Abstract Conduction and convection are two fundamental methods of heat transfer, which are generally considered independent. We manage to unify them by coining a complex thermal conductivity whose real and imaginary parts are related to conduction and convection, respectively. Accordingly, the conduction-convection process with thermal waves is dominated by the complex conduction equation, thus called complex thermotics herein. To go further, we establish the theory of transformation complex thermotics by proving the form-invariance of the complex conduction equation and deriving the transformation principle of complex thermal conductivities. As model applications, we design three devices with functions of cloaking, concentrating, and rotating thermal waves. Moreover, experimental demonstration is suggested with a porous medium whose effective complex thermal conductivity is calculated with the method of weighted average. These findings could broaden the fundamental knowledge of conduction and convection, and have potential applications in designing thermal metamaterials.

中文翻译：

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用转换复合热学控制热波

摘要 传导和对流是两种基本的传热方式，通常被认为是相互独立的。我们设法通过创造一个复杂的热导率来统一它们，其实部和虚部分别与传导和对流相关。因此，具有热波的传导-对流过程以复传导方程为主，因此在本文中称为复热学。为了更进一步，我们通过证明复传导方程的形式不变性和推导复热导率的变换原理，建立了变换复热学理论。作为模型应用，我们设计了三种具有隐身、聚光和旋转热波功能的装置。而且，建议用多孔介质进行实验论证，其有效复热导率是用加权平均法计算的。这些发现可以拓宽传导和对流的基础知识，并在设计热超材料方面具有潜在的应用价值。