Local heat fluxes statistics in two-dimensional models of two-phase composite materials

I. V. Zaginaylo, А. N. Pysarenko, А. А. Broshevan

Abstract


Abstract. Purpose. The goal of this work is to test the statistical hypothesis on the polymodal distribution peaks character of the of the local heat fluxes intensities in two-phase composite material. Another object is to perform a statistical analysis of the matrix and inclusions parameters influence on the characteristics of this distribution.  Methodology. We modeled the steady-state distribution of the thermophysical characteristics of a quasi-two-dimensional two-phase composite with randomly placed inclusions by the Monte Carlo method. The internal Dirichlet problem for a homogeneous stationary heat equation with first kind boundary conditions was solved numerically by the method of the top progressive relaxation. We used the procedure of statistical identification of polymodal distributions of local heat fluxes. Results. Numerical calculations were carried out and scenarios for local heat fluxes were considered when the parameters of both the inclusions and their placement in the matrix are changed. Assuming the lognormal distribution law we separated the polymodal distribution of local heat fluxes into three modes. The influence of the matrix and inclusions parameters on the individual modes dynamics was studied. Comparing heat fluxes charts and histograms of the distribution of heat fluxes intensities, we defined the areas of the composite matrix which corresponded to each mode.  Originality. The areas of the quasi-two-dimensional composite which correspond the local heat fluxes with the distribution of three different types were statistically confirmed and spatially localized for the first time. The analysis of the factors which affect the main characteristics of these distributions was carried out. Practical value. The results of a numerical study of the local heat fluxes distribution can be used both for predicting the results of thermal exploitation of available two-phase composites and for simulating the new composite materials thermophysical characteristics.

Keywords


composite material; Monte Carlo method; local heat fluxes; statistical analysis; dynamics of distribution parameters

References


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Gori F. and Corasaniti S. Effective thermal conductivity of composites. International Journal of Heat and Mass Transfer. 2014, vol. 77, pp. 653-661.

Graham S. and McDowell D. Numerical analysis of the transverse thermal conductivity of composites with imperfect interfaces. Journal of Heat Transfer. 2003, vol. 125, pp. 389-393.

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Zaginaylo I.V., Maksimeniuk Ya.A. and Pysarenko A.N. Two-dimensional numerical simulation study of the effective thermal conductivity statistics for binary composite materials. International Journal of Heat and Technology. 2017, vol. 35, no. 2, pp. 364-370.

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GOST Style Citations


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