The subject of the paper are composite conductors which consist of homogeneous components. The distribution of the components in the conductor can be described with the use of slowly varying functions. The work consists in forming a model of heat conduction in which the Fourier equation with discontinuous highly oscillating coefficients was substituted with an equation with continuous and slowly varying coefficients. The influence of the conductor on the temperature is described with additional functions which determined knowing the averaging temperature from the closed form formulas. In the special case of a periodic conductors the equation of heat conduction contains constant coefficients. The paper presents simple examples of numerical solutions.

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