A. Sellitto

Phonon hydrodynamics and phonon-boundary scattering in nanosystems

We use phonon hydrodynamics with a surface slip flow as a simplified macroscopic model accounting for a reduction in lateral thermal conductivity in nanosystems. For high Knudsen numbers, the corresponding effective thermal conductivity decreases linearly with the radius or the width, in contrast with the quadratic dependence predicted by usual phonon hydrodynamics. The linear dependence is accounted for by the surface slip flow. The difference in the expressions for the surface tangential flow in the hydrodynamic and the diffusive regimes is commented on and the influence of boundary conditions on the form of the effective thermal conductivity is explored.

Pore-size dependence of the thermal conductivity of porous silicon: A phonon hydrodynamic approach

Phonon hydrodynamics is used to analyze the influence of porosity and of pore size on reduction in thermal conductivity in porous silicon, with respect to crystalline silicon. The expressions predict that the thermal conductivity is lower for higher porosity and for smaller pore radius, as a consequence of phonon ballistic effects. The theoretical results describe experimental data better than the assumption that they only depend on porosity.

Second law of thermodynamics and phonon-boundary conditions in nanowires

The restrictions placed by the second law of thermodynamics on the boundary conditions have a special interest in nanosystems, where the Knudsen boundary layer, whose width is of the order of the mean-free path of heat carriers, becomes comparable to the size of the whole system. Here we explore second-order boundary conditions and show that the constraints of the classical irreversible thermodynamics are too restrictive, and that other formalisms going beyond local-equilibrium approach yield more realistic constraints for hydrodynamic phonon flow along nanowires. Furthermore, our analysis suggests a transition to zero thermal conductivity for very thin nanowires due to phonon backscattering.

Temperature dependence of boundary conditions in phonon hydrodynamics of smooth and rough nanowires

In the analysis of nanosystems, the phonon–wall interaction must be incorporated to the usual description of phonon hydrodynamics, as surface effects become comparable to bulk effects in these systems. In the present paper, we analyze the temperature dependence of two phenomenological coefficients describing the specular and diffusive collisions, on one side, and backscattering collisions, on the other side, in silicon nanowires. Furthermore, we also propose for them a qualitative microscopic interpretation. This dependence is important because it strongly influences the temperature dependence of the effective thermal conductivity of nanosystems.

Phonon Boundary Effects and Thermal Conductivity of Rough Concentric Nanowires

By using a phonon hydrodynamics model for heat flow complemented with boundary conditions for smooth or rough boundaries, we study the influence of boundary conditions on the longitudinal thermal conductivity for several kinds of nanowires (single, tubular, and core-shell). The effects of the boundaries are seen to be extremely important.

Heat waves and phonon–wall collisions in nanowires

The dispersion relation of heat waves along nanowires is obtained, displaying the influence of the roughness of the walls. This knowledge may be useful for the development of new experimental techniques based on heat waves, complementary to current steady-state measurements, for the exploration of phonon–wall collisions in smooth and rough walls.

Non-local effects in radial heat transport in silicon thin layers and graphene sheets

We explore non-local effects in radially symmetric heat transport in silicon thin layers and in graphene sheets. In contrast to one-dimensional perturbations, which may be well described by means of the Fourier law with a suitable effective thermal conductivity, two-dimensional radial situations may exhibit a more complicated behaviour, not reducible to an effective Fourier law. In particular, a hump in the temperature profile is predicted for radial distances shorter than the mean-free path of heat carriers. This hump is forbidden by the local-equilibrium theory, but it is allowed in more general thermodynamic theories, and therefore it may have a special interest regarding the formulation of the second law in ballistic heat transport.

A generalized Coleman–Noll procedure for the exploitation of the entropy principle

A generalization of the classical Coleman–Noll procedure for the exploitation of second law of thermodynamics in the presence of first-order non-local constitutive functions is proposed. The local balance of entropy is regarded as a differential inequality constrained by the governing equations for the set of the unknown fields as well as by their gradient extensions. The thermodynamic compatibility of such a class of materials is achieved without any modification of the basic thermodynamic laws. The results so obtained are applied to model nonlinear heat conduction in solids, in the presence of a dynamical semi-empirical temperature scale.

Phonon-wall interactions and frequency-dependent thermal conductivity in nanowires

Phonon-wall collisions (with smooth or rough walls) have a deep influence on the thermal conductivity of nanowires. Usually this influence is analyzed in the steady-state thermal conductivity. Here, by using a phonon-hydrodynamic model with slip heat flow along the walls, we explore the influence of phonon-wall collisions on frequency-dependent thermal conductivity, which imply a reduction of it with increasing frequency. Understanding of this dependence would allow one to obtain information on the collisions complementary to that of the steady states.

A new thermodynamic framework for second-grade Korteweg-type viscous fluids

A model of viscous fluid of Korteweg type, with first-order nonlocal constitutive equations, is developed. The restrictions placed by the dissipation principle are investigated by applying a generalized Liu procedure. Some remarkable nonlocal properties of the entropy function are carried out.