Mathematical modeling of heat flow rectification in contact pairs


Аuthors

Dornyak O. R.*, Popov V. M.*

Voronezh State University of Forestry and Technologies Named after G.F. Morozov, Voronezh, 394087, Russia

*e-mail: ordornyak@mail.ru

Abstract

The results of mathematical modeling of the effect of heat flow rectification in contact pairs made of homogeneous and heterogeneous materials are presented. The contact zone of elements is considered as a heterogeneous medium containing gas and inclusions of the solid phase of contacting materials. Based on the mechanics of multiphase systems, the equations of conservation of mass, equilibrium, and thermal conductivity are formulated, averaged over the volumes occupied by each phase. The influence of temperature deformations on the stress-strain state of the pair under the action of compressive forces is taken into account. In a heterogeneous layer, a three-temperature process is studied for the gas phase and two solid phase components belonging to contact vapor samples from different materials. Two types of pairs are studied: steel 45-alloy DT1 and steel 45-highly porous thermal insulation material based on basalt fibers.

Surface profiles of samples made of 45 steel and DT1 alloy were obtained using fractal curves constructed using the Weierstrass-Mandelbrot equation. The mathematical model does not use micromorphological characteristics of contact surfaces, so reference curves are determined based on them using well-known algorithms. The proposed mathematical model can be used both to study the process of heat flow rectification and to determine the thermal resistance of the contact. A numerical implementation of the one-dimensional stationary approximation of the model based on the finite-difference method is carried out. The model was verified by comparing the data of a computational and field experiment. The results showed good agreement. Calculations have shown that the intensity of heat flow rectification for pairs with a porous element is significantly higher than for pairs made of homogeneous materials. This is due to the fact that the specific area of the interfacial surface of a porous material in a heterogeneous layer is higher than that of a non-porous one. Therefore, the power of heat sources that determine the specific distributions of the temperature profile and the density of the solid phase heat flow near the contact boundary are significantly different. As the compression pressure increases, the rectification coefficient tends to the value corresponding to the ideal contact.

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