A transient transformation theory for the design of convective thermal metamaterials: Cloaks, concentrators, and rotators

Abstract

Convective thermal metamaterials have attracted particular attention since they can simultaneously manipulate the fluid flow and heat transfer. However, the current transformation theory for designing convective thermal metamaterials is only applied to steady state heat-transfer systems or porous media systems. Therefore, we prove the weak forms of convective heat-transfer governing equations with time-dependent terms for non-porous media flows possess form invariant under coordinate transformation and develop the transient transformation theory for creeping viscous potential flows. Based on this theory, three convective thermal metamaterials are designed under transient heat-transfer systems, including cloaks, concentrators, and rotators. The validity of the transient transformation theory is verified through quantitative numerical simulation, which validate the functionalities of the metamaterials in uniform, non-uniform, steady-state, and transient heat-transfer systems. These cloaks, concentrators, and rotators in the transient convective heat-transfer system ensure that the heat fluxes and flows are transported around the object, amplified at specified times in the center region, and are rotated to a specified angle, respectively, without disturbing the background. Especially, the convective thermal cloak is characterized by approximately drag-free characteristics in transient velocity fields. Furthermore, comparative results reveal that transient convective thermal metamaterials constitute an extension of their steady-state counterparts. The established transient theory of transformation heat transfer not only guides the design of more richly functional thermal metamaterials but also broadens their application scenarios.