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Piotr Darnowski, Piotr Furmański and Roman Domanski

Abstract

This paper presents the results of computer simulations carried out to determine coordination numbers for a system of parallel cylindrical fibres distributed at random in a circular matrix according to twodimensional pattern created by random sequential addition scheme. Two different methods to calculate coordination number were utilized and compared. The first method was based on integration of pair distribution function. The second method was the modified sequential analysis. The calculations following from ensemble average approach revealed that these two methods give very close results for the same neighbourhood area irrespective of the wide range of radii used for calculation.

Open access

Piotr Furmański, Mirosław Seredyński, Piotr Łapka and Jerzy Banaszek

Abstract

Heat flow in heterogeneous media with complex microstructure follows tortuous path and therefore determination of temperature distribution in them is a challenging task. Two-scales, micro-macro model of heat conduction with phase change in such media was considered in the paper. A relation between temperature distribution on the microscopic level, i.e., on the level of details of microstructure, and the temperature distribution on the macroscopic level, i.e., on the level where the properties were homogenized and treated as effective, was derived. The expansion applied to this relation allowed to obtain its more simplified, approximate form corresponding to separation of micro- and macro-scales. Then the validity of this model was checked by performing calculations for 2D microstructure of a composite made of two constituents. The range of application of the proposed micro-macro model was considered in transient states of heat conduction both for the case when the phase change in the material is present and when it is absent. Variation of the effective thermal conductivity with time was considered and a criterion was found for which application of the considered model is justified.