Spatial Transformation Based Metamaterial And Thermal Field Manipulation

In recent years,the theory of transformation optics and related metamaterial have attracted great research interests in various fields.Metamaterial is a class of artificial composite materials/structures,which is equipped with extraordinary properties that are not available in conventional materials.The origin of metamaterial is the anomalous medium whose permittivity and permeability are both negative.Owing to the proposition of the theory of transformation optics,the new avenue of designing electromagnetic metamaterials is attractive.Due to the high efficiency,flexibility and adjustability of manipulating electromagnetic field with related spatial transformation theory and metamaterial,such concept is also analogized to other wave fields including matter wave,acoustics,water wave,elastic wave,and diffusive fields of thermodynamics and mass transfer.The extensive investigations of emerging metamaterial in varied fields derive the unprecedented occasion of nontrivial manipulative behaviors.Compared with the researches on metamaterial in wave fields,the design and investigation of manipulating diffusive fields with the spatial transformation based metamaterial is still in its infancy and development stage.Since the physical nature of diffusive field is fundamentally different from the wave field,a large number of phenomena based on metamaterial of wave field require specific analogs in diffusive field,while many unique manipulative behaviors induced by transformation based diffusive metamaterial deserve comprehensive investigations.In addition,taking the thermal metamaterial as an example for diffusive field,the high efficiency,orientation and environmental adaptability of thermal metamaterial in the field manipulations present great potentials on motivating the conventional energy systems and techniques.In this paper,the mechanism of heat flux deflection in arbitrary domains are investigated in details based on related spatial transformation theory and the specific thermal metamaterial designs.Furthermore,a general and flexible spatial transformation theory is proposed accordingly,and a series of non-conformal meta-devices for single/multiple fields with complex transformations and functions are designed.Finally,the thermodynamic properties of the thermal metamaterial and typical designs are further investigated.For the mechanism of heat flux deflection of thermal metamaterial in arbitrary domains,the distributions of thermal conductive components in arbitrary transformed space is obtained based on the combination of steady-state heat transfer equation and related spatial transformation theory.Further plugging the conductive components in the transformed heat conduction equation,the heat flow componentsin each conductive direction and the corresponding heat flux deflections can be obtained.Besides,the findings of heat flux deflections in arbitrary space are introduced into three classical thermal metamaterial structures to investigate the manipulative mechanism of thermal metamaterial.The expressions of heat flux deflections of corresponding meta-devices are obtained,while the influencing factors and control methods of the heat flux deflections in specific metamaterial structures are determined accordingly.A general mapping methodology of rotatory linear map for designing meta-devices in arbitrary domain is proposed based on the conventional transformed theory of transformation optics and affine transformation.Such method can be employed to flexibly achieve metamaterial without considering the problems of singular/limited parameters caused by the transformation process of conventional transformation optics,while the sub-spaces of the traditional affine maps can be also eliminated.Furthermore,a class of non-conformal arbitrary polygon metamaterial harvesting devices are proposed,while the effects of internal anisotropy inside functional regions on the harvesting behaviors are further investigated in such systems.The generally flexible mapping points for spatial transformations are obtained with the motivated and extensive rotatory linear map.Based on the improved rotatory linear map,a new class of meta-devices for manipulating single/multiple fields are proposed and validated.Among these meta-devices,the non-conformal metamaterial thermal cloak is designed to simultaneously demonstrate the heat flux avoidance and thermal invisibility in one arbitrary region.Besides,a class of metamaterial source illusion through directed thermal diffusion is designed,while the directional thermal diffusion and external field manipulation are significantly observed in the functional regions.Furthermore,such method is extended to multiple fields,and the discrete source array for thermal and DC fields are theoretically proposed and experimentally demonstrated.Such discrete source array can be employed to mimic and achieve the field distributions induced by multiple actual thermal/electric sources only with a single field source.Finally,the entropy generation analysis(the second law of thermodynamics)is first introduced into metamaterial system based on the theory of spatial transformations to investigate the thermodynamic properties of thermal metamaterial systems.The expression of local entropy generation rate is obtained under related transformed spatial system.The concepts of “response entropy” and“efficient harvesting entropy” are respectively proposed to estimate and predict the thermodynamic performances of classical metamaterial thermal cloaking and harvesting systems under varied design parameters.Furthermore,the optimal design methods of meta-devices under specific conditions can be also obtained with the findings of the thermodynamic analysis.