scholarly journals Dual-phase-lag one-dimensional thermo-porous-elasticity with microtemperatures

2021 ◽  
Vol 40 (6) ◽  
Author(s):  
Z. Liu ◽  
R. Quintanilla
Keyword(s):  
Heat Conduction ◽  
Elastic Problem ◽  
Linear Operators ◽  
Phase Lag ◽  
Dual Phase ◽  
Polynomial Stability ◽  
One Dimensional ◽  
Semigroups Of Linear Operators ◽  
Relaxation Parameters ◽  
Decay Of Solutions

AbstractThis paper is devoted to studying the linear system of partial differential equations modelling a one-dimensional thermo-porous-elastic problem with microtemperatures in the context of the dual-phase-lag heat conduction. Existence, uniqueness, and exponential decay of solutions are proved. Polynomial stability is also obtained in the case that the relaxation parameters satisfy a certain equality. Our arguments are based on the theory of semigroups of linear operators.

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.

scholarly journals Qualitative aspects in dual-phase-lag heat conduction

2006 ◽  
Vol 463 (2079) ◽  
pp. 659-674 ◽  
Author(s):  
Ramón Quintanilla ◽  
Reinhard Racke
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Uniqueness Result ◽  
Phase Lag ◽  
Dual Phase ◽  
Natural Property ◽  
Unbounded Solutions ◽  
Decay Of Solutions ◽  
Exponentially Stable ◽  
Well Posed

We investigate the equation of the dual-phase-lag heat conduction proposed by Tzou. To describe this equation, we use the phase lag of the heat flux and the phase lag of the gradient of the temperature. We analyse the basic properties of the solutions of this problem. First, we prove that when both parameters are positive, the problem is well posed and the spatial decay of solutions is controlled by an exponential of the distance. When the phase lag of the gradient of the temperature is bigger than the phase lag of the heat flux, the problem is exponentially stable (which is a natural property to expect for a heat equation) and the spatial behaviour is controlled by an exponential of the square of the distance. Also, a uniqueness result for unbounded solutions is proved in this case.

Thermoelastic damping in the size-dependent micro/nanobeam resonator with nonlocal dual-phase-lag heat conduction

2021 ◽  
Vol 169 ◽  
pp. 108437
Author(s):  
Hongyue Zhou ◽  
Haobin Jiang ◽  
Pu Li ◽  
Hongtao Xue ◽  
Billy Bo
Keyword(s):  
Heat Conduction ◽  
Phase Lag ◽  
Dual Phase ◽  
Thermoelastic Damping ◽  
Size Dependent
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