This paper presents a statement of the works performed in L.E.M.T.A by the members of the thermal and mechanical heterogeneous media research group during the last six years concerning the solving of coupled conductiv...This paper presents a statement of the works performed in L.E.M.T.A by the members of the thermal and mechanical heterogeneous media research group during the last six years concerning the solving of coupled conductive and radiative heat transfers within a multilayer and semi-transparent“wall”.Out of the authors,this paper allows to take inspiration from the works of D.Maillet,M.Lazard and V.Manias[19,20,21].The aim of these works is to represent in a macroscopic way,with the minimum number of thermophysical parameters,the heat transfers in a plane system composed of semi-transparent media.The approach we propose is semi-analytic(Kernel substitution technique,Laplace transformation)and allow to obtain in the Laplace domain an analytical solution that can be easily used.This method can be applied in two main scopes of applications:the estimation of thermophysical properties(phononic conductivity,optical thickness,Planck number for instance)of semi-transparent materials(glasses,crystals,glass wool,semi-conductors,synthetic diamonds,vitroceramics and so on)and the modelling of processes with semitransparent walls(for instance bottles forming,flat glass production,drying of paper).The method will be first presented and validated and two examples of applications will be then given.This method can be applied to semitransparent walls that emit,absorb and scatter the radiant energy(participating medium).It appears from the principle of a Kernel substitution technique applied to the radiative flux expression and initially introduced by Lick[1]that allows to change the character of the governing heat equation from the integro-differential form to a purely differential one.In the case of limiting cases of purely scattering and purely absorbing media,the solution of the radiative transfer equation is exact.In the general case,we make a two-flux approximation.In all cases,we assume a linear transfer and use the Laplace transform.The method can be applied to grey or grey by bands media,with isotropic or anisotropic scattering.The advantage of the method is fast computational times for good precision.展开更多
A very simple model based on the Quadrupole method was used in thetheoretical analysis of thermal diffusivity of composite materials of Cu-PVC, PVC-Cu-PVC, andCu-PVC-Cu. The use of MATLAB software with a return to rea...A very simple model based on the Quadrupole method was used in thetheoretical analysis of thermal diffusivity of composite materials of Cu-PVC, PVC-Cu-PVC, andCu-PVC-Cu. The use of MATLAB software with a return to real space using the Stehfest algorithm makesthe time of calculation very short. The thermal responses on the rear face of each consideredsample, which determine the thermal diffusivity were represented. A mathematical demonstration whichconfirmed the results was given. Thermal diffusivity determined from the rear face thermalresponses were compared with the results of the thermal diffusivity calculated by considering thecomposite materials to be homogeneous, and a discussion on the two kinds of results was provided.展开更多
文摘This paper presents a statement of the works performed in L.E.M.T.A by the members of the thermal and mechanical heterogeneous media research group during the last six years concerning the solving of coupled conductive and radiative heat transfers within a multilayer and semi-transparent“wall”.Out of the authors,this paper allows to take inspiration from the works of D.Maillet,M.Lazard and V.Manias[19,20,21].The aim of these works is to represent in a macroscopic way,with the minimum number of thermophysical parameters,the heat transfers in a plane system composed of semi-transparent media.The approach we propose is semi-analytic(Kernel substitution technique,Laplace transformation)and allow to obtain in the Laplace domain an analytical solution that can be easily used.This method can be applied in two main scopes of applications:the estimation of thermophysical properties(phononic conductivity,optical thickness,Planck number for instance)of semi-transparent materials(glasses,crystals,glass wool,semi-conductors,synthetic diamonds,vitroceramics and so on)and the modelling of processes with semitransparent walls(for instance bottles forming,flat glass production,drying of paper).The method will be first presented and validated and two examples of applications will be then given.This method can be applied to semitransparent walls that emit,absorb and scatter the radiant energy(participating medium).It appears from the principle of a Kernel substitution technique applied to the radiative flux expression and initially introduced by Lick[1]that allows to change the character of the governing heat equation from the integro-differential form to a purely differential one.In the case of limiting cases of purely scattering and purely absorbing media,the solution of the radiative transfer equation is exact.In the general case,we make a two-flux approximation.In all cases,we assume a linear transfer and use the Laplace transform.The method can be applied to grey or grey by bands media,with isotropic or anisotropic scattering.The advantage of the method is fast computational times for good precision.
基金The research work is financially supported by National Natural Science Foundation of China (No.50276003).
文摘A very simple model based on the Quadrupole method was used in thetheoretical analysis of thermal diffusivity of composite materials of Cu-PVC, PVC-Cu-PVC, andCu-PVC-Cu. The use of MATLAB software with a return to real space using the Stehfest algorithm makesthe time of calculation very short. The thermal responses on the rear face of each consideredsample, which determine the thermal diffusivity were represented. A mathematical demonstration whichconfirmed the results was given. Thermal diffusivity determined from the rear face thermalresponses were compared with the results of the thermal diffusivity calculated by considering thecomposite materials to be homogeneous, and a discussion on the two kinds of results was provided.
