Ballistic phonons in ultrathin nanowires nano letters. Essentially, a non fourier fluid follows the cattaneovernotte heat equation, where a time derivative of the heat flux is added, multiplied by a relaxation time. Equation of motion of a phonon gas and nonfourier heat conduction, j. Thermal stresses in a nanocomposite slab due to non. A non local constitutive model for nano scale heat conduction. The peak temperature, spatial difference, and time variation of temperature, which are critical to thermal reliability of the chip, are given and compared with that. Non fourier heat conduction e ect on prediction of temperature transients and thermal stress in skin cryopreservation. Fourier versus nonfourier heat conduction in materials with a nonhomogeneous inner structure. The experimental basis and theoretical background of nonfourier heat. Develop a generalized heat conduction law based on the thermomass theory and the phonon boltzmann equation, which can predict the nanoscale heat conduction. The ultrashort pulse laser in material processing of micronanoscale has emerged as a useful application due to its capability of high precision control on heating and heat affected zone. A novel thermomass theory is used as the theoretical basis, which provides a general heat conduction equation for the accurate prediction of nonfourier heat conduction. The solution is expressed in the form of fourier cosine series.
Alnimr 3 used the hyperbolic heat conduction model to investigate. Based on this solution, calculations are conducted to study stress waves induced by nano, pico, and femtosecond laser pulses. Nanoscale heat conduction with applications in nanoelectronics. Analysis and modelling of nonfourier heat behavior using the. In multidimensional heat conduction where the heat is transported in multiple directions, the nonfourier heat conduction has been found to be dependent on more factors, owing to the complex configurations of the system. A nonlinear model of heat propagation is presented, from which a new heat conduction equation is derived. If the inline pdf is not rendering correctly, you can download the pdf file. Finding non fourier heat conduction in room temperature. Heatpulse propagation along nonequilibrium nanowires in. Analysis of fourier and non fourier heat conduction using tiknonov based well conditioned asymptotic waveform evaluation technique sohel rana 1, ahmed wasif reza 2, mohd sayuti 3 1school of engineering, rmit university, 2department of computer science and engineering, faculty of science and engineering, east west university, 3department of mechanical engineering, faculty of engineering.
Oct 26, 2010 wang, haidong, cao, bingyang, and guo, zengyuan. In this paper the according diffusion equation is solved for a nano scaled semiconductor substrate, in order to gain physical insight in the problem. Nonfourier heat conduction in a finite medium with insulated. Theoretical and experimental studies on nonfourier heat conduction based on thermomass theory springer theses kindle edition by haidong wang. We will demonstrate predictions of nonfourier conduction.
The analytic solution has been derived in the laplace transform domain. Fabrication of microdevices with integrated nanowires for. Distinct nonfourier behavior in terms of finite propagation velocity and a hyperbolic wave like character of heat conduction has been reported for certain materials in several studies published recently. Wei and wang 6 established the equivalence between the twophase and non fourier approaches for heat conduction. Instead of the classic fourier equation based on diffusion, a hyperbolic equation based on a wave model has been used to predict the rapid transient heat conduction in ic chips. In the present work, the model of vibration of gold nano beam induced by laser pulse heating is developed in the context of twotemperature generalized thermoelasticity and nonfourier heat conduction. During the past few years, considerable attention has been concerned with using the nonfourier heat conduction in problems with very low temperatures, extremely short period of time, or very high heat flux. Thermal conductivity subjected to sinusoidal heating. The microscopically colliding particles, that include molecules, atoms and electrons, transfer disorganized microscopic. Vibration of nano beam induced by ramp type heating. Pdf nonfourier heat conductions in nanomaterials researchgate.
We study the nonfourier heat conductions in nanomaterials based on the thermomass theory. Molecular dynamics simulations and thermal transport at the nanoscale konstantinos termentzidis, samy merabia. This features a relaxation time for heat flux and results in a hyperbolic energy equation which successfully captures the flux of heat via propagation of thermal waves with finite speed. In this paper, the nonfourier effect on heat conduction, and the coupling effect between temperature and strain rate in the nanoscale beam will be studied when youngs modulus is variable as a function of temperature. Non fourier heat behavior is an important issue for film material. The characteristics of nonfourier and ficks laws respecting je ery nano uid ow over an inclined stretching surface were illustrated by khan et al. Non fourier phase change heat transfer in biological tissues during solidi cation. Chenb it is well known that the continuum model of fouriers law of heat conduction violates the relativity theory, admits an instantaneous thermal response, and assumes a.
Nonfourier thermal conduction in nanoscaled electronic. Traditional methods used to investigate phonon transport in onedimensional structures suffer from uncertainty due to contact resistance. The performance of different theories is compared in case of heat pulse experiments. Boley and weiner 2 presented a complete coverage of thermal stresses based on the diffusion heat conduction model. In the present work, the model of vibration of gold nano beam induced by laser pulse heating is developed in the context of twotemperature generalized thermoelasticity and non fourier heat conduction. Kaminski, hyperbolic heat conduction equations for materials with a. All material properties except relaxation time were assumed vary continuously within the sphere in the radial direction following a power law and the solution was obtained by using numerical inversion of the laplace transform.
Radial ballisticdiffusive heat conduction in nanoscale. Carlo mc,22 lattice dynamics ld,23 nonequilibrium greens function. A general solution for the generalized thermoelastic vibration of. It is relevant to not only materials processing operations 20 but also bioheat transfer 21.
Experimental evidence about the controversy concerning. Nonfourier heat transfer with phonons and electrons. Three different timedependent surface heat flux, namely, continuous, periodic and ramp type are applied on skin surface without. We aim at establishing general equations of heat conduction in continuum media that can fully describe the nonfourier conduction in nanomaterials. Temperature dependent thermal properties of tissue is an important factor to achieve realistic models in thermal treatments. A general solution for the generalized thermoelastic vibration of gold nanobeam resonator induced by. The boundary between the fourier, nonfourier and dualphaselag model is determined. Pdf fourier versus nonfourier heat conduction in materials. In the present work, a generalized solution for the generalized thermoelastic vibration of a nano beam resonator induced by ramp type of heating will be developed. Numerical analysis of nonfourier heat transfer in a solid. Analysis of fourier and non fourier heat conduction using. An exact similarity solution in closed form of this equation is obtained, which reveals the travelling wave characteristics for the transient temperature distribution. Theoretical and experimental studies on non fourier heat conduction based on thermomass theory springer theses kindle edition by haidong wang. Essentially, a nonfourier fluid follows the cattaneovernotte heat equation, where a time derivative of the heat flux is added, multiplied by a relaxation time.
The maxwellcattaneo equations, authormarc calvo schwarzw\alder, year2015 marc calvo schwarzwalder published 2015 mathematics we study the derivation, properties and solution methods of the classical and. Heat conduction modelling heat transfer by conduction also known as diffusion heat transfer is the flow of thermal energy within solids and nonflowing fluids, driven by thermal non equilibrium i. The application of nonfourier and ficks laws to the ow of. Nonfourier heat conduction e ect on prediction of temperature transients and thermal stress in skin cryopreservation. Transient heat conduction in multiwall carbon nanotubes 7 latin american journal of solids and structures 12 2015 711729 ed non fourier heat conduction in nanomaterials by use of the thermomass theory. Vibration of gold nano beam in context of twotemperature. A constitutive equation for nanotomacroscale heat conduction based on the boltzmann transport equation j. However, the deviation from fouriers law exists in common materials room temperature as well. In this paper, the non fourier heat conduction problems with temperature and thermal flux relaxations are investigated based on the wavelet finite element method and solved by the central difference scheme for one and twodimensional media. The heat conduction through the nanotube was observed in terms of spatiotemporal temperature pro.
This book mainly focuses on the theoretical and experimental study of nonfourier heat conduction behavior. Sep 20, 2011 we study the non fourier heat conductions in nanomaterials based on the thermomass theory. The nonfourier effect in heat conduction becomes more predominant as the duration of heating becomes extremely small which is the case of ultrashort pulse laser. Revisit the non equilibrium thermodynamics based on the thermomass theory, propose a. Revisit the nonequilibrium thermodynamics based on the thermomass theory, propose a. This may give rise to a new regime of heat conduction, which can impact thermal energy transport and conversion. In this article, we focus on the nonfourier heat conduction in nanomaterials based on the thermomass theory under the continuum assumption. Classical molecular dynamics simulations junichiro shiomi and shigeo maruyama department of mechanical engineering, the university of tokyo 731 hongo, bunkyoku, tokyo 18656, japan nonstationary heat conduction in a singlewalled carbon nanotube was investigated by applying a.
In this paper, the non fourier effect in heat conduction, and the coupling effect between temperature and strain rate in nanoscale beam will be studied. The comparison suggests that both models can be useful tool in dealing with transient heat conduction problems from nano to macro. This book mainly focuses on the theoretical and experimental study of non fourier heat conduction behavior. It is shown that at the short time both the non fourier and dualphaselag produce a temperature jump at the interface. Some exact solutions to nonfourier heat equations with. A nonlocal constitutive model for nanoscale heat conduction. General theory for transport process and non equilibrium thermodynamics. Outline fouriers law for heat conduction bkd ffilibreakdown of fouriers law in nanosystems experimental evidence of ballistic heat transfer modeling and numerical reconstruction of heatpulse experimentspulse experiments fractional calculus for nonfourier. The performance of different theories is compared in. Nonfourier heat conduction in a singlewalled carbon nanotube. Theories and heat pulse experiments of nonfourier heat conduction. Dynamical analysis of nonfourier heat conduction and its.
When very fast phenomena and small structure dimensions are involved, the classical law of fourier becomes inaccurate. Wei and wang 6 established the equivalence between the twophase and nonfourier approaches for heat conduction. Abstract the nonfourier effect in heat conduction and the coupling effect between temperature and strain rate are the two significant effects in the nanoscale beam. In this paper, the nonfourier heat conduction problems with temperature and thermal flux relaxations are investigated based on the wavelet finite element method and solved by the central difference scheme for one and twodimensional media. Vibration of gold nanobeam with variable youngs modulus due. The phenomenon is usually observed in some laser induced thermal responses. For the transient heat conduction in a onedimensional nanomaterial with a lowtemperature step at both. N2 fouriers law leads to a diffusive model of heat transfer in which a thermal signal propagates infinitely fast and the only material parameter is the thermal conductivity.
In this paper the according diffusion equation is solved for a nanoscaled semiconductor substrate, in order to gain physical insight in the problem. Finite element model for femtosecond laser pulse heating. Apr 25, 2007 when very fast phenomena and small structure dimensions are involved, the classical law of fourier becomes inaccurate. If the inline pdf is not rendering correctly, you can download the pdf file here. In the present work, the solution of vibration of gold nano beam resonator. Analysis and modelling of nonfourier heat behavior using. Transient heat conduction in multiwall carbon nanotubes 7 latin american journal of solids and structures 12 2015 711729 ed nonfourier heat conduction in nanomaterials by use of the thermomass theory. The microscopically colliding particles, that include molecules, atoms and electrons, transfer disorganized microscopic kinetic and potential energy, jointly known as internal energy. The onedimensional stefan problem with nonfourier heat. Tissue temperature dependent thermal conductivity is used to model the pennes bioheat transfer equation in skin with one relaxation time. The cv model 9 accounts for the temporally nonlocal effect of the heat conduction. Nonfourier heat conduction analysis with temperature. Vibration of gold nanobeam with variable youngs modulus. The application of nonfourier and ficks laws to the ow.
Thermal stresses in a nanocomposite slab due to nonfourier. Download it once and read it on your kindle device, pc, phones or tablets. Allow 2 nd sound propagation but fail for ballistic phonons r q qkt t. Babaei and chen 2008 investigated non fourier hyperbolic heat conduction in a heterogeneous sphere. The nonfourier transient heat conduction in a finite medium with insulated boundaries under the influence of arbitrary initial conditions is investigated analytically. Transient heat conduction in multiwall carbon nanotubes. Nonfourier heat conductions in nanomaterials moran wang.
T1 thermal parameter identification for nonfourier heat transfer from molecular dynamics. The fourier law should also break down in the case of heat dissipation from a nanoscale heat source into the bulk. Theoretical and experimental studies on nonfourier heat. The massive utility of nonlinear materials has substantially involved scientists and engineers in their. Nonfourier phase change heat transfer in biological tissues during solidi cation. However, there is some doubt concerning these findings. Cao 2012 investigated heat conduction in cnts based on non equilibrium molecular dynamics simulations. Use features like bookmarks, note taking and highlighting while reading theoretical and experimental studies on nonfourier heat conduction based on thermomass theory.
The objective of this paper is to present experimental evidence for a perfectly fourierlike behavior of heat conduction in those. Nonfourier heat behavior is an important issue for film material. The cv model 9 accounts for the temporally non local effect of the heat conduction. It is shown that at the short time both the nonfourier and dualphaselag produce a temperature jump at the interface. Chenb it is well known that the continuum model of fouriers law of heat conduction violates the relativity theory, admits an instantaneous thermal response, and assumes a quasiequilibrium thermodynamic condition. The boundary between the fourier, non fourier and dualphaselag model is determined. A novel thermomass theory is used as the theoretical basis, which provides a general heat conduction equation for the accurate prediction of non fourier heat conduction. Thermal conduction is the transfer of heat in internal energy by microscopic collisions of particles and movement of electrons within a body. Pdf analytical solution of bioheat transfer equation. Pdf we study the nonfourier heat conductions in nanomaterials based on the thermomass theory. Several theories have been developed to describe heat transport in nanostructured materials 815. Phonons in lowdimensional structures with feature sizes on the order of the phonon wavelength may be coherently scattered by the boundary.
Results of the simulations exhibit nonfourier heat conduction where a distinct amount of. In this paper, the nonfourier effect in heat conduction, and the coupling effect between temperature and strain rate in nanoscale beam will be studied. Cao 2012 investigated heat conduction in cnts based on nonequilibrium molecular dynamics simulations. We study the non fourier heat conductions in nanomaterials based on the thermomass theory. Nonfourier heat conductions in nanomaterials moran wang,1,2,a.
The non fourier transient heat conduction in a finite medium with insulated boundaries under the influence of arbitrary initial conditions is investigated analytically. Asme 2009 second international conference on micronanoscale heat and mass transfer, volume 3. For the transient heat conduction in a onedimensional. Proceedings of the asme 2009 second international conference on micronanoscale heat and mass transfer. Nonfourier heat conduction in a singlewalled carbon. Thermal parameter identification for nonfourier heat. A more sophisticated model is then needed to describe the thermal conduction mechanisms in a physically acceptable way. For the transient heat conduction in a onedimensional nanomaterial with a lowtemperature step at both ends, the temperature response predicted by the present model is consistent with those by the existing theoretical models for small temperature steps.
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