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本文提出了一种求解辐射-导热耦合换热问题的边界单元算法(BEM),该方法将两种传热方式通过辐射热源耦合起来.首先,采用BEM对辐射传热方程、辐射热源方程和含有辐射热源的热传导方程进行离散;其次,利用辐射传热方程消除辐射热源方程中的辐射热流项;然后,根据Stefan-Boltzmann定律形成含有温度四次方以及热流密度表示的非线性代数方程组.出现在所有积分方程中的域积分由径向积分法转换成边界积分,形成了对于参与性介质问题也只需在边界上划分单元的纯边界元算法.最后,用Newton-Raphson迭代法对方程组进行求解.提供的数值算例将表明本文所介绍方法的正确性与有效性.
In this paper, a Boundary Element Algorithm (BEM) is proposed to solve the heat transfer problem of a radiative-thermal coupling, which couples two heat transfer modes through a radiant heat source.Firstly, BEM is used to calculate the radiative heat transfer equation, radiant heat source equation, Secondly, the radiation heat flow equation in the radiative heat source equation is eliminated by using the radiative heat transfer equation. Then, a nonlinear algebraic equation containing the fourth-order temperature and the heat flux density is formed according to the Stefan-Boltzmann law. The domain integrals in all integral equations are converted into boundary integrals by radial integral method, which forms the pure boundary element algorithm which only needs to divide the elements on the boundary for the participative medium problem.Finally, using the Newton-Raphson iterative method, The numerical example provided will show the correctness and validity of the method presented in this paper.