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. A general solution for the generalized thermoelastic vibration of. The non fourier transient heat conduction in a finite medium with insulated boundaries under the influence of arbitrary initial conditions is investigated analytically. Pdf fourier versus nonfourier heat conduction in materials. The obtained analytical closedform solution can be used for validation of numerical solutions. Fabrication of microdevices with integrated nanowires for. Cao 2012 investigated heat conduction in cnts based on non equilibrium molecular dynamics simulations. We aim at establishing general equations of heat conduction in continuum media that can fully describe the nonfourier conduction in nanomaterials. 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. Fourier versus nonfourier heat conduction in materials with a nonhomogeneous inner structure. Nonfourier phase change heat transfer in biological tissues during solidi cation.
The analytic solution has been derived in the laplace transform domain. 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. Nonfourier heat conduction in a singlewalled carbon nanotube. 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. 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. Carlo mc,22 lattice dynamics ld,23 nonequilibrium greens function. The cv model 9 accounts for the temporally nonlocal effect of the heat conduction. Boley and weiner 2 presented a complete coverage of thermal stresses based on the diffusion heat conduction model.
We study the nonfourier heat conductions in nanomaterials based on the thermomass theory. Three different timedependent surface heat flux, namely, continuous, periodic and ramp type are applied on skin surface without. The objective of this paper is to present experimental evidence for a perfectly fourierlike behavior of heat conduction in those. Cao 2012 investigated heat conduction in cnts based on nonequilibrium molecular dynamics simulations. 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. Nonfourier heat transfer with phonons and electrons. Nonfourier heat conductions in nanomaterials moran wang. Oct 26, 2010 wang, haidong, cao, bingyang, and guo, zengyuan. The solution is expressed in the form of fourier cosine series. Finding non fourier heat conduction in room temperature.
Radial ballisticdiffusive heat conduction in nanoscale. The fourier law should also break down in the case of heat dissipation from a nanoscale heat source into the bulk. The heat conduction through the nanotube was observed in terms of spatiotemporal temperature pro. Allow 2 nd sound propagation but fail for ballistic phonons r q qkt t. A non local constitutive model for nano scale heat conduction. 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. For the transient heat conduction in a onedimensional nanomaterial with a lowtemperature step at both. Wei and wang 6 established the equivalence between the twophase and non fourier approaches for heat conduction. It is shown that at the short time both the non fourier and dualphaselag produce a temperature jump at the interface. Non fourier heat behavior is an important issue for film material. The nonfourier transient heat conduction in a finite medium with insulated boundaries under the influence of arbitrary initial conditions is investigated analytically. Kaminski, hyperbolic heat conduction equations for materials with a. 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. Wei and wang 6 established the equivalence between the twophase and nonfourier approaches for heat conduction.
Nonfourier thermal conduction in nanoscaled electronic. A nonlinear model of heat propagation is presented, from which a new heat conduction equation is derived. Numerical analysis of nonfourier heat transfer in a solid. Theoretical and experimental studies on nonfourier heat. Pdf nonfourier heat conductions in nanomaterials researchgate. In this paper, the nonfourier effect in heat conduction, and the coupling effect between temperature and strain rate in nanoscale beam will be studied. 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.
T1 thermal parameter identification for nonfourier heat transfer from molecular dynamics. The application of nonfourier and ficks laws to the ow. Thermal stresses in a nanocomposite slab due to nonfourier. For the transient heat conduction in a onedimensional. Non fourier phase change heat transfer in biological tissues during solidi cation. Nonfourier heat behavior is an important issue for film material. 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.
Results of the simulations exhibit nonfourier heat conduction where a distinct amount of. Sep 20, 2011 we study the non fourier heat conductions in nanomaterials based on the thermomass theory. Vibration of nano beam induced by ramp type heating. 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. 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. Vibration of gold nanobeam with variable youngs modulus. Several theories have been developed to describe heat transport in nanostructured materials 815. It is relevant to not only materials processing operations 20 but also bioheat transfer 21. Ballistic phonons in ultrathin nanowires nano letters. 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 solution of vibration of gold nano beam resonator. A nonlocal constitutive model for nanoscale heat conduction. Thermal conductivity subjected to sinusoidal heating. Theoretical and experimental studies on non fourier heat conduction based on thermomass theory springer theses kindle edition by haidong wang.
General theory for transport process and nonequilibrium thermodynamics. 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. 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. This book mainly focuses on the theoretical and experimental study of non fourier heat conduction behavior. We will demonstrate predictions of nonfourier conduction. 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. General theory for transport process and non equilibrium thermodynamics. 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. Revisit the non equilibrium thermodynamics based on the thermomass theory, propose a. 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. 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. Analysis and modelling of nonfourier heat behavior using.
We study the non fourier heat conductions in nanomaterials based on the thermomass theory. Molecular dynamics simulations and thermal transport at the nanoscale konstantinos termentzidis, samy merabia. Thermal stresses in a nanocomposite slab due to non. 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. The boundary between the fourier, nonfourier and dualphaselag model is determined. The phenomenon is usually observed in some laser induced thermal responses. In this article, we focus on the nonfourier heat conduction in nanomaterials based on the thermomass theory under the continuum assumption. 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. Non fourier heat conduction e ect on prediction of temperature transients and thermal stress in skin cryopreservation. Temperature dependent thermal properties of tissue is an important factor to achieve realistic models in thermal treatments. Nonfourier heat conductions in nanomaterials moran wang,1,2,a. The microscopically colliding particles, that include molecules, atoms and electrons, transfer disorganized microscopic.
Proceedings of the asme 2009 second international conference on micronanoscale heat and mass transfer. Develop a generalized heat conduction law based on the thermomass theory and the phonon boltzmann equation, which can predict the nanoscale heat conduction. Based on this solution, calculations are conducted to study stress waves induced by nano, pico, and femtosecond laser pulses. The performance of different theories is compared in case of heat pulse experiments. Pdf we study the nonfourier heat conductions in nanomaterials based on the thermomass theory.
It is shown that at the short time both the nonfourier and dualphaselag produce a temperature jump at the interface. Essentially, a nonfourier fluid follows the cattaneovernotte heat equation, where a time derivative of the heat flux is added, multiplied by a relaxation time. 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. 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. Analysis of fourier and non fourier heat conduction using.
The massive utility of nonlinear materials has substantially involved scientists and engineers in their. Asme 2009 second international conference on micronanoscale heat and mass transfer, volume 3. In this paper the according diffusion equation is solved for a nanoscaled semiconductor substrate, in order to gain physical insight in the problem. Apr 25, 2007 when very fast phenomena and small structure dimensions are involved, the classical law of fourier becomes inaccurate. Theories and heat pulse experiments of nonfourier heat conduction.
Babaei and chen 2008 investigated non fourier hyperbolic heat conduction in a heterogeneous sphere. The characteristics of nonfourier and ficks laws respecting je ery nano uid ow over an inclined stretching surface were illustrated by khan et al. Analysis and modelling of nonfourier heat behavior using the. 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. 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 first experimental evidences of nonfourier heat conduction show wavelike propagation called second sound and measured in superfluid he.
Use features like bookmarks, note taking and highlighting while reading theoretical and experimental studies on nonfourier heat conduction based on thermomass theory. A general solution for the generalized thermoelastic vibration of gold nanobeam resonator induced by. Tissue temperature dependent thermal conductivity is used to model the pennes bioheat transfer equation in skin with one relaxation time. Download it once and read it on your kindle device, pc, phones or tablets. 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. The boundary between the fourier, non fourier and dualphaselag model is determined. Nonfourier heat conduction in a singlewalled carbon. The microscopically colliding particles, that include molecules, atoms and electrons, transfer disorganized microscopic kinetic and potential energy, jointly known as internal energy. However, the deviation from fouriers law exists in common materials room temperature as well. Vibration of gold nanobeam with variable youngs modulus due. Heatpulse propagation along nonequilibrium nanowires in.
Thermal conduction is the transfer of heat in internal energy by microscopic collisions of particles and movement of electrons within a body. Transient heat conduction in multiwall carbon nanotubes. Theoretical and experimental studies on nonfourier heat conduction based on thermomass theory springer theses kindle edition by haidong wang. Traditional methods used to investigate phonon transport in onedimensional structures suffer from uncertainty due to contact resistance. Nonfourier heat conduction in a finite medium with insulated. 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. A more sophisticated model is then needed to describe the thermal conduction mechanisms in a physically acceptable way. The application of nonfourier and ficks laws to the ow of. If the inline pdf is not rendering correctly, you can download the pdf file. 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. Some exact solutions to nonfourier heat equations with. Nonfourier heat conduction analysis with temperature.
Nonfourier heat conduction e ect on prediction of temperature transients and thermal stress in skin cryopreservation. However, there is some doubt concerning these findings. This book mainly focuses on the theoretical and experimental study of nonfourier heat conduction behavior. Vibration of gold nano beam in context of twotemperature. In this paper the according diffusion equation is solved for a nano scaled semiconductor substrate, in order to gain physical insight in the problem. The performance of different theories is compared in. A constitutive equation for nanotomacroscale heat conduction based on the boltzmann transport equation j. The comparison suggests that both models can be useful tool in dealing with transient heat conduction problems from nano to macro. 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. Revisit the nonequilibrium thermodynamics based on the thermomass theory, propose a. There are some interesting analytical approaches for different nonfourier heat conduction problems 611. Thermal parameter identification for nonfourier heat. This may give rise to a new regime of heat conduction, which can impact thermal energy transport and conversion.
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. 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. An exact similarity solution in closed form of this equation is obtained, which reveals the travelling wave characteristics for the transient temperature distribution. Experimental evidence about the controversy concerning. Pdf analytical solution of bioheat transfer equation. Nanoscale heat conduction with applications in nanoelectronics. Finite element model for femtosecond laser pulse heating. The cv model 9 accounts for the temporally non local effect of the heat conduction. The experimental basis and theoretical background of nonfourier heat. Equation of motion of a phonon gas and nonfourier heat conduction, j.