Exponential and polynomial decay for a laminated beam with Fourier’s law of heat conduction and possible absence of structural damping

In previous work (Z. Angew. Math. Phys. 68(2), 2017), Apalara considered a one dimensional thermoelastic laminated beam under Cattaneo’s law of heat conduction and proved the exponential and polynomial decay results depend on the stability number χT . In this paper, we continue to study the same system and show that the solution of the concerned system lacks of exponential decay result in the case χT ≠ 0 which solves the open problem proposed by Apalara (Z. Angew. Math. Phys. 68(2), 2017).

Download Full-text

Exponential and Polynomial Decay for a Laminated Beam with Fourier's Type Heat Conduction

10.20944/preprints201702.0058.v2 ◽

2019 ◽

Author(s):

Wenjun Liu ◽

Weifan Zhao

Keyword(s):

Heat Conduction ◽

Energy Method ◽

Rotation Angle ◽

Polynomial Decay ◽

Structural Damping ◽

Laminated Beam ◽

Wave Speeds ◽

One Dimensional ◽

Exponentially Stable ◽

Well Posed

In this paper, we study the well-posedness and asymptotics of a one-dimensional thermoelastic laminated beam system either with or without structural damping, where the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is well-posed by using Lumer-Philips theorem, and prove that the system is exponentially stable if and only if the wave speeds are equal, by using the perturbed energy method and Gearhart-Herbst-Prüss-Huang theorem. Furthermore, we show that the system with structural damping is polynomially stable provided that the wave speeds are not equal, by using the second-order energy method.

Download Full-text

Evaluation of the thermal conductance of flip-chip bonding structure utilizing the measurement based on Fourier’s law of heat conduction at steady-state

AIP Advances ◽

10.1063/1.5028318 ◽

2018 ◽

Vol 8 (6) ◽

pp. 065208 ◽

Cited By ~ 3

Author(s):

Chia-Yu Wu ◽

Yin-Hsien Huang ◽

Hsin-Han Wu ◽

Tsung-Eong Hsieh

Keyword(s):

Heat Conduction ◽

Steady State ◽

Flip Chip ◽

Thermal Conductance ◽

Fourier’S Law ◽

Bonding Structure ◽

Flip Chip Bonding ◽

Fourier's Law

Download Full-text

Cooling Dynamics of a Gold Nanoparticle in a Host Medium Under Ultrafast Laser Pulse Excitation: A Ballistic-Diffusive Approach

ASME 2008 First International Conference on Micro/Nanoscale Heat Transfer, Parts A and B ◽

10.1115/mnht2008-52228 ◽

2008 ◽

Author(s):

Majid Rashidi-Huyeh ◽

Sebastian Volz ◽

Bruno Palpant

Keyword(s):

Heat Conduction ◽

Laser Pulse ◽

Gold Nanoparticle ◽

Particle Temperature ◽

Surrounding Medium ◽

Pulse Excitation ◽

Fourier’S Law ◽

Host Medium ◽

The Matrix ◽

Fourier's Law

We present a numerical model allowing to determine the electron and lattice temperature dynamics in a gold nanoparticle under subpicosecond pulsed excitation, as well as that of the surrounding medium. For this, we have used the electron-phonon coupling equation in the particle with a source term linked with the laser pulse, and the ballistic-diffusive equations for heat conduction in the host medium. Our results show that the heat transfer rate from the particle to the matrix is significantly smaller than the prediction of Fourier’s law. Consequently, the particle temperature rise is much larger and its cooling dynamics is much slower than that obtained using Fourier’s law, which is attributed to the nonlocal and nonequilibrium heat conduction in the vicinity of the nanoparticle. These results are expected to be of great importance for interpreting pump-probe experiments performed on single nanoparticles or nanocomposite media.

Download Full-text

Bragg Mirrors for Thermal Waves

10.20944/preprints202110.0174.v1 ◽

2021 ◽

Author(s):

Angela Camacho de la Rosa ◽

David Becerril ◽

Guadalupe Gómez-Farfán ◽

Raul P Esquivel-Sirvent

Keyword(s):

Heat Conduction ◽

Numerical Calculation ◽

Thermal Waves ◽

Wave Surface ◽

Fourier’S Law ◽

Bragg Mirror ◽

Fourier's Law ◽

Very High ◽

Mirror Configuration ◽

High Reflectance

We present a numerical calculation of the heat transport in a Bragg mirror configuration made of materials that do not obey Fourier's law of heat conduction. The Bragg mirror is made of materials that are described by the Cattaneo-Vernotte equation. By analyzing the Cattaneo-Vernotte equation's solutions, we define the thermal wave surface impedance to design highly reflective thermal Bragg mirrors. Even for mirrors with a few layers, very high reflectance is achieved ($>90\%$). The Bragg mirror configuration is also a system that makes evident the wave-like nature of the solution of the Cattaneo-Vernotte equation by showing frequency pass-bands that are absent if the materials obey the usual Fourier's law.

Download Full-text