中文摘要：

为了使热成为传导方程，在学习下面表达物理现象的本质，无尺寸的因素被介绍，短暂的热传导方程和它的边界条件被转变到无尺寸的形式。然后，在一个维的双层的短暂的热传导问题的一个理论答案模型合成媒介被造利用自然特徵函数扩大方法。以便验证模型，的有效性上述理论溶液的结果与有限元素方法的那些相比。由二个方法的结果在一个好协议。当时，由二个方法的最大的错误出现(是 nondimensional 时间) 在 =1 的边界附近等于 0.1 (是 nondimensional 空间坐标) 并且 =4。作为增加，错误逐渐地减少，并且什么时候两个答案的结果几乎不有的 =5 有变化的变化并列。

英文摘要：

To make heat conduction equation embody the essence of physical phenomenon under study, dimensionless factors were introduced and the transient heat conduction equation and its boundary conditions were transformed to dimensionless forms. Then, a theoretical solution model of transient heat conduction problem in one-dimensional double-layer composite medium was built utilizing the natural eigenfunction expansion method. In order to verify the validity of the model, the results of the above theoretical solution were compared with those of finite element method. The results by the two methods are in a good agreement. The maximum errors by the two methods appear when τ（τ is nondimensional time） equals 0.1 near the boundaries of ζ =1 （ζ is nondimensional space coordinate） and ζ =4. As τ increases, the error decreases gradually, and when τ =5 the results of both solutions have almost no change with the variation of coordinate 4.