Arbitrarily-shaped convective thermal cloaks based on multiphysical coordinate transformation theories

Convective thermal cloaks, capable of simultaneously manipulating fluid flow and heat transfer, represent a cutting-edge direction in multi-physics metamaterial research. However, existing studies have been predominantly confined to regular geometric configurations, limiting their applicability in complex engineering environments. To address this, we propose multiphysical coordinate transformation theories for convective thermal cloaks adaptable to arbitrarily-shaped obstacles, facilitating the free manipulation of coupled thermo-hydrodynamic fields. First, based on transformation heat-transfer theory, we derive the analytical transformed dynamic viscosity and thermal conductivity by coupling the parametric equations of the obstacle and cloak geometries. Second, to resolve the physical constraint of negative viscosity components inherent to complex geometric transformations, we introduce an equivalent design scheme based on transformed volumetric forces. This approach effectively converts anisotropic viscosity effects into spatially distributed volumetric forces, thereby circumventing the realizability issues caused by negative viscosity. Numerical simulations demonstrate that our arbitrarily-shaped cloaks effectively manipulate mass, momentum, and energy transport in both uniform and non-uniform thermal convection systems. The designs maintain undisturbed velocity, pressure, and temperature fields external to the cloak, achieving simultaneous hydrodynamic and thermal cloaking. Comparative analysis reveals that the transformed volumetric force approach yields robust cloaking performance comparable to the transformed viscosity approach while offering superior material realizability. This work overcomes the geometric and physical limitations of conventional transformation methods, establishing a foundation for fabricating multi-physics metamaterials with complex geometries. • Theory for arbitrarily-shaped convective thermal cloaks is developed. • Volumetric force scheme overcomes the negative viscosity limitation. • Robust cloaking performance is achieved in non-uniform flow systems. • Volumetric force method yields high-fidelity multi-physical cloaking. • A framework for multi-physics metamaterials in irregular scenarios.