Purpose

This paper aims to develop an efficient numerical method for nonlinear transient heat conduction problems with local radiation boundary conditions and nonlinear heat sources.

Design/methodology/approach

Based on the physical characteristic of the transient heat conduction and the distribution characteristic of the Green’s function, a quasi-superposition principle is presented for the transient heat conduction problems with local nonlinearities. Then, an efficient method is developed, which indicates that the solution of the original nonlinear problem can be derived by solving some nonlinear problems with small structures and a linear problem with the original structure. These problems are independent of each other and can be solved simultaneously by the parallel computing technique.

Findings

Within a small time step, the nonlinear thermal loads can only induce significant temperature responses of the regions near the positions of the nonlinear thermal loads, whereas the temperature responses of the remaining regions are very close to zero. According to the above physical characteristic, the original nonlinear problem can be transformed into some nonlinear problems with small structures and a linear problem with the original structure.

Originality/value

An efficient and accurate numerical method is presented for transient heat conduction problems with local nonlinearities, and some numerical examples demonstrate the high efficiency and accuracy of the proposed method.

中文翻译：

---

基于准叠加原理的局部非线性瞬态热传导问题的有效求解方法

目的

本文旨在针对具有局部辐射边界条件和非线性热源的非线性瞬态热传导问题开发一种有效的数值方法。

设计/方法/途径

根据瞬态热传导的物理特性和格林函数的分布特征，提出了具有局部非线性的瞬态热传导问题的拟叠加原理。然后，开发了一种有效的方法，这表明可以通过求解一些具有小结构的非线性问题和具有原始结构的线性问题来导出原始非线性问题的解。这些问题相互独立，可以通过并行计算技术同时解决。

发现

在一个小的时间步内，非线性热载荷只能引起非线性热载荷位置附近区域的显着温度响应，而其余区域的温度响应非常接近于零。根据上述物理特性，可以将原来的非线性问题转化为一些具有小结构的非线性问题和一个具有原始结构的线性问题。

原创性/价值

针对具有局部非线性的瞬态热传导问题，提出了一种高效准确的数值方法，并通过一些数值算例证明了所提方法的高效性和准确性。