In this article thermoelastic damping in nano-beam resonators is investigated based on nonlocal theory of elasticity and the Euler-Bernoulli beam assumptions. The governing equation of deflection of the beam is obtained from shear and moment resultants and stress–strain relationship of the nonlocal elasticity model and also the governing equations of thermoelastic damping are established by usi...

In this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the strength of the time- dependent heat source using the temperature distribution at a point in a three layer system. Also, the effect of noisy data on final solution is studied. The numerical solution of the governing equations is obtained b...

The decay of a spatially sinusoidal temperature perturbation (thermal grating) via thermal transport by both conduction and radiation is analyzed theoretically. intrinsic non-radiative described the heat diffusion equation while radiative for non-scattering absorbing medium. We solve coupled equations analytically obtain grating rate, which leads to an explicit expression contribution effective...

Lattice networks of oscillators have been considered for a long time as good models for studying macroscopic energy trasport and its diffusion, i.e. for obtaining, on a macroscopic space-time scale, heat equation and Fourier law of conduction ([1]). It is well understood that the diffusive behavior of the energy is due to the non-linearity of the interactions, and that purely deterministic harm...

Heat conduction in an anisotropic inhomogeneous medium is considered. The conductivities vary exponentially in one fixed but arbitrary direction. The Green’s function corresponding to a point source is constructed. Two methods are used, one using Fourier transforms and one involving certain changes of variables in the governing partial differential equation. Solutions in both two and three dime...

A recently developed Shastry formalism for energy transport is used to analyze the temporal behavior of the energy and heat transport in metals. Comparison with Cattaneo’s equation is performed. Both models show the transition between ballistic and diffusive regimes. Furthermore, because the new model considers the discrete character of the lattice, it highlights some new phenomena such as osci...

We propose an efficient boundary collocation method for the solution of certain twoand three-dimensional problems of steady-state heat conduction in isotropic bimaterials. In particular, in two dimensions we consider the case where a circular region composed of one material is coated with an annular region of another material. In three dimensions, we examine the corresponding case for axisymmet...

We investigate the problem of heat conduction across molecular junctions connecting two nanoparticles, both in vacuum and in a liquid environment, using classical molecular dynamics simulations. In vacuum, the well-known result of a length independent conductance is recovered; its precise value, however, is found to depend sensitively on the overlap between the vibrational spectrum of the junct...

We give a uniform bound from below on the temperature for a variant of the compressible Navier-Stokes–Fourier system, under suitable hypotheses. This system of equations forms a mathematical model of the motion of a compressible fluid subject to heat conduction. Building upon the work of [A. Mellet and A. Vasseur, Monatsh. Math., 157 (2009), pp. 143–161], we identify a class of weak solutions s...

Linear boundary value problems in heat conduction have been investigated extensively for a diverse variety of boundary conditions, but almost invariably these have been of the type that produce self-adjoint problems. The property of selfadjointness makes it possible to obtain readily the solution of steady and unsteady-state heat conduction problems in the form of a series expansion of orthogon...