Numerical Simulation Of Thermal Cloak And Heat Flux Control

Heat flux control is a hot topic in recent years.It has broad application prospects in the efficient use of energy,defense security,power devices,and thermal information devices.Referring to the transformation optics,since the heat conduction equation form being not changed after the coordinate transformation,the researchers have promoted the coordinate transformation method to the field of thermodynamics,providing strong theoretical support for heat flux control.Nowadays,thermal cloak is very popular in the field of heat flux control,which can control the heat flux within a certain area that seems not existed from outside.It is often accomplished by constructing thermal metamaterials.The quantitative analysis of heat flux control and the practical design method are of great significance for the promotion and application of heat stealth.At present,most of the researches on thermal cloak and heat flux control are qualitative analysis.Although many functions have been realized,quantitative design ideas have not been given.On the basis of coordinate transformation method,the theoretical model of two-dimensional circular thermal cloak has been designed and parameterized by this paper.Three dimensionless numbers are defined to describe the thermal invisibility parameters and performance.With the help of numerical simulation method,the influence of each system parameter on the controlled area has been given,as well as the fitting equation.Therefore,the thermal cloak can be designed according to the requirements,and the heat flux at the fixed area can be quantitatively controlled by adjusting the parameters.Since thermal cloak requires anisotropic materials,and needs to meet some certain conditions,it is very hard to find the qualified materials in reality.Therefore,by using the equivalent thermal resistance theory and various isotropy materials,this paper has constructed the qualified thermal metamaterial.Based on the constructed thermal metamaterials,two equivalent thermal cloak models have been established,which have heat flux concentration and weakening functions respectively.They have also been analyzed and compared with theoretical models.Two dimensionless numbers are described to describe the perturbation of the external temperature field by the equivalent model and compared with the theoretical model.Finally,the two models have been integrated to provide the thermal cloak model with two functions being realized at the same time.According to different needs,the model parameters can be adjusted to quantitatively control the heat flux at the fixed area.