Mathematical modeling of thermal resistance in contact pairs of homogeneous and heterogeneous materials


Аuthors

Dornyak O. R.*, Popov V. M.*, Anashkina N. A.*

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

*e-mail: ordornyak@mail.ru

Abstract

The mathematical model of the contact thermal resistance for two dissimilar materials is presented. One of the materials is capillary-porous, the second one is homogeneous. The thermal resistivity prediction in the contact pairs of this type is actual for the aerospace industry with reference to the usage of the highly porous ceramics for the thermal protection, as well as for chemical technologies and biotechnologies, which provided the contact drying operations. The mathematical model is based on the mechanics of the multiphase systems. The description of the transfer processes is made for the thermophysical variables averaged over the volumes of the solid and gas phases. A feature of the model is the selection in the contact zone of the intermediate heterogeneous layer, which contains the solid phase inclusions of both materials having different physical and mechanical properties and different temperatures. The mathematical model includes the conservation equations of the mass, the momentum and the energy. The rheological equation is being constructed on the assumption of the elastic nature deformation of the materials. In relation to the heterogeneous regions, one should take into account the influence on the dependence of the material deformability from the phase volume concentrations and the elastic modules as well as the structural framework and the material from which the framework was created. In the general case, the formulated model is non-stationary, three-dimensional, conjugate, non-linear. Refer to the present paper, we investigated the constructed model in the one-dimensional stationary approximation. The problem of the stressedly-deformed state for the contact pair elements is being solved analytically. This solution allows obtaining the textural characteristics of the intermediate heterogeneous layer after the contact pair compression, which specifies the thermal interaction conditions of the samples. The temperature problem was investigated by the control volume method. The thermal resistance values obtained using the mathematical model give the satisfactory agreement with the calculated values obtained using the well-known Yu.P. Shlykov empirical formula. The model numerical study results let us to evaluate the influence of the physical-mechanical parameters of the contact pair elements on the contact thermal resistance. In particular, it has been shown that a decrease in thermal resistance is being facilitated by an increase in the thermal conductivity of the dispersed phase material and the specific surface area. The thermal resistance increases with increasing of the material porosity and the structural frame elastic modulus of the capillary-porous system. The proposed mathematical model allows us to take into account the integral contribution of all these factors.

Keywords:

thermal resistance of the contact, multiphase systems, mathematical modeling

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