有温差两杆件接触的热传导问题

Contacting Heat Conduction between Two Bars with Different Temperatures

研究具有不同初始温度的杆件相互接触后产生的热传导问题 .首先用Laplace变换把一维瞬态热传导方程化为易于求解的常微分方程 ,然后应用留数定理作Laplace反变换 ,第一次得到两杆件接触后温度随时间变化的解析解 .考虑了接触热阻对杆件传热特性的影响 ,给出了对工程实际有应用价值的计算曲线 .

This paper considers the heat conduction between two bars with different initial temperatures when contacted.The equations for one-dimensional transient heat conduction are solved by Laplace transform techniques,and partial differential equations for this problem are turned into the ordinary differential equations whose solutions can be obtained easily.Then the inversion of Laplace transform is implemented by using Residue Theory.The analytical solutions of the temperatures in the bars varying with time are obtained firstly.The effects of the contact heat resistance on the conduct behavior of bars are also considered.The curves that are useful to the engineering practice are given at the end of the paper.