We describe the nonlocal heat transport across a thin film in contact with two thermal baths using discrete variable model. The effective thermal conductivities, the boundary temperature jumps, the steady-state heat flux, and the internal temperature gradient are calculated analytically as functions of the film size and the boundary resistances. As the system size decreases, all the parameters demonstrate the transition from diffusive (Fourier) heat conduction when the scattering occurs mainly inside the film to ballistic transport when scattering occurs at the boundaries, while inside the film there is no scattering and the temperature profile is flat. We show that when the boundary resistance increases, the temperature profile inside the film also tends to be flat, but in this case the scattering, though small, occurs inside the film. The predicted effective thermal conductivity is consistent with classical continuous theories and available experimental data.

我们使用离散变量模型描述了跨过与两个热浴接触的薄膜的非局部传热。有效热导率，边界温度跳跃，稳态热通量和内部温度梯度是根据薄膜尺寸和边界电阻的函数进行解析计算的。随着系统尺寸的减小，所有参数都表明当散射主要发生在薄膜内部时，扩散（傅立叶）热传导过渡到边界处发生散射时的弹道传输，而薄膜内部没有散射，并且温度曲线为平面。我们显示出，当边界电阻增加时，薄膜内部的温度曲线也趋于平坦，但在这种情况下，尽管很小，但在薄膜内部发生了散射。