Dynamic Crack Extension Along the Interface of Materials That Differ in Thermal Properties: Convection and Thermal Relaxation

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Crack Extension ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Crack Edge ◽  
Dynamic Crack ◽  
Solution Behavior ◽  
Special Cases ◽  
Fourier Heat Conduction

Moving surface loads cause crack extension at a constant subcritical speed between perfectly bonded materials. The materials differ only in thermal properties and are governed by coupled thermoelastic equations that admit as special cases Fourier heat conduction and thermal relaxation with one or two relaxation times. Convection from the crack surfaces is allowed and for the latter two models is itself influenced by thermal relaxation. A dynamic steady state of plane strain is assumed. Fourier heat conduction is shown to dominate away from the crack edge at low speeds; solution behavior at the crack edge at high speeds depends upon the particular thermal model. Thermal mismatch is seen to cause solution behavior similar to that for the isothermal bimaterial, and so insight into the case of general material mismatch is provided.

Stoneley Wave Generation in Joined Materials With and Without Thermal Relaxation Due to Thermal Mismatch

2007 ◽  
Vol 74 (5) ◽  
pp. 1019-1025 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Relaxation Time ◽  
Heat Conduction ◽  
Thermal Relaxation ◽  
Interface Temperature ◽  
Stoneley Wave ◽  
Asymptotic Results ◽  
Time Step ◽  
Conduction Model ◽  
Special Cases ◽  
Fourier Heat Conduction

Two perfectly bonded, thermoelastic half-spaces differ only in their thermal parameters. Their governing equations include as special cases the Fourier heat conduction model and models with either one or two thermal relaxation times. An exact solution in transform space for the problem of line loads applied to the interface is obtained. Even though the elastic properties of the half-spaces are identical, a Stoneley function arises, and conditions for the existence of roots are more restrictive than for the isothermal case of two elastically dissimilar half-spaces. Moreover, roots may be either real or imaginary. An exact expression for the time transform of the Stoneley residue contribution to interface temperature change is derived. Asymptotic results for the inverse that, valid for either very short or very long times after load application, is obtained and show that, for long times, residue contributions for all three special cases obey Fourier heat conduction. Short-time results are sensitive to case differences. In particular, a time step load produces a propagating step in temperature for the Fourier and double-relaxation time models, but a propagating impulse for the single-relaxation time model.

Analysis of the Thermal Response in Micromachine under the Thermal Shock

2011 ◽  
Vol 464 ◽  
pp. 583-587
Author(s):  
Ying Ze Wang ◽  
Xin Nan Song
Keyword(s):  
Heat Conduction ◽  
Relaxation Times ◽  
Boundary Surface ◽  
Thermal Relaxation ◽  
Thermal Response ◽  
Heat Propagation ◽  
Hyperbolic Heat Conduction ◽  
Thermal Relaxation Times ◽  
Fourier Heat Conduction ◽  
Sudden Temperature Change

The thermal response for given micromachine with the boundary surface exposed to sudden temperature change is studied by deriving an analytical solution of the hyperbolic heat conduction equation. Using the obtained analytical expression, the temperature profiles at the outer surface and interior of the micro beam are evaluated for various thermal relaxation times. The behaviors of hyperbolic heat propagation in micro beam are analyzed and possible anomalies are discussed by comparing the thermal behaviors of Fourier heat conduction.

Mechanical and thermal properties of the glassy semiconductor chlorinated Se0 997As0 003 used as an X-ray imaging material

1989 ◽  
Vol 67 (7) ◽  
pp. 686-693 ◽  
Author(s):  
S. O. Kasap ◽  
S. Yannacopoulos
Keyword(s):  
Thermal Properties ◽  
Structural Changes ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Mechanical And Thermal Properties ◽  
Debye Relaxation ◽  
X Ray ◽  
Temperature Range ◽  
Glass Transformation ◽  
X Ray Imaging

Mechanical and thermal properties of a typical X-ray imaging material amorphous Se0.997As0.003, chlorinated in the ppm range were investigated using thermal microhardness analysis (TμHA) and differential scanning calorimetry (DSC). The experiments were carried out over a temperature range encompassing the glass transformation to study the nature of structural changes controlling the mechanical and thermal properties. It is shown that the mechanical property microhardness when examined on an Itoh–Shishokin plot of log Vickers hardness number (VHN) vs. temperature (T) exhibits a hardness transition temperature, Tg*, in the glass transformation region. The rates of relaxation of the mechanical and thermal properties in the glass transformation region were studied by investigating the heating rate dependence of the glass transition temperatures, Tg* and Tg, defined empirically on the log VHN vs. T behavior and the DSC glass transformation endotherm, respectively. By applying the present thermoanalytical methods, it has proved possible to identify a typical Vogel–Tammann–Fulcher type of behavior in the mechanical and thermal relaxation times that correlates remarkably well with the viscosity–temperature data of M. Cukierman and D. R. Uhlmann (J. Non-Cryst. Solids, 12, 199 (1973)) as well as the dielectric loss experiments of M. Abkowitz, D. F. Pochan, and J. M. Pochan (J. Appl. Phys. 51, 1539 (1980)). The latter had previously exposed a Williams–Landel–Ferry relation for the Debye relaxation times in a-Se and a-Se: 1% As. It is therefore concluded that the behavior of mechanical, thermal, and dielectric properties of a-Se0997As0003 in the glass transformation region is inversely proportional to the viscosity, which in turn can be adequately described over a temperature range above ~30 °C by a Vogel expression.

The Thermal Behavior Analysis of a Human Eye Subjected to Laser Radiation Under the Non-Fourier Law of Heat Conduction

2021 ◽  
Vol 143 (4) ◽  
Author(s):  
Najat A. Alghamdi ◽  
Hamdy M. Youssef
Keyword(s):  
Heat Conduction ◽  
Laser Irradiation ◽  
Power Density ◽  
Evaporation Rate ◽  
Relaxation Times ◽  
Blood Perfusion ◽  
Absolute Temperature ◽  
Ambient Temperatures ◽  
Human Eye ◽  
Fourier Heat Conduction

Abstract Purpose: The physiological conditions and environment have vital roles in the heat transfer in the human tissues, such as the multilayered human-eye. In this paper, a mathematical model of the human eye subjected to an exponential laser beam concerning the change in blood perfusion, porosity, evaporation rate, and ambient temperatures has been constructed based on non-Fourier heat conduction law. Methods: The human eye has been divided into six layers. Appropriate boundary and interface conditions have been considered. A separable function has been assumed, and the twelve equations have been formulated in matrix form. The solutions have been calculated by using maple 17 software. Results: The results have been shown in figures with different cases. The absolute temperature distribution based on various values of the power density of laser irradiation and relaxation times parameters have been discussed first. The effect of the blood perfusion, porosity, evaporation rate, time, and ambient temperatures have also been discussed. Conclusions: The power density of laser irradiation, blood perfusion, porosity, evaporation rate, time, and ambient temperatures significantly affects the value of the temperature passing through the human eye layers.

Simulation and Optimization Design of the Heat Waveguide Optical Switch on Non-Fourier Heat Conduction Theory

2014 ◽  
Vol 556-562 ◽  
pp. 2093-2096
Author(s):  
Ji Yun Song ◽  
Xiao Min Zhang ◽  
Zhong Xiang Chu ◽  
Long Zhang
Keyword(s):  
Relaxation Time ◽  
Heat Conduction ◽  
Optical Switch ◽  
Thermal Relaxation ◽  
Core Layer ◽  
Response Speed ◽  
Thermal Relaxation Time ◽  
Simulation And Optimization ◽  
Conduction Theory ◽  
Fourier Heat Conduction

The temperature distribution of the heat waveguide optical switch with different cladding materials is simulated on Fourier heat conduction theory and non-Fourier heat conduction theory, discussing effect of the cladding materials on the power consumption and the response speed of the device. The main conclusions as follows: (1)The response speed of waveguide optical switch with silica as cladding is faster than that with PMMA as cladding. (2)Thermal relaxation time has significant influence on the temperature of the core layer: the variation of optical switch core layer temperature gets bigger with the increase of material thermal relaxation time.

scholarly journals On the flexural and extensional thermoelastic waves in orthotropic plates with two thermal relaxation times

2004 ◽  
Vol 2004 (1) ◽  
pp. 69-83 ◽  
Author(s):  
K. L. Verma ◽  
Norio Hasebe
Keyword(s):  
Orthotropic Plate ◽  
Finite Thickness ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Orthotropic Plates ◽  
Special Cases ◽  
Thermal Relaxation Times ◽  
Modes Of Vibration ◽  
The Waves ◽  
Thermoelastic Waves

Analysis for the propagation of plane harmonic thermoelastic waves in an infinite homogeneous orthotropic plate of finite thickness in the generalized theory of thermoelasticity with two thermal relaxation times is studied. The frequency equations corresponding to the extensional (symmetric) and flexural (antisymmetric) thermoelastic modes of vibration are obtained and discussed. Special cases of the frequency equations are also discussed. Numerical solution of the frequency equations for orthotropic plate is carried out, and the dispersion curves for the first six modes are presented for a representative orthotropic plate. The three motions, namely, longitudinal, transverse, and thermal, of the medium are found dispersive and coupled with each other due to the thermal and anisotropic effects. The phase velocity of the waves gets modified due to the thermal and anisotropic effects and is also influenced by the thermal relaxation time. Relevant results of previous investigations are deduced as special cases.

Numerical simulation of non-Fourier effects in combined heat transfer

2010 ◽  
Vol 225 (2) ◽  
pp. 429-436
Author(s):  
E Izadpanah ◽  
S Talebi ◽  
M H Hekmat
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Splitting Method ◽  
Thermal Relaxation ◽  
Conduction Equation ◽  
Hyperbolic Heat Conduction ◽  
Wave Nature ◽  
Fourier Heat Conduction ◽  
Combined Heat Transfer

The non-Fourier effects on transient and steady temperature distribution in combined heat transfer are studied. The processes of coupled conduction and radiation heat transfer in grey, absorbing, emitting, scattering, one-dimensional medium with black boundary surfaces are analysed numerically. The hyperbolic heat conduction equation is solved by flux splitting method, and the radiative transfer equation is solved by P1 approximate method. The transient thermal responses obtained from non-Fourier heat conduction equation are compared with those obtained from the Fourier heat conduction equation. The results show that the non-Fourier effect can be important when the conduction to radiation parameter and the thermal relaxation time are larger. Further, the radiation effect is more pronounced at small values of single scattering albedo and conduction to radiation parameters. Analysis results indicate that the internal radiation in the medium significantly influences the wave nature.

The Model of Non-Fourier Heat Conduction in a Kind of Two-Phase Medium With Great Different Heat Conductivity

2008 ◽  
Author(s):  
Wen-Qiang Lu ◽  
Junfeng Lu
Keyword(s):  
Heat Flux ◽  
Relaxation Time ◽  
Heat Conduction ◽  
Heat Conductivity ◽  
Rapid Heating ◽  
Relaxation Times ◽  
High Heat Flux ◽  
Phase Lag ◽  
Two Phase ◽  
Fourier Heat Conduction

The model of non-Fourier heat conduction in a kind of two-phase mediums with great different heat conductivity is deduced by the idea and mathematics of dual phase lag. It is pointed out that the relaxation times to establish heat flux and temperature gradient include both kinds in this model: the relaxation time appeared under the conditions of applied high heat flux and rapid heating, the relaxation time introduced by the non-equilibrium heat exchange between the two-phase mediums. It is very important to distinguish the both kinds of relaxation times for analyzing and explaining the experimental phenomena of non-Fourier heat conduction in this kind of two-phase mediums.

Sign in / Sign up

Export Citation Format

Share Document