In this paper, a new single interface integral equation method is established for solving non-linear multi-medium heat transfer problems with temperature- dependent thermal conductivity. At first, the boundary-domain integral equation for nonlinear heat transfer in single medium is established based on the fundamental solution of Laplace equation. Then, based on the variation feature of the material properties, a new single integral equation for material nonlinear multi-medium is established according to the degeneration rule from a domain integral to an interface integral. Next, the final system equations are solved by Newton-Raphson iterative method after the discretization. Comparing with conventional multi-domain boundary element method, the presented method is more efficient in computational time, data preparing and program coding. Three numerical examples are given to demonstrate the correctness and robustness of the method presented in the paper.

在本文中，建立了一种新的单界面积分方程方法，用于解决与温度相关的导热系数的非线性多介质传热问题。首先，基于拉普拉斯方程的基本解，建立了单介质非线性传热的边界域积分方程。然后，根据材料特性的变化特征，根据从域积分到界面积分的退化规律，建立了一个新的材料非线性多元单积分方程。接下来，离散化之后，通过牛顿-拉夫森迭代法求解最终的系统方程。与传统的多域边界元方法相比，该方法在计算时间，数据准备和程序编码方面效率更高。