小孔洞群导热的估算及等效导热的表征
Estimation of the heat conducted by a cluster of small cavities and characterization of the equivalent heat conduction
摘要：
我们估计了由许多小空腔组成的一组空腔所传导的热量。我们表明，占主导地位的热量是一个总和，在腔的数量，每个腔相互作用后产生的热量。这种相互作用是通过密度可计算的解决方案的一个封闭的，可逆的，系统的时域积分方程的第二种。作为这些扩展的应用程序，我们推导出有效的热传导率产生近似相同的热量的集群的空腔，分布在一个三维有界域，明确的误差估计的集群。在分析层次，我们使用时域积分方程。要做到这一点，我们有两个选择。首先，我们可以通过将热势减少到与拉普拉斯算子相关的热势来支持空间变量（避免拉普拉斯变换）。其次，我们可以通过将表示简化为Abel积分算子来支持时间变量。由于所研究的模型具有与时间无关的参数，我们在这里遵循第一种方法。
英文摘要：
We estimate the heat conducted by a cluster of many small cavities. We show that the dominating heat is a sum, over the number of the cavities, of the heats generated by each cavity after interacting with each other. This interaction is described through densities computable as solutions of a close, and invertible, system of time domain integral equations of a second kind. As an application of these expansions, we derive the effective heat conductivity which generates approximately the same heat as the cluster of cavities, distributed in a 3D bounded domain, with explicit error estimates in terms of that cluster. At the analysis level, we use time domain integral equations. Doing that, we have two choices. First, we can favor the space variable by reducing the heat potentials to the ones related to the Laplace operator (avoiding Laplace transform). Second, we can favor the time variable by reducing the representation to the Abel integral operator. As the model under investigation has time-independent parameters, we follow here the first approach.
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