Generalized ballistic-conductive heat transport laws in three-dimensional isotropic materials
- PDF / 499,508 Bytes
- 28 Pages / 595.276 x 841.89 pts (A4) Page_size
- 104 Downloads / 140 Views
O R I G I NA L A RT I C L E
A. Famà · L. Restuccia · P. Ván
Generalized ballistic-conductive heat transport laws in three-dimensional isotropic materials
Received: 12 August 2019 / Accepted: 31 July 2020 © The Author(s) 2020
Abstract General constitutive equations of heat transport with second sound and ballistic propagation in isotropic materials are given using non-equilibrium thermodynamics with internal variables. The consequences of Onsager reciprocity relations between thermodynamic fluxes and forces and positive definiteness of the entropy production are considered. The relation to theories of Extended Thermodynamics is discussed in detail. We provide an explicit expression for all the components of the matrices of the transport coefficients. The expressions are cumbersome but are expected to be useful for computer programming for simulations of the corresponding physical effects. Keywords Heat transport · Ballistic propagation · Second sound · Extended Thermodynamics · Onsager relations
1 Introduction There are several generalizations of classical Fourier law conduction that can also model second-sound phenomena (heat waves) and ballistic propagation. These theories are more and more important in nanostructures and are subjects of various challenging physical, mathematical and numerical researches. For example, nonlocal effects and the role of effective temperature are investigated in [1–5], particular special functions were constructed and exact solutions were calculated for both the hyperbolic and Guyer–Krumhansl heat conduction [6–9], adapted numerical methods were developed in [10,11], the role of internal variables in complex media modelling was investigated in [12–14], and the particularities of heat conduction in nanomaterials are discovCommunicated by Andreas Öchsner. A. Famà · L. Restuccia Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Messina, Italy P. Ván (B) Department of Theoretical Physics, Wigner Research Centre for Physics, Konkoly Thege Miklós út. 29-33, Budapest H-1525, Hungary E-mail: [email protected] P. Ván Department of Energy Engineering, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, M˝ugyetem rkp. 3, Budapest 1111, Hungary P. Ván Montavid Thermodynamic Research Group, Budapest, Hungary
A. Famà et al.
ered in [15–17]. These investigations are often related to various concepts of non-equilibrium temperature, too. Second sound, the wavelike propagation of heat, is due to the inertia of internal energy. This property can be modelled by an additional non-equilibrium thermodynamic state variable. A straightforward choice for this additional vectorial state variable is the heat flux [18,19]. This choice leads to theories of Extended Thermodynamics (ET). This one requires a compatibility with kinetic theory [20–25], and the structure of the continuum theory will be compatible with the equations derived by moment series expansion of the Boltzmann equation, considering also a Cal
Data Loading...
