A kinetic approach to analytically considering the lateral heat transfer through a metal layer located between two massive dielectrics. The effective transverse thermal conductivity of such a layered system with an arbitrary thickness of the metal layer is calculated, and the thicknesses at which the size effect is manifested in thermal conductivity, are found. The transverse heat transfer is also analyzed using the phenomenological two-temperature (2TM) model, i.e. in terms of electron and phonon temperatures. Comparing the results of 2TM and the microscopic approach allows us to find out the conditions under which the frequently used two-temperature approach is not applicable.

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This type of heat transfer is sometimes referred to as the Knudsen limit, since in this case the Knudsen parameter Kn, defined as the ratio of the mean free path of heat carriers to the smallest characteristic size of the system, is large.

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