矩形直肋二维稳态导热的解析解及其分析

Analysis on two-dimensional steady-state heat conduction in rectangular fins

为了准确地给出将矩形直肋二维导热问题简化成一维问题的条件,利用分离变量法求解矩形直肋二维稳态导热模型,包括端部散热和绝热两种情况。比较解析解的两种不同的表达式,发现它们基本上是等价的。研究在各种无量纲参数条件下直肋的温度分布和热流,将二维模型所得的结果同一维模型的结果进行了比较,分析了各个无量纲参数对二维解与一维解之间的偏差的影响。在此基础之上,明确了影响一维简化假设成立的两个无量纲参数———H/δ,Bi的具体取值范围。

In order to set up criteria for appropriate one-dimensional approximation of the steady-state heat conduction in rectangular pins, two analytical solutions of the two-dimensional steady-state conduction in rec(tangular) pins were obtained by the variable separation method, one was for insulation boundary condition at the end of rectangular fins, another was for the third kind boundary condition. By comparison between analytical solutions obtained from the two kinds of boundary conditions, we find they are basically equivalent. This paper studies the temperature distribution and heat flow of the fins under conditions of different dimensionless para(meters.) Criteria are set up for appropriate one-dimensional approximation of the heat conduction in rec(tangular) pins by comparing the results obtained from one- and two- dimensional models.