Abstract：Composite materials are widely used in several fields, such as energy industry. Composite materials have complex geometric structures and are usually equivalent to homogeneous materials in the process of thermal design, and then use an effective thermal conductivity model to describe the heat transfer process. Traditional methods for analyzing the effective thermal conductivity of composite materials are typically based on Fourier's law by applying a constant heat flow at both sides of the material to conserve the heat flows of the real and equivalent uniform materials. For composite materials with internal heat sources, such as nuclear fuel, the value and direction of the internal heat flow are affected by the distribution of heat sources; therefore, the method based on Fourier's law will be unsuitable for analyzing the effective thermal conductivity of such materials. To explore the influence of distributed inner heat sources on the effective thermal conductivity of composite materials, this study considers an infinite two-phase composite plate as the research object. The difference between the effective thermal conductivities with and without the inner heat sources is analyzed, and the effective thermal conductivity model is established for predicting the average temperature of the composite plate with inner heat sources. The influence of the distribution of inner heat sources on the effective thermal conductivity is analyzed. Furthermore, the influence of randomly distributed inner heat sources on effective thermal conductivity is quantified. Results show that the effective thermal conductivity for predicting the average temperature of the composite plate with inner heat sources is not affected by the size of the heat sources but by the locations of each heat-generating filling plate, i.e., the distribution of the inner heat sources. Additionally, it is affected by the number and size of the filling plates. The deviation in the effective thermal conductivities when the filling plates are randomly and uniformly distributed can be approximated as a normal distribution, and that for uniformly distributed filling plates is approximately equal to the highest probability case for the randomly distributed plates. The deviation of the effective thermal conductivity for the randomly and uniformly distributed filling plates decreases with the increasing number of plates (i.e., the more dispersed heat source distribution). The effective thermal conductivity of the composite plate with inner heat sources depends on more factors than the plate with no inner heat source, including the number and size of the filling plates and the distribution of the inner heat sources. The effective thermal conductivity of composite flat plate with randomly distributed heat generating plates is approximately same as that when they are uniformly distributed. The ideas and methods present in this study lay the foundation for future research on the effective thermal conductivity of nuclear reactor fuel.
刘子平, 孙俊. 含分布式内热源复合平板等效导热系数模型[J]. 清华大学学报（自然科学版）, 2023, 63(1): 104-113.
LIU Ziping, SUN Jun. An effective thermal conductivity model of composite plates with distributed inner heat sources. Journal of Tsinghua University(Science and Technology), 2023, 63(1): 104-113.
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