[Paper Review] Manipulating local heat flux with different patterns

N. Zhu, Xiangying Shen+1 more|arXiv (Cornell University)|Nov 2, 2014

Advanced Materials and Mechanics24 references21 citations

TL;DR

This paper proposes a thermal illusion device using coordinate transformation to manipulate local heat flux patterns, converting parallel flux into non-parallel patterns and vice versa, while preserving the external heat flux pattern as if the device were absent. The device uses anisotropic thermal conductivities derived from transformation theory, enabling control of heat flow without negative thermal conductivities, validated via finite-element simulations.

ABSTRACT

Since the thermal conduction equation has form invariance under coordinate transformation, one can design thermal metamaterials with novel functions by tailoring materials' thermal conductivities. In this work, we establish a different transformation theory, and propose a layered device with anisotropic thermal conductivities. The device is able to convert heat flux from parallel patterns into non-parallel patterns and vice versa. In the mean time, the heat flux pattern outside the device keeps undisturbed as if this device is absent. We perform finite-element simulations to confirm the converting behavior. This work paves a different way to manipulate the flow of heat at will.

Motivation & Objective

• To develop a thermal metamaterial that manipulates local heat flux patterns without altering the external thermal field.
• To overcome the limitation of requiring negative thermal conductivity in prior thermal illusion devices.
• To enable the conversion of parallel heat flux into non-parallel patterns and vice versa using only positive conductivity tensors.
• To provide a practical design for thermal illusion devices compatible with effective medium theory and fabrication.

Proposed method

• Utilizes coordinate transformation theory to map spatial regions such that heat flux patterns are altered within the device.
• Derives transformed thermal conductivity tensors using the Jacobian matrix and determinant, ensuring form invariance of the thermal conduction equation.
• Applies the transformation to two distinct geometries: a triangular region (Transformation 1) and a circular region (Transformation 2) with a central ring.
• Designs anisotropic thermal conductivities in layered regions (Regions I and II, or I and III) that enable flux convergence or divergence.
• Employs finite-element simulations in COMSOL Multiphysics to validate the behavior of the device under steady-state conditions.
• Uses diagonalized conductivity tensors to simplify implementation via effective medium approximations.

Experimental results

Research questions

• RQ1 Can a thermal device convert parallel heat flux into a non-parallel pattern while leaving the external field undisturbed?
• RQ2 Is it possible to achieve such flux manipulation using only positive thermal conductivity tensors, avoiding negative conductivity materials?
• RQ3 How can coordinate transformation be adapted to create a thermal illusion device that mimics the external thermal signature of a non-existent object?
• RQ4 What are the specific forms of the anisotropic thermal conductivity tensors required for such flux pattern conversion?
• RQ5 Can the device function effectively even with a small central heat source, such as a tiny ring?

Key findings

• Transformation 1 successfully converts parallel heat flux into converging flux toward the vertex of a triangular region, with no distortion in the external field.
• The device maintains the same temperature distribution and flux pattern outside its boundaries as in the original, undisturbed system.
• Transformation 2 converts a divergent flux pattern from a central ring into a parallel flux pattern in a square region, preserving the external divergent pattern.
• The derived thermal conductivity tensors for Regions I and II (in Transformation 1) and Regions I and III (in Transformation 2) are symmetric and diagonalizable, enabling practical implementation.
• Finite-element simulations confirm that the device operates as intended, with flux patterns inside matching the designed transformation and external patterns unchanged.
• The method avoids the need for negative thermal conductivity, making it thermodynamically feasible and compatible with real materials.