论文标题
当规定了相对空间变化时，从单点温度病史中推论通量
Deducing Flux from Single Point Temperature History when Relative Spatial Variation of Flux is Prescribed
论文作者
论文摘要
有时通过在瞬态实验中记录表面温度病史并借助合适的模型来解释对流和辐射环境中的表面热传递，并通过在基板内进行瞬态传导来解释该表面温度。经常采用半无限的一维模型，并提供了几种用于将该模型应用于表面温度数据的发达的技术。但是，当整个表面上存在热通量的空间变化时，半无限的一维方法的应用可能并不总是合理的近似值。在本文中，我们介绍了一种处理测得的表面温度病史的方法，该方法比底物横向传导很重要并且已知通量的相对空间分布是先验的，该方法比半无限的一维近似更准确。这种新方法使用所谓的\ textit {neumann heat kernel}，该{neumann heat necer}在最初沉积在指定点的单位能量上的绝缘域上的温度演变。通过将这种Neumann热核与域表面上的通量空间变化相结合，形成了有用的脉冲响应函数。 Neumann热核是为实心盒，圆柱和球体构建的。通过将热核结果应用于球形的球体使用半球鼻探针分析对流实验，我们演示了理论结果如何增强对瞬态表面温度测量值的实际分析。当前的方法优于以前的方法，依靠半经验近似值，因为使用热核分析以更大的忠诚度对底物内的多维热传导进行了建模。
Surface heat transfer in convective and radiative environments is sometimes measured by recording the surface temperature history in a transient experiment and interpreting this surface temperature with the aid of a suitable model for transient conduction within the substrate. The semi-infinite one-dimensional model is often adopted, and several well-developed techniques for application of this model to surface temperature data are available. However, when a spatial variation of heat flux exists across the surface, the application of the semi-infinite one-dimensional approach may not always be a reasonable approximation. In this paper we introduce a method for treatment of the measured surface temperature history that is more accurate than the semi-infinite one-dimensional approximation when substrate lateral conduction is significant and the relative spatial distribution of the flux is known a priori. This new method uses the so-called \textit{Neumann heat kernel}, which evolves a temperature over an insulated domain with unit energy initially deposited at a specified point. A useful impulse response function is formed by integrating this Neumann heat kernel against the spatial variation of flux over the surface of the domain. Neumann heat kernels are constructed for the solid box, cylinder, and sphere. By applying the heat kernel result for the sphere to the analysis of a convective experiment using hemispherical-nosed probes, we demonstrate how the theoretical results enhance the practical analysis of transient surface temperature measurements. The current approach is superior to former methods relying on semi-empirical approximations because the multi-dimensional heat conduction within the substrate is modelled with greater fidelity using the heat kernel analysis.
