Vito Antonio Cimmelli

Different Thermodynamic Theories and Different Heat Conduction Laws

Abstract We present an overview of the modern approaches to continuum nonequilibrium thermodynamics from the perspective of their connection with the problem of heat conduction with finite speed. The celebrated Cattaneo and Guyer–Krumhansl equations for the evolution of the heat flux are reinspected in the framework of the different thermodynamic theories which, in such a way, are reviewed and compared.

An extension of Liu procedure in weakly nonlocal thermodynamics

An extension of the celebrated Liu procedure for the exploitation of second law of thermodynamics is proposed. The new method is applied to investigate weakly nonlocal extended thermodynamics of rigid heat conductors. Thermodynamic restrictions on the constitutive functions are derived and compared with classical results.

The effects of nonlocality on the evolution of higher order fluxes in nonequilibrium thermodynamics

The role of gradient dependent constitutive spaces is investigated on the example of Extended Thermodynamics of rigid heat conductors. Different levels of nonlocality are developed and the different versions of extended thermodynamics are classified. The local form of the entropy density plays a crucial role in the investigations. The entropy inequality is solved under suitable constitutive assumptions. Balance form of evolution equations is obtained in special cases. Closure relations are derived on a phenomenological level.

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.

Exploitation of the Second Law: Coleman–Noll and Liu Procedure in Comparison

Abstract A comparison is made between two classical methods for the exploitation of the second law of thermodynamics: the Coleman–Noll and the Liu procedure. On the example of a rigid heat conductor with general entropy flux, it is shown that the two procedures are equivalent. This equivalence is demonstrated in the case of a state space including the wanted fields, only, as well as in the case of gradients being relevant for constitutive equations, too. Also, the possible importance of an internal variable or an internal degree of freedom is considered.

Numerical reconstruction of heat pulse experiments

Abstract In the present paper numerical solutions to initial-boundary value problems for a semi-empirical model of heat conduction are compared with available experimental results. The obtained arrival times for heat pulses are almost identical with the measured ones. Further, on the basis of the present numerical solutions, a critical analysis of the basic assumptions of the semi-empirical model is developed.

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.

Exploitation of the entropy principle: Proof of Liu theorem if the gradients of the governing equations are considered as constraints

The exploitation of the entropy principle in thermodynamics with Lagrange multipliers (the so called Liu procedure) is based on the celebrated Liu theorem. In some recent papers, where either rigid heat conductors or Korteweg fluids have been considered, the Liu procedure has been generalized by using the gradients of the governing equations as additional constraints. Here, a rigorous proof of the validity of the extended procedure to arbitrary first-order nonlocal continua is provided, thus explicitly generalizing the Liu theorem. As an application, heat conducting first-order Korteweg-type fluids with a scalar internal variable are analyzed. The thermodynamic restrictions are determined by the extended Liu procedure. Moreover, a comparison with the thermodynamic analysis obtained by the application of an extended Coleman–Noll procedure is performed.

Mesoscopic description of boundary effects in nanoscale heat transport

Abstract We review some of the most important phenomena due to the phonon-wall collisions in nonlocal heat transport in nanosystems, and show how they may be described through certain slip boundary conditions in phonon hydrodynamics. Heat conduction in nanowires of different cross sections and in thin layers is analyzed, and the dependence of the thermal conductivity on the geometry, as well as on the roughness is pointed out. We also analyze the effects of the roughness of the surface of the pores on the thermal conductivity of porous silicon. Thermoelectric effects are considered as well. In memory of Professor Carlo Cercignani

Flux Limiters in Radial Heat Transport in Silicon Nanolayers

By using the thermomass-theory approach, the temperature in a thin layer heated by a hot spot is derived in steady states. It is shown that an anomalous temperature profile, which seems to be at odds with the fundamental laws of continuum physics, may occur. The compatibility of this situation with second law of thermodynamics is analyzed in view of the concept of flux limiter.