Abstract An analytical model using Green's functions for partial external heating of a pipe is developed, which results in an exact mathematical solution for the radial and axial temperature distribution in the pipe wall. Partial heating consists of a constant heat flux function imposed over a small section of the exterior of a pipe and for a limited time duration. The solution comprises steady-state and transient parts, and an algebraic identity is used to decrease the number of summation terms in the slowly-converging steady-state part. Intrinsic verification principles are used to verify the solution. As an example application, this transient solution is applied toward the development of a simple, noninvasive method for in-field measurement of the flow rate in pipes. To simulate this application, a pulse of energy is imposed to the wall of the pipe, and the developed mathematical solution is used to find the flow rate of the fluid inside the pipe. An optimal experiment is designed to find the best measurement location and time.

中文翻译：

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用于测量流体流量的管道外部局部加热的分析解决方案

摘要 建立了使用格林函数对管道局部外部加热的分析模型，从而得到了管壁径向和轴向温度分布的精确数学解。部分加热包括在管道外部的一小部分和有限的持续时间内施加恒定的热通量函数。该解包括稳态部分和瞬态部分，并使用代数恒等式来减少缓慢收敛稳态部分中求和项的数量。内在验证原则用于验证解决方案。作为示例应用，这种瞬态解决方案用于开发一种简单的非侵入式管道流量现场测量方法。为了模拟这个应用程序，将能量脉冲施加到管道壁上，并使用已开发的数学解决方案来计算管道内流体的流速。最佳实验旨在找到最佳测量位置和时间。