Prediction of the effective thermal conductivity of spheroplastics
UDC
536.2DOI:
https://doi.org/10.31429/vestnik-20-1-65-75Abstract
The paper solves the problem of predicting the effective thermal conductivity of a disk-shaped spheroplastic sample with constant, significantly different temperatures maintained on opposite faces of its bases. A two-stage calculation scheme is proposed. The first stage consists in calculating the effective thermal conductivity of a small macroscopic region of the sample, the temperature in which can be considered approximately equal to some average temperature in this region. At the second stage, the effective thermal conductivity of the reference medium sample (of the same shape as that of the original spheroplastic sample) is calculated, in which the local thermal conductivity at each point is equal to the effective thermal conductivity in the corresponding small macroscopic region of the original spheroplastic sample containing this point.
Compositions based on epoxy resin ED-20 with amine hardener PO-300 and spherical microspheres with a shell of borosilicate glass filled with gaseous nitrogen are considered.
Model calculations of the effective thermal conductivity of thin layers of a spheroplastic sample at different temperatures and different sizes of microspheres depending on their volume fraction in the material are carried out. The calculations were performed on the basis of the generalized effective-field approximation for a matrix composite with inclusions in the shell. It has been established that with an increase in the volume fraction of microspheres in the material, the thermal conductivity of the spheroplastic layer can either decrease or increase depending on the ratio between the wall thickness and the radius of the microsphere.
Numerical simulation of the effective thermal conductivity for a disk-shaped spheroplastic sample at temperatures of 150°C and 25°C applied to its opposite bases has been carried out. The calculations took into account the value of the dimensionless structural parameter, which is the ratio of the microsphere shell thickness to its radius. It is shown that the effective thermal conductivity of a spheroplastic sample significantly depends on the volume fraction of microspheres and the value of the structural parameter. It has been established that an increase in the volume fraction of microspheres, depending on the ratio between their wall thickness and radius, leads to both an increase and a decrease in the thermal conductivity of the epoxy compositions under consideration.
Keywords:
effective thermal conductivity, matrix, inclusion, generalized effective-field approximation, Maxwell-Garnett approximation, self-consistency approximation, spheroplastic, microsphere, modelingFunding information
The work was carried out within the framework of the state assignment on project No. 122040800154-7.
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