Research On The Equivalent Thermal Conductivity Defined By The Entransy Dissipation Rate Of Composite Materials

Thermally conductive polymer composite materials have broad application prospects in electronic packaging,aerospace and other fields.Quantitative analysis of the thermal conductivity of polymer composites is an important topic.Thermal conductivity,k,is an important physical quantity to measure the thermal conductive property of homogeneous mediums.But the local thermal conductivity is position-dependent in inhomogeneous mediums.Many expressions of equivalent thermal conductivity(ETC)and resistance(ETR)had been proposed using different homogenization calculation methods to evaluate the thermal conductive property of composites,especially,expressions defined by the entransy dissipation rate,k_eff and R_eff,excel for their wide range of application.Usually,thermal conductivity is considered as a constant material property,which is determined by the thermal conductivity distribution inside.However,we found that it also varies with the boundary temperature gradient distribution(TGD).In this paper,the influence of TGD on k_eff was simulated at the microscopic level using the finite element method.Then,its upper and lower bounds were analyzed and the mathematical proof of TGD affecting k_eff was given.Also,some experimental results were used to explore the variability of the thermal conductivity of composites under different boundary conditions.Main work and conclusions of this thesis are as follows:(1)k_eff of different inhomogeneous mediums were simulated.Three basic representative volume elements(RVEs)of inhomogeneous mediums and two RVEs of mixed inhomogeneous composites were constructed.And k_eff of these RVEs were calculated under different first-,second-,third-type and radiation boundary conditions.Simulation results indicate that k_eff under the uniform TGD boundary condition is higher than that under the non-uniform TGD boundary condition.k_eff is the maximum when TGD of all regions is uniform.And k_eff tends to the minimum when TGD of all regions is extremely non-uniform.(2)Mechanism of the variable k_eff of the inhomogeneous medium was analyzed.It was pointed out in theory that k_eff of the inhomogeneous material is only affected by the thermal conductivity distribution and the boundary temperature gradient,in which the former is the internal factor that affects k_eff and R_eff,and the latter is the external factor.(3)A mathematical proof was given to confirm k_eff and R_eff change with the boundary TGD.The trends of k_eff and R_eff with different boundary TGDs were analyzed applying the monotonicity of the function,and their maximum and minimum values were obtained.This mathematical proof is consistent with the numerical simulation results.And the mathematical proof process after some minor modifications can be used to prove the least principle of the entransy dissipation resistance.(4)Two kinds of polymer-based composites named EP/GNS,PEG/CGPA and the pure EP were prepared,and their thermal conductivities imposed different boundary conditions were test by Hot Disk.In the results,the thermal conductivity of the pure EP changes very little(<0.6%),while the thermal conductivities of composite materials vary greatly,up to 11.2%in our experiments.These results preliminarily verify the variability of the composites'thermal conductivities under different boundary conditions.The present work is important to understand the mechanism of heat conduction,and the analysis of the upper and lower bounds of R_eff are of great value for optimizing the heat transfer and heat insulation ability of materials.