Global existence and asymptotic behavior for one-dimensional thermoelasticity of integral type with hyperbolic heat conduction

2015 ◽  
Vol 113 ◽  
pp. 372-384
Author(s):  
Yuxi Hu
Keyword(s):  
Asymptotic Behavior ◽  
Heat Conduction ◽  
Global Existence ◽  
Hyperbolic Heat Conduction ◽  
Integral Type ◽  
One Dimensional

Analysis of One-Dimensional Hyperbolic Heat Conduction in a Functionally Graded Thin Plate

2011 ◽  
Author(s):  
Mohammad Reza Raveshi ◽  
Shayan Amiri ◽  
Ali Keshavarz
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Functionally Graded ◽  
Dimensionless Temperature ◽  
Hyperbolic Heat Conduction ◽  
Temperature Peak ◽  
Trial Solution ◽  
One Dimensional ◽  
Graded Material ◽  
The Time Domain

This paper presents the analytical solution of one-dimensional non-Fourier heat conduction problem for a finite plate made of functionally graded material. To investigate the influence of material properties variation, exponential space-dependant functions of thermal conductivity and specific heat capacity are considered. The problem is solved analytically in the Laplace domain, and the final results in the time domain are obtained using numerical inversion of the Laplace transform. The trial solution method with collocation optimizing criterion has been applied to solve the hyperbolic heat conduction equation based on polynomial shape function approximation. Due to the reflection and interaction of the thermal waves, the temperature peak happens on the insulated wall of the FGM plate, so the major aim of this paper is to find the amount of temperature peak and the time at which it happens. It has been shown that the dimensionless temperature peak and its happening time increase along with an increase in the dimensionless relaxation time. The results are validated by comparison with the results from an exact available solution solved at special case which shows a close agreement.

One-Dimensional Temperature and Stress Distributions Associated with Hyperbolic Heat Conduction

2012 ◽  
Vol 249-250 ◽  
pp. 962-967
Author(s):  
B. Wang
Keyword(s):  
Heat Conduction ◽  
Physical Mechanism ◽  
Modern Science ◽  
Sufficient Accuracy ◽  
Hyperbolic Heat Conduction ◽  
Stress Distributions ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Practical Engineering ◽  
Fourier Heat Conduction

The classical Fourier heat conduction law gives sufficient accuracy for many practical engineering applications. However, it cannot exactly reflect the real physical mechanism of heat conduction by highly-varying thermal load, at very low temperatures, or at nanoscale. The hyperbolic heat conduction equation can better explain heat conduction in solids. However, such equation is very difficult to solve. This paper studies the temperature field for a 1-D plate and a 1-D cylinder. The associated thermal stress for a 1-D plate is also given. Only in these simple situations, closed form solutions are possible and are given. The results can be used in the future analysis of thermal shock cracking and reliability analysis of materials in modern science and technology.

Heat conduction in one-dimensional functionally graded media based on the dual-phase-lag theory

2012 ◽  
Vol 227 (4) ◽  
pp. 744-759 ◽  
Author(s):  
AH Akbarzadeh ◽  
ZT Chen
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Functionally Graded ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Dual Phase ◽  
Spherical Coordinates ◽  
One Dimensional ◽  
Phase Lags ◽  
Functionally Graded Media

In this article, heat conduction in one-dimensional functionally graded media is investigated based on the dual-phase-lag theory to consider the microstructural interactions in the fast transient process of heat conduction. All material properties of the media are assumed to vary continuously according to a power-law formulation with arbitrary non-homogeneity indices except the phase lags which are taken constant for simplicity. The one-dimensional heat conduction equations based on the dual-phase-lag theory are derived in a unified form which can be used for Cartesian, cylindrical, and spherical coordinates. A semi-analytical solution for temperature and heat flux is presented using the Laplace transform to eliminate the time dependency of the problem. The results in the time domain are then given by employing a numerical Laplace inversion technique. The semi-analytical solution procedure leads to exact expressions for the thermal wave speed in one-dimensional functionally graded media with different geometries based on the dual-phase-lag and hyperbolic heat conduction theories. The transient temperature distributions have been found for various types of dynamic thermal loading. The numerical results are shown to reveal the effects of phase lags, non-homogeneity indices, and thermal boundary conditions on the thermal responses for different temporal disturbances. The results are verified with those reported in the literature for hyperbolic heat conduction in cylindrical and spherical coordinates.

Numerical Simulation of One-Dimensional Hyperbolic Heat Conduction Equation in Longitudinal Fins With Different Profiles

2010 ◽  
Author(s):  
Keivan Bamdad Masouleh ◽  
Hossein Ahmadikia ◽  
Aziz Azimi
Keyword(s):  
Heat Conduction ◽  
Numerical Solutions ◽  
Discontinuity Point ◽  
Cross Sectional Area ◽  
Hyperbolic Heat Conduction ◽  
Variable Cross ◽  
Sectional Area ◽  
Cross Sectional ◽  
One Dimensional ◽  
Temperature Distributions

In this paper, the steady/unsteady heat conduction in the longitudinal fins with variable cross sectional area under the periodic thermal conditions is examined. Three different one-dimensional fins are considered and solved numerically by implicit finite difference method. In the hyperbolic equation the heat wave propagates with the finite speed hence the sharp discontinuities appear at the temperature distributions. In the explicit solution oscillations appear at discontinuity point which is greatly improved at the implicit method. In the present study temperature distributions are obtained for non-Fourier fins with different profiles. The effects of frequency of temperature oscillation, relaxation time and fin cross sectional area are studied on the temperature and location of the discontinuity of temperature. In order to validate the obtained results of the present study, these results have been compared to those of numerical solutions of the non-Fourier fin with constant cross sectional area. This comparison confirms the correctness of the current results.

Sign in / Sign up

Export Citation Format

Share Document