Predicting and analyzing interaction of the thermal cloaking performance through response surface method

Abstract Thermal cloaks have been widely studied and experimented with. However, discussions on cloaking performance based on different design parameters effects are lacking. In this paper, we focus on predicting the cloaking performances of 2D thermal cloak schemes with different design parameters such as layer number, thickness, temperature difference, and relative thermal conductivity. The concept of response entropy, which is based on entropy generation analysis and is used to characterize the cloaking performance, is proposed. A regression model is established to predict the response entropy of the variational design parameters using response surface method (RSM). Five confirmation tests are conducted to verify the accuracy of the prediction. The relationship between the response entropy and the interaction effects of the design parameters are described with the help of 3D response surfaces using analysis of variance (ANOVA). In conclusion, we propose that a core-shell cloaking scheme with modest parametric values of 1–18 layers, a thickness of 1–5 mm, a small relative thermal conductivity, and large temperature difference can provide a better cloaking performance. This paper presents a theoretical prediction of the cloaking performance and provides suggestions on fabricating better thermal cloaks under different parameters.

[1]  W. Hu,et al.  An experimental acoustic cloak for generating virtual images , 2013 .

[2]  Tianzhi Yang,et al.  Transient thermal camouflage and heat signature control , 2016 .

[3]  Y. Wang,et al.  An ultrathin invisibility skin cloak for visible light , 2015, Science.

[4]  Run Hu,et al.  Exploring the proper experimental conditions in 2D thermal cloaking demonstration , 2016 .

[5]  M. Wegener,et al.  An elasto-mechanical unfeelability cloak made of pentamode metamaterials , 2014, Nature Communications.

[6]  Ying Li,et al.  Thermal cloak-concentrator , 2015, 1506.01532.

[7]  Claude Amra,et al.  Transformation thermodynamics: cloaking and concentrating heat flux. , 2012, Optics express.

[8]  Martin Wegener,et al.  Pentamode metamaterials with independently tailored bulk modulus and mass density , 2014, 1407.4894.

[9]  Martin Wegener,et al.  Invisibility cloaking in light‐scattering media , 2016 .

[10]  H. Scheffé.  The Analysis of Variance , 1960 .

[11]  A. Aziz,et al.  Entropy generation in a hollow cylinder with temperature dependent thermal conductivity and internal heat generation with convective–radiative surface cooling ☆ , 2012 .

[12]  Tungyang Chen,et al.  Materials with constant anisotropic conductivity as a thermal cloak or concentrator , 2015 .

[13]  Ole Sigmund,et al.  Towards all-dielectric, polarization-independent optical cloaks , 2012 .

[14]  Wei Jiang,et al.  A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity , 2013 .

[15]  Baile Zhang,et al.  Active thermal cloak , 2015 .

[16]  Peng Yang,et al.  Prediction and parametric analysis of acoustic streaming in a thermoacoustic Stirling heat engine with a jet pump using response surface methodology , 2016 .

[17]  Cheng-Wei Qiu,et al.  Homogeneous Thermal Cloak with Constant Conductivity and Tunable Heat Localization , 2013, Scientific Reports.

[18]  David R. Smith,et al.  Metamaterial Electromagnetic Cloak at Microwave Frequencies , 2006, Science.

[19]  Haochun Zhang,et al.  A concept of heat dissipation coefficient for thermal cloak based on entropy generation approach , 2016 .

[20]  Linzhi Wu,et al.  Thermal transparency with the concept of neutral inclusion. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  M. Wegener,et al.  Experiments on transformation thermodynamics: molding the flow of heat. , 2012, Physical review letters.

[22]  Jiping Huang,et al.  Shaped graded materials with an apparent negative thermal conductivity , 2008 .

[23]  Ying Li,et al.  Temperature Trapping: Energy-Free Maintenance of Constant Temperatures as Ambient Temperature Gradients Change. , 2016, Physical review letters.

[24]  Baowen Li,et al.  Experimental demonstration of a bilayer thermal cloak. , 2014, Physical review letters.

[25]  G. Box,et al.  On the Experimental Attainment of Optimum Conditions , 1951 .

[26]  Ying Li,et al.  Temperature-Dependent Transformation Thermotics: From Switchable Thermal Cloaks to Macroscopic Thermal Diodes. , 2015, Physical review letters.

[27]  Jiping Huang,et al.  Thermally hiding an object inside a cloak with feeling , 2014 .

[28]  Fedor Gömöry,et al.  Experimental Realization of a Magnetic Cloak , 2012, Science.

[29]  Fei Gao,et al.  Ultrathin three-dimensional thermal cloak. , 2014, Physical review letters.