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Diffusion and convective transport of particles
Published in S. Mostafa Ghiaasiaan, Convective Heat and Mass Transfer, 2018
Heat transfer due to ballistic phonon effects. According to the hyperbolic heat conduction theory, heat waves propagate at a finite speed, named the speed of second sound. According to quantum mechanics theory, heat diffusion takes place as a result of the motion of phonons which are fictitious particles that move with the latter speed of second sound. The mean free path of phonons can be calculated from Debye’s theory: λphonon=10aTmγT,
Nanoscale Energy Transport
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2019
Jafar Ghazanfarian, Zahra Shomali, Shiyun Xiong
Below the lambda point, the superfluidity characteristics appear including zero viscosity, the second velocity of sound, and very high thermal conductivity. The second sound regime originates from fluctuations in the density of phonons. The second sound becomes important in applications such as superfluids, cryogenic liquid helium, heat pulses, and dielectrics [9].
Thermal Wave in Phonon Hydrodynamic Regime by Phonon Monte Carlo Simulations
Published in Nanoscale and Microscale Thermophysical Engineering, 2020
One advantage of the MC method is that it deals with N process and R process individually and it is easy to analyze the influences of each process. According to the differences in phonon scatterings, the thermal waves are divided into two categories, namely ballistic thermal wave and hydrodynamic thermal wave. They are sorted by the scattering type, traveling length, speed, and shapes. The concept of second sound is thought to be the experimental observation of the combination of these two kinds of waves. When thermal wave propagates, two kinds of dissipation are involved, that is, spatial dissipation and resistance dissipation. The former keeps the conservation of phonon momentum, but lengthens the wavelength and decreases the peak value, while the latter reduces the phonon momentum and maintains the wavelength. Besides, the temperature profiles predicted by the phonon MC simulations are compared with those hyperbolic heat conduction equations. The influences of viscous term and convective term are revealed by numerical simulations. It is found that the current models are not suitable to describe the spatial dissipation effect, which results from the spatial dispersion of phonon directions. More accurate hyperbolic models are required in further investigation.
Stress waves in laser-material interaction: From atomistic understanding to nanoscale characterization
Published in Journal of Thermal Stresses, 2023
Here ρ, cp, B, G, and βT are the density, specific heat, bulk and shear moduli of elasticity, and thermal expansion coefficient of the target. T and u are temperature and displacement in the x direction, and β is the laser beam absorption coefficient as β = 1/τe (τe the laser beam absorption depth). I is the laser intensity that varies with time. Under the validity of Fourier’s law of heat conduction, we will have with k as the thermal conductivity of the target. Under very fast laser heating, e.g., the laser pulse width is comparable to or shorter than the energy carriers thermal relaxation time, or called mean free time τ, this relation has to be modified as to account for the time delay between heat flux and temperature gradient. This effect is termed “non-Fourier effect”. Such consideration will lead to the second sound wave, which is usually observed under reduced temperatures where the energy carriers experience significantly reduced phonon scattering and will have a much longer mean free time. Recent work has reported second sound wave over 200 K in graphite, whose very high thermal conductivity and low phonon scattering enabled this observation [10]. The displacement and temperature of the target are similar to the displacement and kinetic energy of a harmonic oscillator, whose potential and potential energies exchange with each other continuously. Therefore, in fact the temperature of the target could be varied by the strong local stress (related to potential energy). Under such frame, the right side of Eq. (1) will have an extra term as where T0 is the equilibrium temperature [11].
Exponential decay and numerical solution of nonlinear Bresse-Timoshenko system with second sound
Published in Journal of Thermal Stresses, 2022
Salim Adjemi, Ahmed Berkane, Salah Zitouni, Tahar Bechouat
From the physical point of view, it is well known that the model using the classic Fourier’s law leads to the physical paradox of infinite speed of heat propagation. Many theories have subsequently emerged, to overcome this physical paradox but still keeping the essentials of a heat conduction process. One of which is the advent of the second sound effects observed experimentally in materials at a very low temperature. Second sound effects arise when heat is transported by a wave propagation process instead of the usual diffusion. This theory suggests replacing the classic Fourier’s law where γ is the coefficient of thermal conductivity and q is the heat flux by a modified law of heat conduction called Cattaneo’s law Here, the parameter represents the relaxation time describing the time lag in the response of the heat flux to a gradient in the temperature. The obtained heat system is of hyperbolic type and hence, automatically, eliminating the paradox of infinite speeds. Among the works that have been realized in this field, we refer the reader to [1, 2]. In the following Figure, we introduce the displacements and the rotation angle in the plane as well as the temperature distribution with its contribution to the deformation of the beam as shown in many works for instance [3]. where the longitudinal displacement of points lying on the x1-axis, the angle of rotation for the normal to the x1-axis,