In this paper, effects of non-Fourier thermal wave interactions in a thin film have been investigated. The non-Fourier, hyperbolic heat conduction equation is solved, using finite difference method with an implicit scheme. Calculations have been carried out for three geometrical configurations with various film thicknesses. The boundary condition of a symmetrical temperature step-change on both sides has been used. Time history for the temperature distribution for each investigated case is presented. Processes of thermal wave propagation, temperature peak build-up and reverse wave front creation have been described. It has been shown that (i) significant temperature overshoot can appear in the film subjected to symmetric thermal load (which can be potentially dangerous for reallife application), and (ii) effect of temperature amplification decreases with increased film thickness.
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.
Transverse effective thermal conductivity of the random unidirectional fibre-reinforced composite was studied. The geometry was circular with random patterns formed using random sequential addition method. Composite geometries for different volume fraction and fibre radii were generated and their effective thermal conductivities (ETC) were calculated. Influence of fibre-matrix conductivity ratio on composite ETC was investigated for high and low values. Patterns were described by a set of coordination numbers (CN) and correlations between ETC and CN were constructed. The correlations were compared with available formulae presented in literature. Additionally, symmetry of the conductivity tensor for the studied geometries of fibres was analysed.