# Transformation thermal convection: Cloaking, concentrating, and camouflage

## TL;DR

This paper develops the first general transformation theory for thermal convection, enabling control of heat transfer involving fluids by combining convection, conduction, and radiation, with applications in cloaking and camouflage.

## Contribution

It introduces a unified transformation framework for thermal convection using coupled equations, expanding transformation thermotics to fluid heat transfer.

## Key findings

- The theory predicts cloaking, concentrating, and camouflage effects in thermal convection.
- Finite element simulations confirm the theoretical predictions.
- The approach can be extended to mass diffusion and related fields.

## Abstract

Heat can generally transfer via thermal conduction, thermal radiation, and thermal convection. All the existing theories of transformation thermotics and optics can treat thermal conduction and thermal radiation, respectively. Unfortunately, thermal convection has never been touched in transformation theories due to the lack of a suitable theory, thus limiting applications associated with heat transfer through fluids (liquid or gas). Here, we develop, for the first time, a general theory of transformation thermal convection by considering the convection-diffusion equation, the Navier-Stokes equation, and the Darcy law. By introducing porous media, we get a set of coupled equations keeping their forms under coordinate transformation. As model applications, the theory helps to show the effects of cloaking, concentrating, and camouflage. Our finite element simulations confirm the theoretical findings. This work offers a general transformation theory for thermal convection, thus revealing some novel behaviors of thermal convection; it not only provides new hints on how to control heat transfer by combining thermal conduction, thermal radiation, and thermal convection, but also benefits the study of mass diffusion and other related fields that contain a set of equations and need to transform velocities at the same time.