Heat flow along two-dimensional strips as a function of the Knudsen number is examined in two different versions of heat-transport equations with non-local terms, with or without heat slip flow. In both of them, a parabolic heat profile corresponding to the Poiseuille phonon flow may appear in some domains of temperature, or of the Knudsen number, in the transition from the Fourier regime to the ballistic one. The influence of the slip heat flow on such a transition is discussed

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The correct analysis of heat transport at nanoscale is one of the main reasons of new developments in physics and nonequilibrium thermodynamic theories beyond the classical Fourier law. In this paper, we provide a two-temperature model which allows to describe the different regimes which electrons and phonons can undergo in the heat transfer phenomenon. The physical admissibility of that model is showed in view of second law of thermodynamics. The above model is applied to study the propagation of heat waves in order to point out the special role played by nonlocal and nonlinear effects.

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