Inversion Of Solid Thermal Conductivity Based On Transient Plane Heat Source Method

Accurate measurement of the material thermo-physical properties is significance to the development and application of new materials in physics,chemistry,biology and other fields.Thermal conductivity is one of the important parameters in the thermo-physical properties.For the different measurement principles of the thermal conductivity,measurement methods can be divided into steady-state method and transient method.Transient method has short measurement time,low requirements on the environment and the shape and size of materials.Transient method has become the main method to measure the thermal conductivity.Transient plane heat source method is typical transient measurement method,according to the green’s function and the temperature response of the heat source,the analytical solution of the thermal conductivity is obtained,this method must be carried out on the physical model of measurement process,the finite heat capacity of the heating element is not considered,assuming that the heating power of the heat stability,heat source infinitesimal volume.The assumption of physical model makes the analytical solution of transient plane heat source method have some error.Based on the transient plane heat source method,this paper focuses on the inversion method of thermal conductivity.In this paper,the physical model is based on the transient plane heat source method has been established,this model considers the thermal heat capacity and size of probe.The numerical calculation program based on finite element discrete method was written by MATLAB to obtain the temperature rise response of the heat source,and the simulation results were compared with the existing commercial CFD software(COMSOL),the relative error of the heat source temperature response is about 1%without considering the thermal resistance at the interface between thermal probe and material.Considering the contact thermal resistance,the temperature response of the heat source is within 5%,which indicates that the calculation results of the numerical program based on the finite element discrete method are reliable.COMSOL simulation results were used as test data,and MATLAB self-programmed calculation results were used as constraints in the inversion process,the selection of the bayesian optimization algorithm inversion measured material coefficient of thermal conductivity,calculated the relative errors of inversion results,analyzes the scope of initial population and the number of initial population impact on the accuracy of the inversion results.The study found that the smaller the initial population range.The more the initial population,the higher the inversion accuracy,the slower the convergence rate.Inversion algorithm in operation to improve the accuracy of the inversion results,before adding the initial population of adaptive optimization processes,the optimized inversion results show that the inversion accuracy is not affected by initial population search scope,to steady at around 3%,compared with before optimization iteration inversion process greatly decreases,and can achieve convergence within 5 iterations.To verify the advantages of bayesian optimization algorithm in the process of thermal conductivity inversion,genetic algorithm inversion was used in this paper to compare the inversion results.It was found that the inversion results of the two algorithms were basically consistent within the same initial population range.The inversion speed of bayesian optimization algorithm is about 3～4 times that of genetic algorithm,which indicates that bayesian optimization algorithm can greatly improve the inversion efficiency while ensuring the inversion accuracy.To solve the influence of the contact thermal resistance on the inversion results,the contact thermal resistance is added into the forward problem solving program,and the bayesian optimization algorithm is used to invert the thermal conductivity of the tested material under the condition of unknown thermal resistance.This study found that the coefficient of thermal conductivity inversion result and the actual coefficient of thermal conductivity of relative error is within 5%,and the inversion accuracy is higher,the relative error between the inversion results and the actual thermal resistance can reach 16.33%,the inversion accuracy is worse,shows that COMSOL software error between the forward problem solver and can bring more to the contact thermal resistance of inversion of relative error.When the contact thermal resistance of the interface increases,the relative error between the inversion results of thermal conductivity and the real value decreases,and the relative error between the inversion results of thermal conductivity and the real value is basically unchanged,indicating that the bayesian optimization algorithm in this study can be used to invert the thermal conductivity with high accuracy under the condition of unknown thermal resistance.