Anisotropic conductivity rotates heat fluxes in transient regimes

Abstract

We present a finite element analysis of a diffusion problem involving a coated cylinder enabling the rotation of heat fluxes. The coating consists of a heterogeneous anisotropic conductivity deduced from a geometric transformation in the time dependent heat equation. In contrast to thermal cloak and concentrator, specific heat and density are not affected by the transformation in the rotator. Therein, thermal flux diffuses from region of lower temperature to higher temperature, leading to an apparent negative conductivity analogous to what was observed in transformed thermostatics. When a conducting object lies inside the rotator, it appears as if rotated by certain angle to an external observer, what can be seen as a thermal illusion. A structured rotator is finally proposed inspired by earlier designs of thermostatic and microwave rotators.

A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity

“…[1][2][3][4][5][6][7][8] The TO technique has also led to the creation of many other important EM devices with functionalities previously deemed impossible or unconceivable. [9][10][11] In general, this coordinate operation can be applied to different partial differential equations governing the behaviors of other physical phenomena such as thermal flux, [12][13][14][15][16][17][18][19][20][21][22][23] acoustic wave, [24][25][26][27] and matter or quantum [28][29][30] waves, demonstrating important scientific and application potentials.…”

“…35 This need requires addressing the general time-dependent heat diffusion equation, that is, rc Á qu/qt ¼ r Á (kru), where r and c are the density and the specific heat capacity of the medium, respectively. 15,16,18,22,23 This equation describes the heat diffusion in a solid out of the source region. Applying a coordinate mapping from the virtual (x, y) into the physical (x 0 , y 0 ) spaces, Guenneau et al 15 first derived the transformed medium that equally satisfied the heat equation with the new material parameters r 0 c 0 ¼ rc/det(J) and j 0 ¼ JkJ T / det(J), where J is the Jacobean matrix expressed by q(x 0 , y 0 )/q(x, y).…”

A concept of heat dissipation coefficient for thermal cloak based on entropy generation approach

“…[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] A 2D micro-structured thermal cloak has been fabricated and experimentally demonstrated. 15 The thermal conductivity in the distorted coordinates [16][17][18][19][20] and the mechanism of predefined heat flux paths are further researched. [21][22][23][24] Considering the difficulty in fabricating a 3D cloak, the study of 3D thermal cloaks has a late start.…”

Converting the patterns of local heat flux via thermal illusion device

“…This cloaking originates from the fact that the thermal conduction equation remains form-invariant under coordinate transformation, and it helps to pave a new way to steer heat flux. As a result, much attention has been paid by theorists and experimentalists, [2][3][4][5][6][7][8] and there come out a lot of thermal metamaterials with novel thermal properties beyond cloaking, 6,10-13 such as concentrators (which are used to enhance the temperature gradient in a specific region), 3,14 inverters (which allow heat to apparently flow from a colder to a warmer region without violating the second law of thermodynamics), 1,15 rotators (which can rotate the flow of heat as if the heat comes from a different direction), 3,15 and camouflage. 16 Controlling the flow of heat enlightens us to design an illusion device for thermal conduction.…”