Transient Heat Conduction in Functionally Graded Hollow Cylinders and Spheres

2012 ◽  
Author(s):  
A. H. Akbarzadeh ◽  
Z. T. Chen
Keyword(s):  
Heat Conduction ◽  
Transient Heat Conduction ◽  
Functionally Graded ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Dual Phase ◽  
Conduction Theory ◽  
Hollow Cylinders ◽  
Fourier Heat Conduction ◽  
Cylinders And Spheres

In the present work, transient heat conduction in functionally graded (FG) hollow cylinders and spheres is investigated based on the non-Fourier heat conduction theories. Since the heat transmission has been observed to propagate at a finite speed for applications with very low temperature, short-pulse thermal-heating, and micro temporal and spatial scales, dual phase lag (DPL) and hyperbolic heat conduction theories are considered in current study instead of the conventional Fourier heat conduction theory. Except the phase lags which are assumed to be constant, all the other material properties of the hollow cylinders and spheres are taken to change continuously along the radial direction according to a power-law formulation with different non-homogeneity indices. The heat conduction equations are written based on the dual phase lag theory which includes the hyperbolic heat conduction theory as well. These equations are applied for axisymmetric hollow cylinders of infinite lengths and spherically symmetric hollow spheres. Using the Laplace transform and Bessel functions, the analytical solutions for temperature and heat flux are obtained in the Laplace domain. The solutions are then converted into the time domain by employing the fast Laplace inversion technique. The exact expression is obtained for the speed of thermal wave in FG cylinders and spheres based on the DPL and hyperbolic heat conduction theories. Finally, the current results are verified with those reported in the literature based on the hyperbolic heat conduction theory.

DUAL PHASE LAG HEAT CONDUCTION IN FUNCTIONALLY GRADED HOLLOW SPHERES

2014 ◽  
Vol 06 (01) ◽  
pp. 1450002 ◽  
Author(s):  
A. H. AKBARZADEH ◽  
Z. T. CHEN
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Hollow Spheres ◽  
Functionally Graded ◽  
Inversion Method ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Spherically Symmetric ◽  
Dual Phase ◽  
Phase Lags

In the present work, the dual phase lag heat conduction in functionally graded hollow spheres is investigated under spherically symmetric and axisymmetric thermal loading. The heat conduction equation is given based on the dual phase lag theory to consider the details of energy transport in the material in comparison with the non-Fourier hyperbolic heat conduction. All the material properties of the sphere are taken to vary continuously along the radial direction following a power-law with arbitrary non-homogeneity indices except the phase lags which are assumed to be constant for simplicity. The specified spherically symmetric and axisymmetric boundary conditions of the sphere lead to a 1D and 2D heat conduction problem, respectively. Employing the Laplace transform to eliminate the time dependency of the problem, analytical solutions are obtained for the temperature and heat flux. The final results in the time domain are obtained by a numerical Laplace inversion method. The speed of thermal wave in the functionally graded sphere based on the dual phase lag is compared with that of the hyperbolic heat conduction. Furthermore, the numerical results are shown to clarify the effects of phase lags and non-homogeneity indices on the thermal response. The current results are verified with those reported in the literature.

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 Heat Transfer Mechanisms During Femtosecond Laser Heating of Nano-Films Using 3-D Dual Phase Lag Model

Volume 4 ◽  
2004 ◽  
Author(s):  
Illayathambi Kunadian ◽  
J. M. McDonough ◽  
K. A. Tagavi
Keyword(s):  
Heat Conduction ◽  
Femtosecond Laser ◽  
Laser Heating ◽  
Three Dimensions ◽  
Grid Function ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Dual Phase ◽  
Time Step ◽  
Eigenmode Analysis

In the present work we investigate femtosecond laser heating of nanoscale metal films irradiated by a pulsating laser in three dimensions using the Dual Phase Lag (DPL) model and consider laser heating at different locations on the metal film. A numerical solution based on an explicit finite-difference method has been employed to solve the DPL heat conduction equation. The stability criterion for selecting a time step size is obtained using von Neumann eigenmode analysis, and grid function convergence tests have been performed. The energy absorption rate, which is used to model femtosecond laser heating, has been modified to accommodate for the three-dimensional laser heating. We compare our results with classical diffusion and hyperbolic heat conduction models and demonstrate significant differences among these three approaches. The present research enables us to study ultrafast laser heating mechanisms of nano-films in 3D.

Assessment of Models for Extracting Thermal Conductivity From Frequency Domain Thermoreflectance Experiments

2020 ◽  
Author(s):  
Siddharth Saurav ◽  
Sandip Mazumder
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Frequency Domain ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Computational Domain ◽  
Fourier Heat Conduction

Abstract The Fourier heat conduction and the hyperbolic heat conduction equations were solved numerically to simulate a frequency-domain thermoreflectance (FDTR) experimental setup. Numerical solutions enable use of realistic boundary conditions, such as convective cooling from the various surfaces of the substrate and transducer. The equations were solved in time domain and the phase lag between the temperature at the center of the transducer and the modulated pump laser signal were computed for a modulation frequency range of 200 kHz to 200 MHz. It was found that the numerical predictions fit the experimentally measured phase lag better than analytical frequency-domain solutions of the Fourier heat equation based on Hankel transforms. The effects of boundary conditions were investigated and it was found that if the substrate (computational domain) is sufficiently large, the far-field boundary conditions have no effect on the computed phase lag. The interface conductance between the transducer and the substrate was also treated as a parameter, and was found to have some effect on the predicted thermal conductivity, but only in certain regimes. The hyperbolic heat conduction equation yielded identical results as the Fourier heat conduction equation for the particular case studied. The thermal conductivity value (best fit) for the silicon substrate considered in this study was found to be 108 W/m/K, which is slightly different from previously reported values for the same experimental data.

Nonhomogeneous Dual-Phase-Lag Heat Conduction Problem: Analytical Solution and Select Case Studies

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Simon Julius ◽  
Boris Leizeronok ◽  
Beni Cukurel
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Generation ◽  
Integral Transform ◽  
Heat Conduction Problem ◽  
Relaxation Times ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Dual Phase

Finite integral transform techniques are applied to solve the one-dimensional (1D) dual-phase heat conduction problem, and a comprehensive analysis is provided for general time-dependent heat generation and arbitrary combinations of various boundary conditions (Dirichlet, Neumann, and Robin). Through the dependence on the relative differences in heat flux and temperature relaxation times, this analytical solution effectively models both parabolic and hyperbolic heat conduction. In order to demonstrate several exemplary physical phenomena, four distinct cases that illustrate the wavelike heat conduction behavior are presented. In the first model, following an initial temperature spike in a slab, the thermal evolution portrays immediate dissipation in parabolic systems, whereas the dual-phase solution depicts wavelike temperature propagation—the intensity of which depends on the relaxation times. Next, the analysis of periodic surface heat flux at the slab boundaries provides evidence of interference patterns formed by temperature waves. In following, the study of Joule heating driven periodic generation inside the slab demonstrates that the steady-periodic parabolic temperature response depends on the ratio of pulsatile electrical excitation and the electrical resistivity of the slab. As for the dual-phase model, thermal resonance conditions are observed at distinct excitation frequencies. Building on findings of the other models, the case of moving constant-amplitude heat generation is considered, and the occurrences of thermal shock and thermal expansion waves are demonstrated at particular conditions.

New Interpretation of Non-Fourier Heat Conduction in Processed Meat

2005 ◽  
Vol 127 (2) ◽  
pp. 189-193 ◽  
Author(s):  
Paul J. Antaki
Keyword(s):  
Heat Conduction ◽  
Experimental Evidence ◽  
Human Tissue ◽  
Processed Meat ◽  
Phase Lag ◽  
Dual Phase ◽  
Hyperbolic Case ◽  
Fourier Heat Conduction ◽  
New Interpretation ◽  
Hyperbolic Conduction

This work uses the “dual phase lag” (DPL) model of heat conduction to offer a new interpretation for experimental evidence of non-Fourier conduction in processed meat that was interpreted previously with hyperbolic conduction. Specifically, the DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. In addition, comparing the new interpretation to Fourier-based alternatives suggests that further study of all the interpretations could help advance the understanding of conduction in the processed meat and other biological materials such as human tissue.

Thermal Stress Associated With Non-Fourier Heat Conduction in Femtosecond Laser Heating of Multilayer Metallic Films

2018 ◽  
Author(s):  
Swarup Bag ◽  
M. Ruhul Amin
Keyword(s):  
Thin Film ◽  
Heat Conduction ◽  
Thermal Stress ◽  
Temperature Distribution ◽  
Pulse Laser ◽  
Laser Heating ◽  
Laser Source ◽  
Phase Lag ◽  
Dual Phase ◽  
Fourier Heat Conduction

In the present work, the deformation behavior in metallic film subjected to ultra-short laser heating is investigated. Static thermo-elastic behavior is predicted for 100 nm thin film of either single layer or multiple layers. The temperature distribution is estimated from dual-phase lag non-Fourier heat conduction model. The maximum temperature after single pulse is achieved 730 K. The temperature profile for this pulse laser is used to compute elastic stress and distortion field following the minimization of potential energy of the system. In the present work, the simulation has been proposed by developing 3D finite element based coupled thermo-elastic model using dual phase lag effect. The experimental basis of transient temperature distribution in ultra-short pulse laser is extremely difficult or nearly impossible, the model results have been validated with literature reported thermal results. Since the temperature distribution due to pulse laser source varies with time, the stress analysis is performed in incremental mode. Hence, a sequentially coupled thermo-mechanical model is developed that is synchronized between thermal and mechanical analysis in each time steps of transient problem. The maximum equivalent stress is achieved 0.3 GPa. Numerical results show that the predicted thermal stress may exceeds the tensile strength of the material and may lead to crack or damage the thin film.

Sign in / Sign up

Export Citation Format

Share Document