Transformation thermodynamics: cloaking and concentrating heat flux

Abstract

We adapt tools of transformation optics, governed by a (elliptic) wave equation, to thermodynamics, governed by the (parabolic) heat equation. We apply this new concept to an invibility cloak in order to thermally protect a region (a dead core) and to a concentrator to focus heat flux in a small region. We finally propose a multilayered cloak consisting of 20 homogeneous concentric layers with a piecewise constant isotropic diffusivity working over a finite time interval (homogenization approach).

Manipulating DC Currents with Bilayer Bulk Natural Materials

“…By using the same materials as dc magnetic cloak, the theoretical realization of a dc magnetic concentrator is also demonstrated [15] . On the basis of form invariance of the heat conduction equation, transformation thermodynamics is investigated to manipulate diffusive heat flow [16] ; through tailoring inhomogeneity and anisotropy of conductivities, transient thermal cloaking has been experimentally demonstrated [17] . In addition, manipulation of heat flux with only two kinds of materials (by utilizing a multilayered composite approach) has been reported [18,19] .…”

“…Besides making objects invisible [1][2][3][4] , many other novel devices are rapidly emerging, with a representative one being a concentrator [5,6] that can enhance the energy density of incident waves in a given area. In addition to manipulation of EM waves [1][2][3][4][5][6] , the theoretical tool of coordinate transformation has been extended to other areas of physics (such as acoustic waves [7] , matter waves [8] and elastic waves [9] ).Recently, many significant achievements have been made in the manipulation of magnetostatic field [10][11][12][13][14][15] , thermal conduction [16][17][18][19] , and electrostatic field [20][21][22][23][24] . In 2007, Wood and Pendry proposed a dc metamaterial that pointed the way towards the design of static magnetic cloak [10] , and the dc metamaterial was experimentally verified soon afterwards [11] .…”

“…Recently, many significant achievements have been made in the manipulation of magnetostatic field [10][11][12][13][14][15] , thermal conduction [16][17][18][19] , and electrostatic field [20][21][22][23][24] . In 2007, Wood and Pendry proposed a dc metamaterial that pointed the way towards the design of static magnetic cloak [10] , and the dc metamaterial was experimentally verified soon afterwards [11] .…”

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.…”

Collection of low-grade waste heat for enhanced energy harvesting

“…7,8 Heat flux focusing is one manner in which heat flow may be controlled, [2][3][4][5]9,10 and different effects, such as heat flux cloaking or reversal, have also been demonstrated theoretically 9,11 and experimentally for thick devices, 10 planar structures, 12,13 and three-dimensional objects. 14 Recently, thermoelectric devices have also been applied to facilitate the manipulation of heat flow for an active thermal cloak around arbitrarily shaped regions.…”