A Reverse Thermal Cloak Design Method Based on Inverse Problem Theory

Abstract

A reverse thermal cloak design method is developed based on inverse problem theory. The design of thermal conductivity distribution within a cloak can be regarded as the density-based topology optimization with that penalization parameter equals to 1. The relative density is explored using conjugate gradient method with an adjoint equation (CGMAE). A prescribed objective function is used to evaluate the design result, and the function is no larger than 6.41×10-6. The maximum deviation between background temperature with and without cloak position is no larger than 0.9% for background with uniform gradient and no larger than 5% for background with non-uniform gradient. The dimension of a cloak can also be designed in case of known material thermal conductivity to avoid complex material synthesis process. Compared with coordinate transformation, the reverse design method is able to remove anisotropy of thermal conductivity and is appropriate for design of irregularly shaped cloak. It is easy to implement programming for proposed method and can boost the flexibility of cloak design. Thus, the proposed method offers a practicable scheme for thermal cloak design to control heat conduction at will.

Interface Engineered Microcellular Magnetic Conductive Polyurethane Nanocomposite Foams for Electromagnetic Interference Shielding

“…With extensive deployment and development of electronic equipment and communication devices, serious electromagnetic interference (EMI) interrupts the functions of equipment and affects the human organs [1][2][3][4][5][6]. Recently, more efforts have been made to seek for novel lightweight and high-performance EMI shielding materials [7][8][9][10][11][12].…”

Passive Ultra‐Conductive Thermal Metamaterials

“…The 3D channel is unfolded to a 2D pattern. The profile of the unfolded channel is optimized by a semi-analytical hybrid approach including boundary element method [40][41] and topology optimization [15,42] to meet the demand of boundary heat flux q f = Φν (Note S4, Supporting Information).…”

“…[2][3] On the other hand, the emerging metamaterials [4][5][6][7][8][9][10][11][12] based on digital conductivity distributions also reveal significant advances in guiding heat fluxes in elaborate formations. [13][14][15][16][17][18][19][20][21][22][23][24] The recent discoveries of advective metamaterials further enrich such a regime with conductive and inhomogeneous tunability. [25][26][27] The use of extra energy payload is taken for granted as a necessary means to realize and the background, as illustrated in Figure 1a.…”

Designing nonlinear thermal devices and metamaterials under the Fourier law: A route to nonlinear thermotics

“…Actually, transformation theory has an intrinsic relationship with the famous inverse problem (Calderón's problem) to hide an object in electrical impedance tomography [266][267][268]. We haven't covered numerical optimization in this review, the general and powerful tool in inverse problems, which have been used in inverse design of linear thermal metamaterials and other functional devices [269][270][271][272][273][274][275]. Some works have also studied multi-physical [276,277] cases including nonlinear thermo-mechanical metadevices [276].…”

“…Some works have also studied multi-physical [276,277] cases including nonlinear thermo-mechanical metadevices [276]. Since it's usually not easy to do analytical calculations in nonlinear equations and the transformation theory might have restrictions on the forms of equations and target solutions, numerical optimization based on various algorithms, whether they're gradient-based [270,[274][275][276] or black boxes [271][272][273]277], can have potential applications to more flexible designs of nonlinear thermal elements.…”