Hello,

Are you asking whether there is a thermal dual for electrical self inductance?  If there were, then the analogy would be complete, as you say, since electrical conductance has a thermal dual in thermal conductivity, and electrical capacitance has a thermal dual in heat capacity.

Regards,

Tom Cuff

Yes this is exactly my question: Are you asking whether there is a thermal dual for electrical self inductance?

Dear Sougrati,

you may find this reference of interest:

https://dl.dropboxusercontent.com/u/102255847/papers/ID%20335_PROENG_BSMEICTE2012towardsanelectricalanalogue.pdf

As far as I am aware, there is no inductance equivalent, certainly not with conventional physics, as it would violate the laws of thermo-dynamics. (not sure about the quantum level see this as an example: https://en.wikipedia.org/wiki/Quantum_fluctuation )

An inductance equivalence would have to generate heat flow (leading current) before there was a temperature difference.

Best Regards

Paul

Hello,

As I understand it, temperature is the dual of voltage, and heat flow is the dual of current.  If one considers the electrical mnemonic ELI the ICE man, then if there were a thermal dual for self inductance, this would imply - via the ELI - that the temperature would lead the heat flow across a thermal inductance in the case of sinusoidal stimulation.  

I am unaware of how the presence of a thermal inductance would violate the laws of thermodynamics, and, specifically, which of these laws it would violate and how.

Testing for a thermal inductance would be tricky for a number of practical reasons.  In solids, for example, heat is carried by both free (or nearly free) electrons (Thomson effect) in metals, and by lattice vibrations (phonons) in both metals and nonmetals. Since electrons can transport both heat and electrical charge (current), and because electrons have mass, they exhibit self inductance due to the inertia associated with their mass.  Distinguishing among electrical and thermal self inductances due to free electrons in metals and the thermal inductance due to phonons might be difficult to do.

Even in the case of an insulator, where there would only be the thermal conductivity contribution by phonons, there is still the problem of creating a large enough thermal inductive reactance to measure.  Since the thermal  inductive reactance - like its electrical counterpart  - is proportional to the frequency of the excitation, one would have to provide a high frequency thermal input signal, say heat flux, and have a wide bandwidth temperature sensor to measure the response, or vice versa.

Regards,

Tom Cuff

Some researchers talk about a prospective  presence of thermal inductance when it is question of what they call " the high-speed thermal" like when crossing the space shuttle in atmospheric zone.

Hello,

Can you provide any citations to the work of these researchers, who - you say - are speculating about the presence of thermal inductance?

Regards,

Tom Cuff

Ther is no written or published citation about that, I attended a discussion, long ago, in the laboratory between researchers about this question and our honorable Professor at that time P.Thery of USTL University advanced this idea, obviously, without proof .

Now I am thinking about that and I am asking  is there the new about that ?

Consider the attached Circuit of resistor and inductor.

In the electrical case, when the switch is closed, initially voltage across the inductor is the same as the voltage source it decreases to zero as the inductor is charged with a current of  voltage source / charge resistor. When the switch is open, the output voltage increases, theoretically to infinity, in practice until a breakdown occurs somewhere.

In the thermal case, there are two problems.

Firstly, the only known substance that has zero heat flow with a temperature across it, is a vacuum.

Secondly and more importantly, The temperature across any thermionic inductor, can never be greater than the applied temperature as this contravenes the second law of thermo-dynamics.

https://en.wikipedia.org/wiki/Second_law_of_thermodynamics

Even rapid changes in heat sources such as found on re-entry of the shuttle can never produce more temperature than the external system provides.

So there is no thermal equivalent of an inductor, certainly in non-quantum physics

I hope this clears this up.

Please mark up any answers you find useful.

Best Regards

Paul

Hello,

Two points: First, to make a perfect inductor, i.e., one without internal resistance and intra-winding capacitance, the electrical conductivity of the metal wire must be infinite. In the case of the thermal inductor, the same procedure should hold true, i.e., for a perfect thermal inductor, the thermal conductivity must be infinite so there is no internal thermal resistance, which also implies that the heat capacity is zero, and so there is no internal thermal resistance or thermal capacitance.  Now, a vacuum has zero thermal capacitance but infinite thermal resistance so it cannot be a candidate for a thermal inductor.

Second, Regardless of whether we are considering the mechanical duals of an electrical inductor, a capacitor, and a resistor, i.e., a mass, a spring, and a dashpot, or the thermal duals, i.e., a thermal resistor (inversely proportional to the thermal conductivity), a thermal capacitor (directly proportional to the heat capacity), and a thermal inductor, all such systems must obey the 1st and 2nd laws of thermodynamics.  For example, a mass, a spring, and a dashpot connected in series, with the mass initially at rest but the spring compressed, will exhibit oscillations of the mass for times greater than zero, but this does not violate thermodynamic laws.  Oscillations of temperature, due to thermal inductance, would likewise not violate thermodynamics laws provided energy was simply being transformed from one form to another or simply moved from one place to another.  Unlike in the mechanical and electrical situations, which can be theoretically represented and experimentally realized as lumped elements, the thermal situation offers no such lumped elements, i.e., everything is integral to the material.

One last thing, in the case of the mechanical duals, the mass can have finite extent, i.e., it does not need to be a point mass, but to be a perfect mass of finite extent, it must have infinite stiffness (it must be rigid), otherwise it will have parasitic springiness and damping.

I have not mentioned anything about quantum mechanics as I am not sure that it improves the arguments in any way.

Regards,

Tom Cuff

Hello,

I have just used the research database portal at FCC (Frederick Community College), where I am a student, to search for science articles whose title or abstract contains the term "thermal inductance".  Using the EBSCOhost database, I found three articles:

1) B. Hong, et al.; Measurement of fast-time heatflux with inverse thermoacoustic algorithms; Journal of Vibroengineering; Vol. 18; No. 1; 2/2016; pp. 577-586.

2) B. Hong, et al.; Realization of thermal inertia in frequency domain; Entropy; Vol. 16; No. 2; 2/2014; pp. 1101-1121.

3) B. Hong, et al.; Realization of non-Fourier phenomenon in heat transfer with 2D transfer function; Applied Mathematical Modelling; Vol. 35; No. 8; 8/2011; pp. 4031-4043.

Unfortunately, I do not have easy access to these journals.  Has anyone searched other research databases for the term "thermal inductance"?

Regards,

Tom Cuff

Dear Tom,

Taking your points one by one:

".. for a perfect thermal inductor, the thermal conductivity must be infinite so there is no internal thermal resistance, which also implies that the heat capacity is zero"

This is incorrect. In the electrical domain, a real-world inductor can be simplified by a perfect inductor and resistor in series. If the series resistor is zero, then one is left with a perfect inductor. The inductor can store charge v = Ldi/dt. In the thermal analogy, if an inductor were to exist (which it does not) then it would store heat. You appear to have misunderstood the basics of stored elements.

" For example, a mass, a spring, and a dashpot connected in series, with the mass initially at rest but the spring compressed, will exhibit oscillations of the mass for times greater than zero, but this does not violate thermodynamic laws ".

Thermodynamic laws refer to heat engines, not electrical circuits. It may be best if you read the references given and understand them before replying. 

"..Oscillations of temperature, due to thermal inductance..". There is no such phenomena of thermal oscillations, which is another reason why thermal inductance does not exist, this is a good point you make for the non-existence of thermal inductance.

With reference to your last post, it may be best for you to read references and understanding them before quoting them. I have spent 8 years of my career in thermo-acoustics, and can assure you that there is no thermal inductance present. There are complex thermal and acoustic interactions that can be described by wave theory as per the reference I gave earlier.

One last point, it is a pity your answers were voted down, it is always better to have the debate so we can all learn.

Best Regards

Paul

Thanks

Hi,

I have just read the discussion and I wanna add something on it according to my exprience.

Accepting the existance of thermal inductance depends on our knowledge about non-Fourier heat transfer in nanoscale (time/dimension). However, some mathematical relations have proved that it has contradiction with second law of thermodynamic, but I don't think so! By advanced nanoscale mesurement equipments in future, complete analogy between nature phenomena will be approved!

for more information, you can see the following papers:

- Thermal transport at the nanoscale: A Fourier's law vs. phonon Boltzmann equation study, http://aip.scitation.org/doi/abs/10.1063/1.4974872

-Thermal Inductance in GaN Devices, http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=7572880

-The dilemma of hyperbolic heat conduction and its settlement by incorporating spatially nonlocal effect at nanoscale, http://www.sciencedirect.com/science/article/pii/S0375960115008178

-Solving hyperbolic heat conduction using electrical simulation, https://link.springer.com/article/10.1007/s12206-013-0933-x

Regards,

Amir

you may find our recent article on this interesting:

Article Heat flowing from cold to hot without external intervention ...

Following

Just one thing to note:

" Since electrons can transport both heat and electrical charge (current), and because electrons have mass, they exhibit self inductance due to the inertia associated with their mass. "

In electromagnetism, inductance is caused by the energy storage of the magnetic field, not by the inertia and thus the kinetic energy of the electrons.

Hello Endre,

I suppose one can take your argument about energy storage and use it to explain capacitance, and even resistance. Though for resistance, you would probably talk about energy dissipation. But what is it about the charge carriers, say, electrons in metallic conduction, that ultimately gives rise to self-inductance, capacitance, and resistance? Saying it is energy storage (self-inductance and capacitance) and energy dissipation (resistance) is a high abstraction. What properties of the electron itself give rise to inductance, capacitance, and resistance? My answer would be mass, charge, and size, respectively. And I know that this is a classical and mechanical way to think about the process of metallic conduction, but it appeals to me. A quantum mechanical explanation of self-inductance, capacitance, and resistance would, no doubt, consider the electron as a wave packet propagating through an (infinite or finite) lattice of potential wells. And, of course, since the only classical law used to derive quantum mechanics is conservation of energy, one could equally say that energy storage/dissipation gives rise to these three properties of electronic conduction, but is this approach intuitively satisfying?

For instance, in the case of electrical resistance, one could explain it quantum mechanically by invoking scattering of the electron wave packet by things such as phonons, impurities, defects in the lattice, presence of surfaces both external and internal (due to grain boundaries in polycrystalline materials), etc. But ultimately, the reason for the scattering itself must be explained. In other words, what is it about the electron wave packet that makes it scatter? Of course, using the word 'makes' is cheating in quantum mechanics because it implies causation, it would probably be better to say that scattering just happens and leave it at that. I believe the party line with respect to scattering of electron wave packets by infinite or even finite arrays of periodic potential wells is that the waves making up the packet interfere either constructively or destructively depending on the pitch (spacing) of the potential wells. In which case, one could say that size or wavelength is the determining factor.

Anyway, I think you bring up a very interesting point.

Regards,

Tom Cuff

Hello, again, Endre,

I noticed that you gave a recommendation to a post by Paul Howard Riley from 2 years ago. Does this mean that you agree with or endorse some or all of his statements? For example, he stated that thermodynamics does not apply to circuits. This statement is false since a simple circuit of a battery in series with a resistor must obey the first law of thermodynamics, i.e., conservation of energy: the electrical energy dissipated in the resistor is converted to another form of energy, heat. It also must obey the second law of thermodynamics in the sense that the system evolves in a direction of increasing entropy, even if the system is isolated. He also states that an inductor stores charge. I was always taught that a capacitor stores charge in the electric field between its plates. An inductor resists a change in current flowing through it via the magnetic field created by the flow of current. And finally, he employed the oldest invalid argument to support his contention that there can't possibly be a thermal inductance, i.e., an appeal to authority, specifically his authority, as if he was and is infallible.

I did not respond to his post because it seemed to me that no one would have believed it since it was demonstrably false, and his attitude was so imperious that I thought it spoke for itself.

Regards,

Tom Cuff

Dear Tom,

" Thermodynamic laws refer to heat engines, not electrical circuits. "

" The inductor can store charge v = Ldi/dt. "

I definitely do not agree with these statements. You are right, I read it too fast and didn't notice these. Sorry for this.

However, I agree with him that "thermal inductivity" would violate the 2nd law of thermodynamics.

I also recommended your previous answer :) , although I do not agree with this idea:

"What properties of the electron itself give rise to inductance, capacitance, and resistance? My answer would be mass, charge, and size, respectively. "

The mass of the electron has no importance when we consider how the magnetic field is created (of course it counts when they are accelerated by a field, a=F/m...). The EM induction happens in bare vacuum as well, without any electrons, and this is classical electrodynamics, Maxwell equations...

you may click on the article link I posted above - there is a description of a device composed of an electrical inductance and a Peltier element, which both together behave exactly as a thermal self inductance

Hello Andreas and Amir,

I apologize for not replying to your posts. Andreas, I have downloaded your article and I have started to read it. Amir, you mentioned 4 articles. Which one of the four articles would you recommend as a good starting point?

Regards,

Tom Cuff

Hello Endre,

I did notice your recommendations of my posts, thank you. I think these discussions about the possibility of thermal inductance are very interesting because they tend to make us think more deeply about physics in general.

Let me briefly reply to two of your assertions. First, you believe that if thermal inductance were to existence, it would violate the second law of thermodynamics. You state this assertion without any proof. If something violates the second law of thermodynamics, you can usually tell because it would allow you to construct a perpetual motion machine of either the first or second type. Can you do this? I will return to this question in a later post as I am currently pressed for time.

Second, you state that EM induction occurs in free space. Let me object to your terminology "EM induction" for the following reason. Induction, whether it is mutual induction (discovered by Michael Faraday) between two unconnected circuits each with a coil in its respective circuit, or self-inductance (suggested to Faraday by certain experiments done by William Jenkins) where a single circuit with a coil in it resists changes in the current following through it, is essentially different from the propagation of EM waves. In other words, "EM induction" is a contradiction in terms, an oxymoron, if you will. Induction is a near field effect due solely to a magnetic field. EM waves, which is a far field effect, are photons moving at the speed of light. David Hughes, who transmitted and received radio waves before Heinrich Hertz, was dismissed by the leading scientific figures of the day, include George Stokes, because they thought that his transmitter and receiver were simply coupled inductively, i.e., magnetically via mutual inductance. Hertz eventually showed that true EM waves are transverse waves that could be polarized, reflected, refracted, etc. In other words, they had all the properties of light including the same velocity.

Regards,

Tom Cuff

Dear Tom,

" a single circuit with a coil in it resists changes in the current following through it, is essentially different from the propagation of EM waves. In other words, "EM induction" is a contradiction in terms, an oxymoron, "

In classical physics, these are described by the same Maxwell equations (Faraday law...) and as fas as I know, we call all these phenomena (when changing M field (or vector potential) induces E field) EM induction. On the other hand, I'm absolutely not an expert of QED.

I apologize, but can not write any proof because of the lack of free time. I didn't even want to start a new wave of debate, only to help by clarifying one little point of the debate.

Hello Andreas,

I had to daisy chain back through your references in order to help me understand your paper as I found it daunting to read by itself. To the extent that I understand anything, I usually do best if I approach the subject from a historical perspective. Here is my synopsis of how you and Bossen arrived at your startling experimental result.

Beginning in the late 1800's, researches were interested in the behavior of the newly invented glow lamps (incandescent light bulbs). In particular, they wondered about the behavior of these lamps when they were excited by alternating current rather than by direct current. Both carbon filament and the, then, recently introduced metal filament glow lamps were investigated. Numerous papers were written about the phase relationship between maximum power dissipated and the applied alternating voltage and resulting alternating current. All of this work apparently led O. M. Corbino to try and estimate the thermal heat capacity of the filament in the glow lamp by an in situ method.

Your 2011 paper with Bossen in the Review of Scientific Instruments was inspired by Corbino's approach to measuring the heat capacity. Your novel approach was to construct essentially an electro-thermal LC circuit with no losses by the application of external amplification to cancel any losses that were present. In other words, you thermally connected a gadolinium sample, whose heat capacity you wished examine below (where it is ferromagnetic) and above (where it is simply paramagnetic) its Curie temperature, to a heat reservoir via a Peltier heater/cooler and drove the Peltier device through a very large valued electrical inductor. Because it was impractical to construct such a high valued inductor, it was realized with a gyrator circuit employing opamps. An electronic amplifier circuit was used to compensate for any losses in the electro-thermal system, such as the presence of a finite thermal resistance of the gadolinium sample. When the electro-thermal system was caused to oscillate at its resonant frequency, you were able to use the formula (2*pi*f)2=1/(L*C) to determine C, which is related to the thermal heat capacity since you knew the frequency, f, and the value of the electrical inductor, L.

As I understand it, you leveraged the above technique to construct an electro-thermal system with losses that exhibited under-damped oscillations whereby heat was made to flow uphill (cold to hot) and then downhill (hot to cold).

Is this synopsis in any way accurate?

Regards,

Tom Cuff

Hello Endre,

I was simply trying to point out that inductance occurs between circuits that are usually made of metals, and the metal have electrons as their charge carriers, and the electrons have mass, which causes them to resist changes in their motion. If the circuits were constructed of P-type semiconductors, then the charge carriers would be holes, which also have an effective mass, and, hence, inductance. If the circuits were constructed of a conducting material with charge carriers that had zero mass, then the mutual inductance and self-inductance would be zero.

With regard to your statement that, " The EM induction happens in bare vacuum as well, without any electrons, ...", I disagree. The mutual inductance, for example, is measured in the circuits connected by free space, not in free space itself. At least, that is my understanding of the matter. If free space had distributed inductance and capacitance, like a coaxial cable or a wave guide, then there would be a definite upper limit to the frequencies of EM waves that could propagate through free space.

Regards,

Tom Cuff

Dear Tom,

I disagree with you, sorry.

For example: the usual drift velocity of the conduction electrons is so small that the kinetic energy due to this motion is negligible, compared to the total kinetic energy of the electrons or (I guess) the energy of the magnetic field in a coil. Without EM induction, the electrons would completely slow down in 1 nanosecond after switching off the voltage, because of the resistance of the coil.

Hello Endre,

I agree that the drift velocity of conduction electrons in metals is quite low, and hence the kinetic energy of a single conduction electron is small. However, there are two things that make the kinetic energy of conduction electrons measurable and significant in a macroscopic piece of metal: 1) the number of conduction electrons, roughly one per metal atom, and 2) the fact that drift velocities due to an imposed electric field are correlated, whereas the kinetic energy of valence electrons are not correlated.

In the metal traces used to connect transistors in high density integrated circuits, for example, the electron wind can be so great, due to a high current density (current per unit area perpendicular to the flow of current), that the lattice atoms are actually knocked from their positions causing voids to appear, eventually resulting in device failure. The effect is known as electromigration. But even before the phenomenon of electromigration was discovered, it was shown experimentally, in a series of very famous papers, that the resulting kinetic energy of accelerated conduction electrons was easily detected. The following references are to the famous Tolman-Stewart experiments.

R. C. Tolman, T. D. Stewart; The electromotive force produced by the acceleration of metals; Physical Review; Vol. 8 (2nd Series); No. 2; August 1916; pp. 97-116.

R. C. Tolman, T. D. Stewart; Mass of electric carrier in copper, silver and aluminum; Physical Review; Vol. 9; Feb. 1917; p. 164-167.

Also see, Edward M. Purcell; Electricity and Magnetism, Berkeley Physics - Volume 2; Education Development Center, Inc.; 1965; p. 423, Problem 4.26.

R. C. Tolman, S. Karrer, E. W. Guernsey; Further experiments on the mass of the electric carrier in metals; Physical Review; Vol. 21; No. 5; May 1923; pp. 525-539.

R. C. Tolman, L. M. Mott-Smith; A further study of the inertia of the electric carrier in copper; Physical Review; Vol. 28; Oct. 1928; pp. 794-832.

Also consider the following statement:

"If a current in a circular coil of wire free to move about its axis is started or stopped or altered, the free electricity will be accelerated, and the coil itself will be accelerated in the opposite direction."

S. J. Barnett; Models to illustrate gyromagnetic and electron-inertia effects; The American Physics Teacher [from 1940 onward: American Journal of Physics]; Vol. 5; No. 1; Feb. 1937; p. 1-6 [Above quotation on p. 6, 2nd column.].

The original experiment demonstrating angular momentum transfer between electrons and the metal lattice is found in,

S. J. Barnett; A new electron-inertia effect and the determination of m/e for the free electrons in copper; Philosophical Magazine; Vol. 42; 1931; pp.349-360.

Regards,

Tom Cuff

Dear Tom, I was not very precise in my previous answer. A few electrons can have significant drift velocities in the current, but the average drift velocity is small under usual circumstances. Also, this velocity does not depend on the shape of the wire significantly, but the induced current does. I mean L is greater for e. g. a toroid than for a straight wire. Especially if there is an iron core in the coil.

I've just found this paper (you can google and download it), the first few paragraph is exactly about this question:

ELECTROMAGNETIC MOMENTUM AND ELECTRON INERTIA IN A CURRENT CIRCUIT

Anyway, the phenomenon of electromigration is very interesting, thank you for drawing my attention to it. :)