| Summary: | <p>The process of heat conduction can be modeled via random motion of particles of heat energy, although these particles do not physically exist: they are considered as special formal objects. The speed of diffusion of heat particles in each material is proportional to its temperature conductivity coefficient. This mathematical model underlying the method of obtaining the effective heat conductivity coefficient of a composite material described in the previous paper \Heat conductivity of composite materials with included balls of zero heat conductivity" now is being modified in order to deal with materials with various nonzero heat conductivity and capacity coefficients. Namely, when a particle passes from one material to another one, having smaller heat conductivity, it is reflected from the frontier with a certain probability.</p><p>As a criterion of heat conductivity, we consider the probability that a heat particle starting on one surface of a composite layer, goes to its other surface in a time shorter than T. For a homogeneous material, this probability is calculated theoretically.</p><p>For a layer of a composite, we perform a multiple computational experiment modeling heat conduction, and for the desired probability we find the confidence interval, wherefrom we obtain the confidence interval for the effective temperature conductivity coefficient, and, finally, calculate the effective heat conductivity coefficient.</p><p>We have considered inclusions of materials with heat conductivity and volume heat capacity coefficients differing from those of the matrix in 3 times up or down. Ball inclusions of equal size were situated in a cubic order or chaotically. The ratio of the ball radius to the size of cubes was 0.2, 0.3, or 0.4.</p><p>In series of 4300 randomly moving particles, in all cases considered, the difference between the effective heat conductivity coefficients and those calculated by other methods does not exceed a statistical error.</p><p>The developed method makes it possible to obtain effective heat conductivity coefficients for composites with inclusions of any size and shape; it can be applied also in a case of inclusions from several materials. The results obtained are reliable and only the computer capability restricts their exactness.</p>
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