Related papers: Lagrangian based heat conduction
In the literature, one can find numerous modifications of Fourier's law from which the first one is called Maxwell-Cattaneo-Vernotte heat equation. Although this model has been known for decades and successfully used to model…
The second law of thermodynamics is a useful and universal tool to derive the generalizations of the Fourier's law. In many cases, only linear relations are considered between the thermodynamic fluxes and forces, i.e., the conduction…
A novel equation of heat conduction is derived with the help of a generalized entropy current and internal variables. The obtained system of constitutive relations is compatible with the momentum series expansion of the kinetic theory. The…
The propagation of heat and thermal signals in the form of travelling waves is investigated for a nonlinear Maxwell-Cattaneo-Vernotte equation. The exact wave solutions are derived by expressing the thermal conductivity and the relaxation…
In our former study (J. Phys. A: Math. Theor. 43, (2010) 325210 or arXiv:1002.0999v1 [math-ph]) we introduced a modified Fourier-Cattaneo law and derived a non-autonomous telegraph-type heat conduction equation which has desirable…
Among the three heat conduction modes, the ballistic propagation is the most difficult to model. In the present paper, we discuss its physical interpretations and showing different alternatives to its modeling. We highlight two of them: a…
For heat flux $q$ and temperature $T$ we introduce a modified Fourier--Cattaneo law $q_t+ l \frac{q}{t}= - kT_x .$ The consequence of it is a non-autonomous telegraph-type equation. % $\epsilon S_{tt} + \frac{a}{t} S_t = S_{xx}$ . This…
Analytic solutions for cylindrical thermal waves in solid medium is given based on the nonlinear hyperbolic system of heat flux relaxation and energy conservation equations. The Fourier-Cattaneo phenomenological law is generalized where the…
A linear irreversible thermodynamic framework of heat conduction in rigid conductors is introduced. The deviation from local equilibrium is characterized by a single internal variable and a current intensity factor. A general constitutive…
We study nonlinear heat conduction equations with memory effects within the framework of the fractional calculus approach to the generalized Maxwell-Cattaneo law. Our main aim is to derive the governing equations of heat propagation,…
Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order…
Heat conduction in dielectric crystals originates from the propagation of atomic vibrations, whose microscopic dynamics is well described by the linearized phonon Boltzmann transport equation. Recently, it was shown that thermal…
We establish some fixed-time decay estimates in Lebesgue spaces for the fractional heat propagator $e^{-tH^{\beta}}$, $t, \beta>0$, associated with the harmonic oscillator $H=-\Delta + |x|^2$. We then prove some local and global…
A new equation, rooted in the theory of Brownian motion, is proposed for describing heat conduction by phonons. Though a finite speed of propagation is a built-in feature of the equation, it does not give rise to an inauthentic wave front…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…
We obtain explicit expressions for one unknown thermal coefficient (among the conductivity, mass density, specific heat and latent heat of fusion) of a semi-infinite material through the one-phase fractional Lam\'e-Clapeyron-Stefan problem…
We propose a prescription based on the Fokker-Planck equation in the Stratonovich approach, with the diffusion coefficient dependent on temporal and spatial coordinates, for describing heat conduction by phonons in small structures. This…
We present a general framework for studying strongly coupled radiative and conductive heat transfer between arbitrarily shaped bodies separated by sub-wavelength distances. Our formulation is based on a macroscopic approach that couples our…
This paper introduces a Bayesian inference framework for two-dimensional steady-state heat conduction, focusing on the estimation of unknown distributed heat sources in a thermally-conducting medium with uniform conductivity. The goal is to…
We develop a self-consistent theoretical formalism to model the dynamics of heat transfer in dissipative, dispersive, anisotropic nanoscale media, such as metamaterials. We employ our envelope dyadic Green's function method to solve…