Analytical Solution of Problems about the Radiative and Radiative–Conductive Stationary Heat Transfer in a Medium with an Arbitrary Dependence of the Scattering and Absorption on Frequency Boundary Conditions

Eugene Shamparov,Sergey Rode,Anatoly Bugrimov,Inna Zhagrina

doi:10.3390/en14196339

Eugene Shamparov, Sergey Rode + Show 2 more

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https://doi.org/10.3390/en14196339

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Journal: Energies	Publication Date: Oct 4, 2021
Citations: 1	License type: CC BY 4.0

Affiliation: A. N. Kosygin Moscow State Textile University

Abstract

We defined a method for the analytical solution of problems on stationary radiative and radiative–conductive heat transfer in a medium with an arbitrary frequency dependence of absorption and scattering near its boundary. We obtained formulas for the heat conductance of the remote surface and the thickness of the radiative–conductive relaxation of the medium. We determined characteristics of radiant heat transfer from the medium to free space such as the radiation spectrum, the radiation temperature and the medium outer boundary temperature. In addition, we solved the problem on the radiative–conductive heat transfer from one of two parallel surfaces to another with a medium between them.

Highlights

Stationary Heat Transfer in a Medium with an Arbitrary Dependence of the Scattering and Absorption on Frequency Boundary Conditions. This is theoretical work from the classical thermodynamics field, which touches on the fundamental issues of heat transfer in the medium
We considered stationary radiative and radiative–conductive heat transfer near the boundary of the scattering and absorbing medium
Based on the fundamental laws of physics, to solve the tasks set, we proved the possibility of using a one-dimensional approximation, which significantly simplifies obtained results

Summary

Introduction

This is theoretical work from the classical thermodynamics field, which touches on the fundamental issues of heat transfer in the medium. Based on the fundamental laws of physics, to solve the tasks set, we proved the possibility of using a one-dimensional approximation, which significantly simplifies obtained results. We used this approximation to find some more detailed solutions for several well-known problems of thermal physics [1,2,3,4] and several new and essential problems. Most of the problems of radiative–conductive heat transfer in a medium are solved based on “the radiation transfer equation” [4,5,6,7,8,9]. All the last seven mentioned works were performed using computer modelling

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