solutions for heat conduction in composites of infinite, semi-infinite, and finite laminates in unsteady, periodic, and steady states. For compactness and generality, Green’s functions are used. The method of analysis applies for composites of any number of layers, but only solutions for two material composites are presented in this paper. Some calculated results of an example in steady and periodic states are shown and discussed.

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

2021 ◽  
Vol 2090 (1) ◽  
pp. 012150
Author(s):  
de Oliveira Eduardo Peixoto ◽  
Gilmar Guimaräes
Keyword(s):  
Heat Transfer ◽  
Green's Functions ◽  
Green’S Functions ◽  
Transfer Problem ◽  
Blood Perfusion ◽  
The Body ◽  
Mathematical Background ◽  
Number Of Layers ◽  
Pennes Equation ◽  
Transfer Problems

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.

scholarly journals Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions

2016 ◽  
Vol 2016 ◽  
pp. 1-22
Author(s):  
Inês Simões ◽  
António Tadeu ◽  
Nuno Simões
Keyword(s):  
Heat Conduction ◽  
Frequency Domain ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Integral Transforms ◽  
Heat Diffusion ◽  
One Dimensional ◽  
The Time Domain ◽  
Point Line

This paper presents a set of fully analytical solutions, together with explicit expressions, in the time and frequency domain for the heat conduction response of homogeneous unbounded and of bounded rectangular spaces (three-, two-, and one-dimensional spaces) subjected to point, line, and plane heat diffusion sources. Particular attention is given to the case of spatially sinusoidal, harmonic line sources. In the literature this problem is often referred to as the two-and-a-half-dimensionalfundamental solutionor 2.5D Green’s functions. These equations are very useful for formulating three-dimensional thermodynamic problems by means of integral transforms methods and/or boundary elements. The image source technique is used to build up different geometries such as half-spaces, corners, rectangular pipes, and parallelepiped boxes. The final expressions are verified here by applying the equations to problems for which the solution is known analytically in the time domain.

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