DOCSLIB.ORG

Relativistic Heat Conduction

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Relativistic Heat Conduction International Journal of Heat and Mass Transfer 48 (2005) 2397 2406 www.elsevier.com/locate/ijhmt Relativistic heat conduction Y.M. Ali *, L.C. Zhang School of Aerospace, Mechanical and Mechatronic Engineering, J07, University of Sydney, NSW 2006, Australia Received 5 December 2003; received in revised form 5 January 2005 Available online 19 March 2005 Abstract The hyperbolic heat conduction equation (HHCE), which acknowledges the finite speed of heat propagation, is based on microscopic evidence from the kinetic theory and statistical mechanics. However, it was argued that the HHCE could violate the second law of thermodynamics. This paper shows that a HHCE like equation (RHCE) can be derived directly from the theory of relativity, as a direct consequence of space time duality, without any consider ation of the microstructure of the heat conducting medium. This approach results in an alternative expression for the heat flux vector that is more compatible with the second law. Therefore, the RHCE brings the classical field theory of heat conduction into agreement with other branches of modern physics. Ó 2005 Published by Elsevier Ltd. Keywords: Relativity; Thermodynamics; Entropy; Hyperbolic above argument is true, it is a very strong and restrictive I think that theory cannot be fabricated out of the interpretation of the relativity theory. A weaker inter results of observation, but that it can only be pretation can be proposed: Relativity is concerned with invented. objects that move or propagate at speeds comparable Albert Einstein [1] with a limiting speed characteristic of the field or med ium involved. For example, electromagnetic objects propagate at speeds comparable with the maximum speed of propa 1. Introduction gation of an electromagnetic signal (photon), i.e. the speed of light in vacuum. Similarly, cosmological objects The theory of relativity is often overlooked within the move at significant speeds, when compared with the context of classical engineering sciences based on the fol maximum speed of propagation of a gravitational signal lowing argument: Relativity is concerned with objects (graviton). However, there are physical fields that are moving at speeds comparable with the speed of light, less fundamental in nature, for which the limiting speeds while most mechanical systems involve objects moving of propagation are (numerically) small compared with at speeds negligible compared with the speed of light; the speed of light. Yet, they still impose restrictions on therefore, relativistic effects can be ignored. While the the propagation of objects moving across them. For example, the potential field of a pressure wave propagat * Corresponding author. Fax: +61 2 9351 7060. ing through a fluid is restricted by the speed of sound in E mail address: [email protected] (Y.M. Ali). that fluid, especially near a unit Mach number. 0017 9310/$ see front matter Ó 2005 Published by Elsevier Ltd. doi:10.1016/j.ijheatmasstransfer.2005.02.003 2398 Y.M. Ali, L.C. Zhang / International Journal of Heat and Mass Transfer 48 (2005) 2397 2406 Nomenclature A [ ] relativistic operator Greek symbols c specific heat a thermal diffusivity C speed of heat (second sound) b arbitrary parameter d total derivative o partial derivative D substantial derivative h temperature dx,dy,dz spatial distances q density ds space like time distance r entropy production f, h arbitrary functions s space like time H heat flow vector s0 relaxation time i imaginary transformation i, j, k spatial unit vectors Other symbols k thermal conductivity $ gradient operator o time unit vector $2 Laplacian operator q heat flux vector h quad operator s specific entropy h2 dÕAlembertian operator t real time Æ vector dot product u specific energy \ intersection operator U source velocity vector ! implication operator x, y, z spatial dimensions A similar effect equally applies to heat conduction, 2. The hyperbolic heat conduction equation which can be viewed as propagation of hypothetical par ticles (phonons) in a hypothetical gas (historically know For any rigid stationary material without internal as ÔCaloricÕ). The limiting speed on heat propagation heat generation, energy balance within a control mass (the speed of second sound) has been measured in vari can be expressed as [13]: ous media [2 4]. A thermal Mach number has also been oh reported for heat conduction through solids [5,6]. Fur qc o þrÁq ¼ 0; ð1Þ thermore, thermal resonance has been suggested in cases t of high frequency periodic thermal loading [7,8]. where q is density, c is specific heat (at a given tempera The Fourier equation of heat conduction is funda ture h), q is the thermal heat flux vector, and $ is the gra mentally wrong because it assumes an infinite speed of dient operator: propagation of heat, which is physically inadmissible. This anomaly has been (supposedly) overcome by the o o o r¼ i þ j þ k: ð2Þ hyperbolic heat conduction equation (HHCE), which in ox oy oz cludes a component (presumably) recognising the finite speed of heat signals. The HHCE was developed based If the material is isotropic, homogeneous, and the on microscopic considerations [2,9,10] that are cumber variation in temperature is so small that material prop some, and seem to violate at least on statement of the erties can be assumed constant, then substituting Fou second law of thermodynamics [11]. rierÕs linear approximation of heat flux, This paper will show that the HHCE can be consis q ¼ krh; ð3Þ tently developed based on a weak interpretation of the theory of relativity, as originally proposed in [12], with into Eq. (1) leads to the well known Fourier equation of out any microscopic or material specific considerations. heat conduction: The following sections will argue that: (1) the HHCE oh does not really comply with the relativity theory, and ¼ ar2h; ð4Þ (2) that it can violate the second law of thermodynamics. ot The alternative model aims at overcoming both difficul where k is thermal conductivity, a k/(qc) is thermal ties, and hopes to help in resolving the existing contro diffusivity, and $2 is the Laplacian operator: versies about the heat equation. The new model of o2 o2 o2 heat conduction will bring it into better agreement with r2 ¼ þ þ : ð5Þ other branches of modern physics. ox2 oy2 oz2 Y.M. Ali, L.C. Zhang / International Journal of Heat and Mass Transfer 48 (2005) 2397 2406 2399 Several investigators have argued that Eq. (4) is fun equation), it is not conceptually relativistic. The laws of damentally wrong because it assumes an infinite speed of motion employed in the derivation of the HHCE are propagation of heat signals [14]. This means that a ther essentially Newtonian. The expression in Eq. (7), the mal disturbance can be detected instantaneously at an misleading symbol C, and even Eq. (6), are only first or infinitely far distance from the source, which is physi der approximations of some very complex and cumber cally unacceptable. One of the implications of the theory some statistical computations. These computations do of relativity is the principle of ‘‘no action at a distance’’ not consider the theory of relativity at all, and are classic which requires a finite speed of propagation of any sig in nature. A relativistic treatment of the problem was at nal, and necessitates a time lag between a cause and its tempted by some authors [22 25], by including a relativ effect [15]. Morse and Feshbach [16] recognised this istic correction due to the speed of the heat carrying problem, and proposed that Eq. (4) should be modified particles, e.g. electrons. Yet, this is followed by classical into a more acceptable (Telegraph) form: statistical treatments that are mathematically complex, and lead to Eqs. (6) and (7) as first order approxima 1 o2h 1 oh þ ¼r2h: ð6Þ tions. A review of various approaches to deriving Eqs. 2 o 2 o C t a t (6) and (7) can be found in [26]. This form is known as MaxwellÕs equation, because it resembles the equation of propagation of an electromag netic field, i.e. light. However, in Eq. (6) the speed of 3. Controversies about the HHCE heat propagation, C, is not a fundamental property of the field, but is related to the mean free path of gas mol This artificiality in the relationship between the ecules. The idea is extended to solids, by assuming that HHCE and the relativity theory is not the only serious heat is conducted by gas like phonon or electron objection facing that equation. Several investigators, streams. e.g. [27], argued that Eq. (6) is not necessary because, Tisza (1938) and Landau (1941) predicted that the for most practical situations, C2 is very large compared speed of heat can be different from the speed of sound with a such that the second order term is negligible, and and called it the speed of second sound [17]. Peshkov Eq. (6) will converge quantitatively to Eq. (4). This argu [3] found experimentally that in liquid Helium II, it is ment can be challenged on two grounds. Firstly, there one order of magnitude less than the speed of sound. are experimental evidences that C is not always very There are evidences to suggest the same ratio or more large. A relaxation time up to 10 s has been measured for non homogeneous solids [4,18]. in non homogeneous materials [18]. Polymeric and vitre Eq. (6) is often attributed to Cattaneo [19], Vernotte ous materials are important engineering materials that [20], as well as Chester [2] who considered the case of are almost thermal insulators. While experimental data second sound in solids. Based on the kinetic theory cal may not be available yet, there is no reason to believe culations and Boltzmann equations for a rarefied gas that C, for these materials, should as high as for metallic [21], they proposed that FourierÕs linear heat flux, Eq.
Load more

Recommended publications
  • Numerical Investigation of Second Sound in Liquid Helium
    NUMERICAL INVESTIGATION OF SECOND SOUND IN LIQUID HELIUM by Udo Piram A Thesis Submitted to the Faculty of the DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING In the Graduate College THE UNIVERSITY OF ARIZONA In Partial Fulfillment of the Requirements For the Degree of DIPLOMINGENIEUR at the UNIVERSITY STUTTGART 1991 ACKNOWLEDGMENTS I would like to thank Dr. Fran¸cois Cellier for guidance and assistance during my studies at the University of Arizona and the preparation of this paper. I would also like to thank Prof. Dr. Voß at the University Stuttgart, who organized the exchange program, which made it possible for me to attend school at the University of Arizona. I would like to thank the German Academic Exchange Service for the financial support of the exchange program. Finally, I would like to express my gratitude to my parents for their support of my studies in Germany and the USA. Contents Contents ii List of Figures iii 1 Introduction 1 1.1MechanicalandElectricalSystems...................... 1 1.2ThermodynamicalSystems........................... 2 2 Helium II and Second Sound 4 3 Heat Conduction Modeled With Time–Variant R–C–Networks 7 3.1 R–C–Networks . 7 3.2ModelinginTermsofBondGraphs...................... 9 3.3HeliumIIModeledinTermsofBondGraphs................. 10 3.4NumericalValuesfortheThermalParameters................ 12 3.4.1 Model 1: Initial Temperature 1.4K . 13 3.4.2 Model 2: Initial Temperature 2.1728K . 14 3.5SimulationandResults............................. 16 4 Heat Transport and Two Fluid Model 20 4.1TwoFluidModel................................ 20 4.2HydrodynamicalEquations........................... 22 4.3NumericalValuesfortheThermalParameters................ 23 4.4NumericalMethod............................... 24 i CONTENTS ii 4.5 Boundary Conditions . 25 4.6SimulationandResults............................. 26 5 Conclusions 29 5.1Conclusions................................... 29 5.2Zusammenfassung...............................
    [Show full text]
  • Causal Heat Conduction Contravening the Fading Memory Paradigm
    entropy Article Causal Heat Conduction Contravening the Fading Memory Paradigm Luis Herrera Instituto Universitario de Física Fundamental y Matematicas, Universidad de Salamanca, 37007 Salamanca, Spain; [email protected] Received: 1 September 2019; Accepted: 26 September 2019; Published: 28 September 2019 Abstract: We propose a causal heat conduction model based on a heat kernel violating the fading memory paradigm. The resulting transport equation produces an equation for the temperature. The model is applied to the discussion of two important issues such as the thermohaline convection and the nuclear burning (in)stability. In both cases, the behaviour of the system appears to be strongly dependent on the transport equation assumed, bringing out the effects of our specific kernel on the final description of these problems. A possible relativistic version of the obtained transport equation is presented. Keywords: causal dissipative theories; fading memory paradigm; relativistic dissipative theories 1. Introduction In the study of dissipative processes, the order of magnitude of relevant time scales of the system (in particular the thermal relaxation time) play a major role, due to the fact that the interplay between this latter time scale and the time scale of observation, critically affects the obtained pattern of evolution. This applies not only for dissipative processes out of the steady–state regime but also when the observation time is of the order of (or shorter than) the characteristic time of the system under consideration. Besides, as has been stressed before [1], for time scales larger than the relaxation time, transient phenomena affect the future of the system, even for time scales much larger than the relaxation time.
    [Show full text]
  • Second Sound and Ballistic Heat Conduction: Naf Experiments Revisited ⇑ R
    International Journal of Heat and Mass Transfer 117 (2018) 682–690 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt Second sound and ballistic heat conduction: NaF experiments revisited ⇑ R. Kovács , P. Ván Department of Theoretical Physics, Wigner Research Centre for Physics, Institute for Particle and Nuclear Physics, Budapest, Hungary Department of Energy Engineering, BME, Budapest, Hungary Montavid Thermodynamic Research Group, Hungary article info abstract Article history: Second sound phenomenon and ballistic heat conduction, the two wave like propagation modes of heat, Received 25 August 2017 are the two most prominent, experimentally observed non-Fourier effects of heat conduction. In this Received in revised form 4 October 2017 paper we compare three related theories by quantitatively analyzing the crucial NaF experiments of Accepted 8 October 2017 Jackson, Walker and McNelly, where these effects were observed together. We conclude that with the Available online 17 October 2017 available information the best comparison and insight is provided by non-equilibrium thermodynamics with internal variables. However, the available data and information is not the best, and further, new Keywords: experiments are necessary. Non-equilibrium thermodynamics Ó 2017 Elsevier Ltd. All rights reserved. Ballistic propagation NaF experiments Kinetic theory 1. Introduction reflected and scattered only on the boundaries. In the framework of non-equilibrium thermodynamics with internal variables [5], Due to the technological development, manufacturing and the ballistic propagation is represented as a coupling between material designing achieved the level where the classical laws of the thermal and mechanical fields and propagates with the elastic physics and the related engineering methodologies do not hold.
    [Show full text]
  • Arxiv:1501.04234V1 [Cond-Mat.Stat-Mech] 17 Jan 2015 Rmapyia on Fve U Nrdcsrmral Titrest Strict Weak Remarkably a Introduces Is but Law View Second Equations
    THEORIES AND HEAT PULSE EXPERIMENTS OF NON-FOURIER HEAT CONDUCTION P. VAN´ Abstract. The experimental basis and theoretical background of non-Fourier heat conduction is shortly reviewed from the point of view of non-equilibrium thermodynamics. The performance of different theories is compared in case of heat pulse experiments. 1. Introduction There are several extensive reviews of heat conduction beyond Fourier [1, 2, 3, 4, 5, 6]. When non-equilibrium thermodynamics is concerned, usually Extended Thermodynamics is in the focus of surveys in this subject. In this short paper heat conduction phenomena is reviewed from a broader perspective of non-equilibrium thermodynamics. The performance of different theories is compared on the example of heat pulse experiments. There are two preliminary remarks to underline the particular point of view of this work. The first remark concerns the so called heat conduction paradox of the infinite speed of signal propagation in Fourier theory. Infinite propagation speeds are frequently mentioned as a disadvantage [7, 8] and this is a main motivation for looking symmetric hyperbolic evolution equations in general [9]. However – the relativistic formulation of heat conduction is a different matter and parabolic equations may be compatible with relativity [10, 11, 12]. – The finite characteristic speeds of hyperbolic equations are determined by material parameters. Therefore, in principle, in nonrelativistic spacetime they can be larger than the speed of light. – In case of parabolic equations the speed of real signal propagation is finite, e.g. because the validity condition of a continuum theory determines a propagation speed. Moreover, the sensitivity of the experimental devices is finite, therefore they can measure only finite speeds [13, 10, 14, 15].
    [Show full text]
  • Size Effects in Superfluid Helium II - I
    Size effects in superfluid helium II - I. Experiments in porous systems E. Guyon, I. Rudnick To cite this version: E. Guyon, I. Rudnick. Size effects in superfluid helium II - I. Experiments in porous systems. Journal de Physique, 1968, 29 (11-12), pp.1081-1095. 10.1051/jphys:019680029011-120108100. jpa-00206747 HAL Id: jpa-00206747 https://hal.archives-ouvertes.fr/jpa-00206747 Submitted on 1 Jan 1968 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. LE JOURNAL DE PHYSIQUE TOME 29, NOVEMBRE-DÉCEMBRE 1968, 1081. SIZE EFFECTS IN SUPERFLUID HELIUM II I. EXPERIMENTS IN POROUS SYSTEMS By E. GUYON (1) and I. RUDNICK (2), Physics Department, University of California, Los Angeles, California, (Reçu le 22 avril 1968.) Résumé. 2014 Les propriétés de la phase superfluide de l’hélium liquide sont fortement modi- fiées par les effets de taille. Nous discutons dans ce travail une étude experimentale de l’hélium. contenu dans des poudres très fines (~ 100 à 104 Å) : abaissement de la température d’établis- sement de l’état superfluide, T0, et propriétés superfluides pour T To : vitesse d’écoulement critique, chaleur spécifique, densité superfluide.
    [Show full text]
  • THE VELOCITY OP SECOND SOUND NEAR the LAMBDA POINT By
    1 cS\oo THE VELOCITY OP SECOND SOUND NEAR THE LAMBDA POINT by DAVID LAWHENCE JOHNSON B.Sc, The University of British Columbia, 1963 M.So., The University of British Columbia, 1967 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of Physics We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April, 1969 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and Study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics The University of British Columbia Vancouver 8, Canada Date May 15, 1969 11 DEDICATED to my wife ELIZABETH whose contribution to education was twofold and without whose help this work would have been impossible. iii ABSTRACT Direct measurements have been made of the velocity of second sound in liquid helium over the temperature 2 6 range TA-T from 1.3 x 10" K to 5 i 10" K. Using previously determined relationships for the specific heat, superfluld density, and thermal conductivity near the lambda point, consistency has been demonstrated between the measurements, velocities predicted by superfluld hydrodynamics,
    [Show full text]
  • Systematic Studies of a Cavity Quench Localization System
    SYSTEMATIC STUDIES OF A CAVITY QUENCHLOCALIZATIONSYSTEM Systematische Studien eines Systems zur Lokalisierung von Cavity Quenches Master Thesis BOSSEBEIN Prof. Dr. Wolfgang Hillert Dr. Lea Steder University of Hamburg Deutsches Elektron Synchrotron, DESY May 23, 2019 ZUSAMMENFASSUNG Es gibt eine Vielzahl von Techniken zur Lokalisierung von Quenchen bei Supraleitenden Radio Frequenz Cavities. Eine davon nutzt dafür Temperaturwellen im flüssigen Helium unterhalb des Lambda-Punktes. Sie werden von einem Quench der Cavity Oberfläche ausgelöst und werden zweiter Schall geannt. Sensoren wie die Oscillating Superleak Transducers sind in der Lage diese Wellen zu detektieren und somit auch die Signallaufzeit des zweiten Schalls zu bestimmen. Diese Technik erlaubt es während eines Cavity Leistungstests parallel den Quench-Ort zu bestimmen. Andere Methoden benötigen einen eigenen kalten Cavity Test oder sie bergen das Risiko die Cavity Oberfläche zu verschmutzen, die dann vor weiteren Tests gereinigt werden muss. Um den wahrscheinlichsten Quench-Ort mit Hilfe der Laufzeiten des zweiten Schalls zu berechnen, existieren unterschiedliche Methoden. Zwei davon werden am DESY genutzt: Multilateration und Raytracing. Auf Basis dieser beiden Methoden wurden im Rahmen dieser Arbeit neue Algorithmen implementiert. Diese schließen einen Algorithmus zur Einführung eines Laufzeit Offsets und einen von der Ausbreitungs- geschwindigkeit der Wellen abhängigen Rekonstruktionsmeachnismus für den Quench-Ort ein. Die Genauigkeiten und die zugrundeliegen- den Randbedingungen dieser Algorithmen werden in der vorliegenden Arbeit untersucht. Ein Datensatz von fast 200 Quench-Ereignissen der 18 getesteten Einzellercavities wird genutzt um eine stochastische Beur- teilung zu erhalten. Um die große Anzahl von Ereignissen auszuwerten, wurden zwei Automatisierungsprozesse eingeführt. In dem Datensatz wurde eine Winkel- und eine Höhenabhängigkeit des rekonstruierten Quench-Ortes beobachtet und den spezifischen Eigenschaften des Experimentaufbaus zugeordnet.
    [Show full text]
  • A CONVECTIVE MODEL of a ROTON VI Tkachenko
    PACS: 67.40.Bz, 67.40.Pm A CONVECTIVE MODEL OF A ROTON V.I. Tkachenko1,2 1)National Science Center “Kharkov Institute of Physics and Technology” The National Academy of Sciences of Ukraine 61108, Kharkov 1, Akademicheskaya str., tel./fax 8-057-349-10-78 2)V.N. Karazin Kharkiv National University, 61022, Kharkov,4, Svobody sq., tel./fax 8-057-705-14-05 E-mail: [email protected] Received March 17, 2017 A convective model describing the nature and structure of the roton is proposed. According to the model, the roton is a cylindrical convective cell with free horizontal boundaries. On the basis of the model, the characteristic geometric dimensions of the roton are estimated, and the spatial distribution of the velocity of the helium atoms and the perturbed temperature inside are described. It is assumed that the spatial distribution of rotons has a horizontally multilayer periodic structure, from which follows the quantization of the energy spectrum of rotons. The noted quantization allows us to adequately describe the energy spectrum of rotons. The convective model is quantitatively confirmed by experimental data on the measurement of the density of the normal component of helium II, the scattering of neutrons and light by helium II. The use of a convective model for describing the scattering of light by Helium II made it possible to estimate the dipole moment of the roton, as well as the number of helium atoms participating in the formation of the roton. KEY WORDS: superfluid helium, convection, elementary convective cell, roton, energy spectrum of helium II, density of the normal component of helium II, neutron scattering, light scattering, dipole momentum EXPERIMENTS TO DETERMINE THE ENERGY SPECTRUM OF ROTON In [1] Landau presented a quantitative theory of superfluid Helium, which described almost all known at that time experimental results and predicted the number of new phenomena.
    [Show full text]
  • Some Applications of Second Sound in Liquid Helium
    SOME APPLICATIONS OF SECOND SOUND IN LIQUID HELIUM r A. G. M. VAN DER BOOG SOME APPLICATIONS OF SECOND SOUND IN LIQUID HELIUM SOME APPLICATIONS OF SECOND SOUND IN LIQUID HELIUM PROEFSCHRIFT TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE WISKUNDE EN NATUURWETENSCHAPPEN AAN DE RIJKSUNIVERSITEIT TE LEIDEN, OP GEZAG VAN DE RECTOR MAGNIFICUS DR. A. A. H. KASSENAAR. HOOGLERAAR IN DE FACULTEIT DER GENEESKUNDE, VOLGENS BESLUIT VAN HET COLLEGE VAN DEKANEN TE VERDEDIGEN OP WOENSDAG 12 SEPTEMBER 1979 TE KLOKKE 15.15 UUR DOOR ALOYSIUS GERARDUS MARIA VAN DER BOOG GEBOREN TE LEIDEN IN 1948 KRIPS REPRO MEPPEL 1979 PROMOTOR: DR. H.C. KRAMERS. This investigation is part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materie" (FOM), which is financial- ly supported by the "Nederlandse Organisatie voor Zuiver-Wetenschap- pelijk Onderzoek11 (ZWO). \/SXr\ KWMV> ouofers CONTENTS. GENERAL INTRODUCTION. CHAPTER I. AC JOSEPHSON EFFECT IN % II. 11 1. Introduction 11 2. Order parameter and phase slippage by quantized vortex motion 12 3. The Richards-Anderson experiment 14 CHAPTER II. THE PARALLEL-FLOW APPARATUS. 17 1. Introduction 17 2. Principle of the apparatus 17 3. Experimental set-up 21 r 3.1. The apparatus 21 3.2. Registration of a helium level 22 3.3. Detection and generation of second sound 24 3.4. Constrictions 26 CHAPTER III. ATTEMPTS TO OBSERVE QUANTIZED VORTEX CREATION. 29 1. Introduction 29 2. Experiment on a single orifice 30 3. Experiment on a large number of parallel channels 33 3.1. Introduction 33 3.2. Experiment with CFI 34 3.3.
    [Show full text]
  • Theories and Heat Pulse Experiments of Non-Fourier Heat Conduction
    Communications in Applied and Industrial Mathematics ISSN 2038-0909 Research Article Commun. Appl. Ind. Math. 7 (2), 2016, 150–166 DOI: 10.1515/caim-2016-0011 Theories and heat pulse experiments of non-Fourier heat conduction P´eterV´an1* 1Department of Theoretical Physics Wigner Research Centre for Physics, IPNF, Budapest, Hungary and Department of Energy Engineering Budapest University of Technology and Economics, Budapest, Hungary Montavid Thermodynamic Research Group *Email address for correspondence: [email protected] Communicated by Vito Antonio Cimmelli and David Jou Received on January 17, 2015. Accepted on March 30, 2015. Abstract The experimental basis and theoretical background of non-Fourier heat conduction is shortly reviewed from the point of view of non-equilibrium thermodynamics. The per- formance of different theories is compared in case of heat pulse experiments. Keywords: ballistic propagation, second sound, non-equilibrium thermodynamics, kinetic theory AMS subject classification: 80A05 1. Introduction There are several extensive reviews of heat conduction beyond Fourier [1{6]. When non-equilibrium thermodynamics is concerned, usually Ex- tended Thermodynamics is in the focus of surveys in this subject. In this short paper heat conduction phenomena is reviewed from a broader per- spective of non-equilibrium thermodynamics. The performance of different theories is compared on the example of heat pulse experiments. There are two preliminary remarks to underline the particular point of view of this work. The first remark concerns the so called heat conduction paradox of the infinite speed of signal propagation in Fourier theory. Infi- nite propagation speeds are frequently mentioned as a disadvantage [7,8] and this is a main motivation for looking symmetric hyperbolic evolution equations in general [9].
    [Show full text]
  • Systematic Studies of the Second Sound Method for Quench Detection of Superconducting Radio Frequency Cavities L
    19th Int. Conf. on RF Superconductivity SRF2019, Dresden, Germany JACoW Publishing ISBN: 978-3-95450-211-0 doi:10.18429/JACoW-SRF2019-FRCAB8 SYSTEMATIC STUDIES OF THE SECOND SOUND METHOD FOR QUENCH DETECTION OF SUPERCONDUCTING RADIO FREQUENCY CAVITIES L. Steder∗, B. Bein, W. Hillert1, D. Reschke, DESY, Hamburg, Germany 1 also at University of Hamburg, Germany Abstract DESY conducts research and development for supercon- ducting radio frequency cavities. One part of the manifold activities are vertical performance tests. Besides the determi- nation of accelerating gradient and quality factor, additional sensors and diagnostic methods are used to obtain more information about the cavity behaviour and the test envi- ronment. The second sound system is a tool for spatially resolved quench detection via oscillating super-leak trans- ducers, they record the second sound wave, generated by the quench of the superconducting Niobium. The mounting of the sensors was improved to reduce systematic uncertain- ties and results of a recent master thesis are presented in the following. Different reconstruction methods are used to determine the origin of the waves. The precision, constraints and limits of these are compared. To introduce an external reference and to qualify the different methods a calibration tool was used. It injects short heat pulses to resistors at exact known space and time coordinates. Results obtained by the different algorithms and measurements with the calibration tool are presented with an emphasis on the possible spatial Figure 1: Single-cell cavity in R&D insert equipped with resolution and the estimation of systematic uncertainties of OST sensors for second sound quench localisation.
    [Show full text]
  • The Two-Fluid Theory and Second Sound in Liquid Helium
    The two-fluid theory and second sound in feature liquid helium Russell J. Donnelly Laszlo Tisza’s contributions to our understanding of superfluid helium are often overshadowed by Lev Landau’s, but Tisza’s insights are still paying dividends—and not just for helium. Russell Donnelly is a professor of physics at the University of Oregon in Eugene. Early research with liquid helium showed that it had re- dissipation. The uncondensed atoms, in contrast, constituted markable new properties, especially below the so-called a normal fluid that was responsible for phenomena such as lambda transition near 2.2 K, where there is a sharp, narrow the damping of pendulums immersed in the fluid. That rev- peak in the specific heat (see figure 1a). The liquid below the olutionary idea demanded a “two-fluid” set of equations of transition was named helium II to distinguish it from the liq- motion and, among other things, predicted not only the exis- uid above the transition, called helium I. Three properties dis- tence of ordinary sound—that is, fluctuations in the density covered in the late 1930s were particularly puzzling. First, a of the fluid—but also fluctuations in entropy or temperature, test tube lowered partly into a bath of a b helium II will gradually fill by means of 120 a thin film of liquid helium that flows Roton branch without friction up the tube’s outer wall. Second, in the thermomechanical effect, if two containers are connected by a 80 Phonon branch very thin tube that can block any vis- Helium II Helium I cous fluid, an increase in temperature in Δ one container will be accompanied by a 40 ENERGY rise in pressure, as seen by a higher liq- Roton energy uid level in that container.
    [Show full text]