继续上几篇文章的主题，我们将再次看一个具有固体中不稳定热传导的传热示例。
验证固体中的热传导（即共轭传热）；let us consider unsteady heat conduction in a solid.将FloEFD预测值与分析溶液（参考文献1）进行比较，we will solve a one-dimensional problem.
具有规定初始温度和热绝缘侧表面的热固体棒突然变冷（在恒定温度t下w=300 k）两端（见图1）。研究了棒内温度的演变过程。考虑了沿杆的恒定初始温度分布：tinitial(x) = 350 K.
图1。从初始温度冷却到杆端温度的热固体杆。
该问题由以下微分方程描述：
where ρ,Ck是固体物质密度，比热，and thermal conductivity,分别τ是时间，with the following boundary condition: T = T0
在x=0和x=l时。
In the general case,i.e.,在任意初始条件下，the problem has the following solution:
where coefficients Cn are determined from the initial conditions (see Reference 1).
初始温度分布均匀，according to the initial and boundary conditions,the problem has the following solution:
使用FloEFD进行时间相关分析，已经创建了一个表示尺寸为1 x 0.2 x 0.1 m的实心平行六面体的模型（见图2）。
Figure 2.The model used for calculating heat conduction in a solid rod with FloEFD (the computational domain envelopes the rod).
最大棒温的演变，用Flefd预测并与理论比较，如图3所示。FloEFD预测已在结果分辨率级别5下执行。可以看出它与理论曲线是一致的。
图3。Evolution of the maximum rod temperature,predicted with FloEFD and compared to theory
The temperature profiles along the rod at different time moments,predicted by FloEFD,与理论进行比较，如图4所示。我们可以看到，Floefd预测与理论剖面非常接近。The maximum prediction error not exceeding 2 K occurs at the ends of the rod and is likely caused by calculation error in the theoretical profile due to the truncation of Fourier series.
图4。沿棒的温度分布演变，predicted with FloEFD and compared to theory
If you would like a downloadable version of this validation please click the link below.
REFERENCE
1。Holman,J.P.传热。第八版，麦格劳希尔New York,1997.
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