Mass Nature of Heat and Its Applications I: Motion of Thermomass Fluid and General Heat Conduction Law

2010 ◽  
Author(s):  
Zeng-Yuan Guo ◽  
Bing-Yang Cao
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Gas Flow ◽  
Short Pulse ◽  
Rest Mass ◽  
Inertial Force ◽  
High Heat Flux ◽  
Phase Lag ◽  
Energy Relation ◽  
Inertial Terms

The concept of thermomass is defined as the equivalent mass of thermal energy according to the Einstein’s mass-energy relation. Hence, the phonon gas in dielectrics can be regarded a weighty, compressible fluid. Heat conduction in the medium, where the rest mass lattices or molecules acts the porous framework, resembles the gas flow through the porous medium. Newton mechanics has been applied to establish the equation of state and the equation of motion for the phonon gas as in fluid mechanics, since the drift velocity of a phonon gas is normally much less than the speed of light. The momentum equation of the thermomass gas, including the driving, inertial and resistant forces, is a damped wave equation, which is in fact the general conduction law. This is because it reduces to the CV (Cattaneo-Vernotte) model or the single phase-lag model as the heat flux related inertial terms are neglected, and reduces to Fourier’s heat conduction law as all inertial terms are neglected. Therefore, the underlying physics of Fourier’s heat conduction law is the balance between the driving force and the resistant force of the heat motion, and Fourier’s law will break down when the inertial force is comparable to the resistant force, for instance, in the case of ultra-short pulse laser heating or heat conduction in carbon nanotubes at ultra-high heat flux.

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.

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.

Dual-phase-lag thermoelastic problem in finite cylindrical domain with relaxation time

2018 ◽  
Vol 14 (5) ◽  
pp. 837-856 ◽  
Author(s):  
Gaurav Mittal ◽  
Vinayak Kulkarni
Keyword(s):  
Heat Flux ◽  
Relaxation Time ◽  
Heat Conduction ◽  
Generalized Thermoelasticity ◽  
Phase Lag ◽  
Dual Phase ◽  
Cylindrical Domain ◽  
Content Type ◽  
Thick Circular Plate ◽  
Lag Model

Purpose The purpose of this paper is to frame a dual-phase-lag model using the fractional theory of thermoelasticity with relaxation time. The generalized Fourier law of heat conduction based upon Tzou model that includes temperature gradient, the thermal displacement and two different translations of heat flux vector and temperature gradient has been used to formulate the heat conduction model. The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration. Design/methodology/approach The work presented in this manuscript proposes a dual-phase-lag mathematical model of a thick circular plate in a finite cylindrical domain subjected to axis-symmetric heat flux. The model has been designed in the context of fractional thermoelasticity by considering two successive terms in Taylor’s series expansion of fractional Fourier law of heat conduction in the two different translations of heat flux vector and temperature gradient. The analytical results have been obtained in Laplace transform domain by transforming the original problem into eigenvalue problem using Hankel and Laplace transforms. The numerical inversions of Laplace transforms have been achieved using the Gaver−Stehfast algorithm, and convergence criterion has been discussed. For illustrative purpose, the dual-phase-lag model proposed in this manuscript has been applied to a periodically varying heat source. The numerical results have been depicted graphically and compared with classical, fractional and generalized thermoelasticity for various fractional orders under consideration. Findings The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration. This model has been applied to study the thermal effects in a thick circular plate subjected to a periodically varying heat source. Practical implications A dual-phase-lag model can effectively be incorporated to study the transient heat conduction problems for an exponentially decaying pulse boundary heat flux and/or for a short-pulse boundary heat flux in long solid tubes and cylinders. This model is also applicable to study the various effects of the thermal lag ratio and the shift time. These dual-phase-lag models are also practically applicable in the problems of modeling of nanoscale heat transport problems of semiconductor devices and accordingly semiconductors can be classified as per their ability of heat conduction. Originality/value To the authors’ knowledge, no one has discussed fractional thermoelastic dual-phase-lag problem associated with relaxation time in a finite cylindrical domain for a thick circular plate subjected to an axis-symmetric heat source. This is the latest and novel contribution to the field of thermal mechanics.

Nonclassical Heat Transfer Models for Laser-Induced Thermal Damage in Biological Tissues

2011 ◽  
Author(s):  
Jianhua Zhou ◽  
J. K. Chen ◽  
Yuwen Zhang
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Conduction ◽  
Temperature Gradient ◽  
Thermal Wave ◽  
Thermal Damage ◽  
Blood Perfusion ◽  
Biological Tissues ◽  
Phase Lag ◽  
Fourier Heat Conduction

To ensure personal safety and improve treatment efficiency in laser medical applications, one of the most important issues is to understand and accurately assess laser-induced thermal damage to biological tissues. Biological tissues generally consist of nonhomogeneous inner structures, in which heat flux equilibrates to the imposed temperature gradient via a thermal relaxation mechanism which cannot be explained by the traditional parabolic heat conduction model based on Fourier’s law. In this article, two non-Fourier heat conduction models, hyperbolic thermal wave model and dual-phase-lag (DPL) model, are formulated to describe the heat transfer in living biological tissues with blood perfusion and metabolic heat generation. It is shown that the non-Fourier bioheat conduction models could predict significantly different temperature and thermal damage in tissues from the traditional parabolic model. It is also found that the DPL bioheat conduction equations can be reduced to the Fourier heat conduction equations only if both phase lag times of the temperature gradient (τT) and the heat flux (τq) are zero. Effects of laser parameters and blood perfusion on the thermal damage simulated in tissues are also studied. The result shows that the overall effects of the blood flow on the thermal response and damage are similar to those of the time delay τT. The two-dimensional numerical results indicate that for a local heating with the heated spot being smaller than the tissue bulk, the variations of the non-uniform distributions of temperature suggest that the multi-dimensional effects of thermal wave and diffusion not be negligible.

Mathematical model and sensor development for measuring energy transfer from wildland fires

2014 ◽  
Vol 23 (7) ◽  
pp. 995 ◽  
Author(s):  
Erik A. Sullivan ◽  
André G. McDonald
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Finite Length ◽  
Scale Model ◽  
Transient Temperature ◽  
High Heat Flux ◽  
Length Scale ◽  
Infinite Length ◽  
Wildland Fires ◽  
Loss Cone

Current practices for measuring high heat flux in scenarios such as wildland forest fires use expensive, thermopile-based sensors, coupled with mathematical models based on a semi-infinite-length scale. Although these sensors are acceptable for experimental testing in laboratories, high error rates or the need for water cooling limits their applications in field experiments. Therefore, a one-dimensional, finite-length scale, transient-heat conduction model was developed and combined with an inexpensive, thermocouple-based rectangular sensor, to create a rapidly deployable, non-cooled sensor for testing in field environments. The proposed model was developed using concepts from heat conduction and with transient temperature boundary conditions, to avoid complicated radiation and convection conditions. Constant heat flux and tree-burning tests were respectively conducted using a mass loss cone calorimeter and a propane-fired radiant panel to validate the proposed analytical model and sensor as well as test the sensor in a simulated forest fire setting. The sensor was mounted directly beside a commercial Schmidt–Boelter gauge to provide data for comparison. The proposed heat flux measurement method provided results similar to those obtained from the commercial heat flux gauge to within one standard deviation. This suggests that the use of a finite-length scale model, coupled with an inexpensive thermocouple-based sensor, is effective in estimating the intense heat loads from wildland fires.

Non-Fourier Heat Conduction in Carbon Nanotubes

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Hai-Dong Wang ◽  
Bing-Yang Cao ◽  
Zeng-Yuan Guo
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Carbon Nanotubes ◽  
Heat Flux ◽  
Heat Conduction ◽  
Thermal Inertia ◽  
Energy Relation ◽  
Fourier’S Law ◽  
Fourier Heat Conduction ◽  
Fourier's Law

Fourier’s law is a phenomenological law to describe the heat transfer process. Although it has been widely used in a variety of engineering application areas, it is still questionable to reveal the physical essence of heat transfer. In order to describe the heat transfer phenomena universally, Guo has developed a general heat conduction law based on the concept of thermomass, which is defined as the equivalent mass of phonon gas in dielectrics according to Einstein’s mass–energy relation. The general law degenerates into Fourier’s law when the thermal inertia is neglected as the heat flux is not very high. The heat flux in carbon nanotubes (CNTs) may be as high as 1012 W/m2. In this case, Fourier’s law no longer holds. However, what is estimated through the ratio of the heat flux to the temperature gradient by molecular dynamics (MD) simulations or experiments is only the apparent thermal conductivity (ATC); which is smaller than the intrinsic thermal conductivity (ITC). The existing experimental data of single-walled CNTs under the high-bias current flows are applied to study the non-Fourier heat conduction under the ultrahigh heat flux conditions. The results show that ITC and ATC are almost equal under the low heat flux conditions when the thermal inertia is negligible, while the difference between ITC and ATC becomes more notable as the heat flux increases or the temperature drops.

Analysis of dual-phase-lag heat conduction in short-pulse laser heating of metals with a hybrid method

2013 ◽  
Vol 52 (2) ◽  
pp. 275-283 ◽  
Author(s):  
Haw-Long Lee ◽  
Wen-Lih Chen ◽  
Win-Jin Chang ◽  
Eing-Jer Wei ◽  
Yu-Ching Yang
Keyword(s):  
Heat Conduction ◽  
Pulse Laser ◽  
Hybrid Method ◽  
Laser Heating ◽  
Short Pulse ◽  
Phase Lag ◽  
Dual Phase ◽  
Short Pulse Laser ◽  
Pulse Laser Heating
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