傅里叶热传导方程和牛顿冷却定律在流体热学研究中的数学模型应用

摘要

Pillar fluid’s conduction of heat is of value in researching on the natural fluid.The paper is basic on a ideal model of the moving hot water in a bathtub.By using Fourier Heat-Conduction Equation and the Method of fitting, and by using the Newton’s Cooling Law to optimize the process of heat-conduction, the paper transmit the three-dimensional problem into one-dimensional problem and try to discuss the process of the heat distribution and temperature balance in this model,in order to provide some mentality to the later research in fluid thermal analysis.%柱形流体热传导过程对于研究自然界热流体有着重要的实际意义。本文以浴缸中流动的热水为模型。通过利用傅里叶—维热传导方程和插值拟合的手段，辅以利用牛顿冷却定律对流体边缘热传导过程优化，将三维问题一维化，探讨其热量分布和温度平衡的过程，从而为实际流体热学的研究提供一些方法上的思路。