Copyright © 1998 Harold Aspden

In this Lecture we will show why it is that the heat generated in a transformer core can be regenerated as electricity, now relying on that experimental evidence presented in Lecture No. 18. In this Lecture 19 some further evidence will also be drawn from the author's experimental research as reported in his Ph.D. thesis and in the author's papers published in the Proceedings of the Institution of Electrical Engineers. The prospect of exploiting such a regeneration phenomena is discussed and deemed viable.


Once it is suspected that the heat generated by magnetization loss in a transformer has a way of regenerating electricity it is logical to look at the physics governing thermoelectricity. In the transformer we do not have current circuits involving junctions between two metals. This rules out the Peltier and Seebeck Effects. The Thomson Effect is one discovered and reported by Lord Kelvin (then Professor William Thomson) in 1855. He showed that an EMF can be set up within a metal simply by there being a temperature gradient in that metal. In the transformer lamination we have such a temperature gradient owing to need for the heat to find an exit path. However there is no circuital EMF such as is needed to enhance eddy current flow and so the Thomson Effect does not account for regeneration. At best, owing to the Thomson Effect, there is an electric potential difference as between the middle section of a lamination and its edges. What we seek is some connection in a metal between EMF or electric current and a temperature gradient. Such an effect was discovered by H.W. Nernst and A. von Ettinghausen, Wied. Ann., v. 29, p. 343; 1886. We shall refer to this as the Nernst Effect, taking note that there is a complementary phenomenon known as the Ettinghausen Effect, the latter being the setting up of a temperature difference in a metal in a direction mutually orthogonal to a magnetic field and a flow of current. The Nernst Effect is the reciprocal phenomenon, namely the production of an EMF in a direction mutually orthogonal with respect to a magnetic field and a flow of heat through that field consequential upon there being a temperature gradient. We have such a situation in the core of a transformer.

Here I should have said that we have such a situation in the magnetic domains existing within that transformer core, meaning within those domains which happen to have their magnetic polarizations suitably orientated. The action of the magnetic field is to cause the heat flow in the plane of a transformer core lamination to develop a Nernst EMF across the thickness of the lamination, thereby encouraging the eddy currents in that lamination to flow selectively through those domains which generate a supporting EMF.

Note my use of the word 'generate' because what we have here is nothing less than the generation of electricity from heat and the action is not related to temperature as an absolute measure, but rather the difference of temperature effective in promoting heat flow by thermal conduction in metal.

Our 20th century eddy current anomaly can be explained simply by taking account of the Nernst Effect, which dates from 1886. It is difficult to believe our ignorance of this as being the true cause accounting for the mysterious loss of billions of dollars worth of electricity every year in power transformers.

Simply stated, the Nernst Effect converts heat into electricity and is very efficient in that action. Indeed, the conversion efficiency can but be 100%. The only problem is that of tapping the electric power generated before it dissipates itself as eddy currents in the metal. It is no wonder that what we see in our power transformers is simply that, the anomalous generation of heat owing to the enhancement of the eddy current action.

In order to understand a little better what I have just described, consider the following Fig. 1.

Fig. 1
This illustrates the cross-section of a steel lamination such as is used in a transformer. The transformer usually comprises large rectangular laminations stacked together but separated by an insulating coating to prevent the induced eddy currents from flowing from one lamination to an adjacent lamination, thereby restricting their effects to the thin metal section of each lamination. The EMF induced as the source of the power developing these parasitic currents is that set up by the rate of change of the magnetic flux local to that lamination.

So one must imagine that that flux is directed at right angles to the illustration of Fig. 1 and it really comprises the combined action of contributions by magnetic domains all polarized to a state of magnetic saturation in a preferred direction governed by the crystal structure of the steel. In practice the magnetic polarization will tend to be along one of the crystal axes that is closest to the plane of the lamination. For our purpose it suffices to depict two domain polarization states, one shown in pink which has its polarization directed in the same direction as the magnetic flux in the transformer core and one shown in pale green which has its polarization set in the opposite direction.

As the core flux increases the domain walls between domains shift so that, more and more, the red domain regions dominate and when the flux decreases the green domains grow until, at the point where the core flux reverses, they become the dominant domain species. However, while this is an ongoing process in the operation of a power transformer, those eddy currents are induced with a appropriate phase lag and these circuital eddy currents, shown as having rectangular flow paths duly reverse direction with an out-of-phase relationship relative to the transformer core polarization.

The key point I wish to make is that the magnetization losses associated with these eddy currents and the hysteresis of the core produce heat in the lamination and that heat, along with the current, is confined by that insulation between the laminations and obliged to flow laterally to get to the outside edges where the core interfaces with a cooling medium. Taking the shortest route, the main heat flow is lateral to the core magnetization direction and so is as shown in Fig. 1 and also in Fig. 2, which applies to the periods when the eddy currents have reversed direction.

Fig. 2

The difference between Figs. 1 and 2 is the different current flow paths near the edges of the lamination. The currents take the paths of least resistance or rather the path of maximum forward EMF, because the heat is converted into an electrical action all the way along the flow path owing to the Nernst Effect interaction with those domains. The potentials developed at intermediate positions are acting against the insulation or are opposed to the induced EMFs that drive the eddy currents or they may aid eddy current flow but that only deploys heat locally. However, in the relevant magnetic domain type at the edges of the lamination the two actions invariably supplement one another to add impetus to the basic eddy current flow. There is then a cooling action adjacent the edges of the lamination as heat is deployed in that effort and the overall result is that far more current flows as eddy-current than one expects theoretically from calculation based on magnetic induction theory. The heat deployed by that cooling reappears as resistance loss in the central regions of the lamination. Hence there is what has been termed 'the eddy current anomaly'.

Indeed, in a sense, here we see the room temperature action of what amounts to 'warm superconductivity' except that we do not see the 'over-run' condition where the thermally-induced EMF overtakes the potential drop associated with the normal resistance property which is still there in those so-called 'warm superconductors'. However, the latter phenomenon is not dependent upon the Nernst Effect, but rather the simple phenomenon of magnetic induction preserving current flow when two electric charges of opposite polarity come into collision owing to their motion in opposite directions. The energy stored by induction prior to collision survives the collision and sets up the EMFs needed to restore the opposed motions of the charge after their collision. However, in the process the heat energy of the heavier ions, atoms and molecules, involved has been depleted and transferred to the magnetic induction state of the region surrounding the collision, only to be returned as the electrical drive power which keeps the current flow ongoing. I have discussed that subject elsewhere in these Web pages towards the end of Lecture No. 9 under the heading Supergravitons and Cold Fusion.

From a technological point of view the fact that transformers operate at normal ambient temperatures and exhibit the eddy current anomaly tells us that we should be able to develop energy converters which run on ambient heat to deliver electrical power. Conversion efficiencies are, it seems 100% in the 'warm superconductor', but we have yet to see that technology develop to become reliable at room temperature and it will need a leap beyond that to reach a margin of excess allowing some of the self-generating action can be tapped to deliver electrical power for useful purposes. One day we may perhaps see large induction coils composed of superconductors carrying a high current and, by cyclically altering the inductance, it could well become possible to take off electricity as the system cools to absorb ambient heat. That must remain a pipe dream at this time, but meanwhile one can take stock of the eddy current anomaly and what that may imply.

As will be understood by those familiar with the calculation of eddy current loss in transformers, the passage of the eddy currents through the very thin layer of metal section is the seat of heat generation by eddy current loss. One seeks to obstruct the current flow by using steel of high resistivity consistent with good magnetic properties and by making the laminations thin one can minimize the current flow and so contain such losses. However, remember that Nernst Effect and note that there is in excess of 20,000 gauss acting as a magnetic field strength in each magnetic domain. Therefore, the flow of heat through those domains will induce an EMF mutually orthogonal with respect to the direction of heat flow and the direction of magnetic polarization. Consider this and you will see that one domain type, say the green form illustrated will act in Fig. 1 to develop an EMF adjacent one edge, the right hand one shown, acting between the faces of the lamination but in a direction which opposes the flow of eddy currents, whereas the pink domains shown will develop an EMF which strengthens the flow of eddy currents.

The result of this is that, whatever be the momentary phase of the flux or the eddy currents, the Nernst Effect will always capture some of the heat flow that is trying to escape from the edges of the lamination and cause it to generate an EMF which strengthens the current. The current will always flow along the path where it is assisted rather than opposed.

Indeed, without knowing the Nernst coefficient of the metal forming the laminations or its composition and physical properties, such as resistivity, but knowing the eddy current anomalous loss factor, one can estimate the actual value of that coefficient. The Nernst Effect is quite difficult to measure under normal circumstances because one needs to set up a known temperature gradient in what is a good thermal conductor and, though an EMF can be measured under zero current flow conditions, it is the operating state where that Nernst EMF promotes current flow that one seeks to explore in measurements having a technological objective. The standard transformer affords the means of measurement, simply by virtue of the phenomenon of the eddy current anomaly.

The method is implicit in the numerical examples recorded in the preceding Lecture No. 18 entitled The Eddy Current Anomaly. Note that the wider the lamination, the greater the mass of steel generating the magnetization loss. This means that the heat generated will escape by conduction through the metal at a rate which sets a temperature gradient somewhat independent of the lamination width, but dependent, of course, on lamination thickness. As to the latter one presumes that the same steel lamination stock is used in transformers large and small, so the core thickness becomes the next parameter we need to consider. The larger this thickness, the more the number of laminations in a core stack. Now, the thicker the core, the greater the induced EMF which generates the eddy currents, the ratio being linear for a given core width. So, this width dimension, being that of the direction in which the thermoelectric Nernst EMF is developed, governs the magnitude of this EMF. It will increase pro rata with that core thickness. Therefore, the induced EMF responsible for the primary eddy current flow and that EMF added by the Nernst Effect will be in linear proportion. It follows that, regardless of the size of the transformer, the measurement of the eddy-current anomaly factor, meaning the ratio of the actual and theoretical eddy current loss components, will allow one to estimate the actual Nernst coefficient effective in the steel used in the transformer core.

What this means, of course, is that one cannot escape the consequences of the eddy-current anomaly by scaling up the size of a transformer. Conversely, if one contrives to find away of exploiting the phenomenon described to tap into the potential power output from that anomalous increment of EMF, the task will not be thwarted by incorporation in very large power generating units. The phenomenon can be used in the large scale implementations of the technology.


To add further confirmation of this interpretation of the anomalous loss phenomenon, ask yourself what happens when a transformer core is d.c. biased, meaning that the magnetic polarization has displaced the hysteresis cycle towards core saturation. As mentioned in TEC III, if the bias is substantial, this will reduce hysteresis loss for a magnetization cycle having the same flux density range. However, if the flux change occurs at the same frequency and the voltage waveform is sinusoidal in form, there should, by standard teaching, be no change in the theoretical eddy current loss. Yet, what we have done is to set up a higher proportion of magnetic domains with their magnetic polarization in one direction than applies in the opposite direction. This reduces the scope for the Nernst Effect to be active in enhancing the bidirectional oscillation of those eddy currents and it will reduce the anomaly. In short, we should expect tests such as are confined to regions near magnetic saturation of the core to show very little anomaly.

This also means that even during the normal magnetization cycle, with no polarizing bias applied to the core, there will be strong enhancement of eddy current flow when the flux density is of low value but much reduced enhancement at high flux densities. Tests expressly conducted to see how the anomaly factor varies instantaneously as we progress around the whole of the B-H loop of the core should confirm this, if the Nernst Effect interpretation is correct.

I am able to report such confirmation because I made those tests long before I came to realize that it was the Nernst Effect that was causing the problem. The following Fig. 3 was in my paper entitled 'An Investigation of the Eddy-current Anomaly in a Low Silicon Sheet Steel', Proc. I.E.E., vol. 104C, pp. 2-7 (1957).

Fig. 3

I had devised a technique for measuring the instantaneous loss anomaly factor arising at different parts of the normal B-H magnetization loop. Fig. 3 shows the mean loss anomaly factor, such as one would find by normal measurements. Thus the sample tested had a mean loss anomaly factor of the order of 1.5, but this reduced for magnetization over a cycle that ranged between the higher flux densities. That is shown by the broken curve.

The full line curve, however, shows how the loss anomaly factor varied as the flux density climbed during the magnetization cycle. It dropped virtually to the zero anomaly level over the upper flux range where all the magnetic domains are polarized in a common direction.

The technique of measurement used for this purpose depended upon knowledge of the effective incremental permeability over the selected range, the sector selected for test having substantially linear permeability. However, the measurement of that permeability value had to be based on the analysis of the static hysteresis loop, meaning the B-H loop measured by fluxmeter tests at zero frequency rather than one involving a.c. activation. Assuming discrepancy between the measured permeability and that effective owing to a.c. excitation, it was appropriate to estimate a worst case scenario, one, however, which just cannot possibly prevail, just to see if it was at all possible to escape the evidence of that loss anomaly. That worst case adjustment is indicated by the arrows and the findings were clear that there was just no way of avoiding the acceptance of a significant anomalous energy loss. The eddy current anomaly is not something that is fortuitous in the sense that it can be attributed as a consequence of misinterpretation of the measurement data.

When an entirely different method of measurement was tried, one reported in my paper entitled 'The Eddy-Current Anomaly in Electrical Sheet Steel, Proc. I.E.E., vol. 103C, pp. 279-285 (1956), in this case restricting the measurement to instantaneous rate of loss as the magnetic flux traversed to zero flux density state in the B-H loop cycle, some quite substantial anomaly factors were measured.

A typical result, taken from Table I of that paper, applies to Superstalloy laminations having 4.3 Si composition, a lamination thickness of 0.309 mm and a specific resistivity of 59 microhm-cm. It was found that the instantaneous anomaly factor effective at zero B flux density was 4.81 when the B-H loop ranged up to a maximum flux density of 6,775 gauss, 5.22 for a loop having a maximum flux density of 10,250 gauss and 5.03 for one having a maximum flux density of 13,550 gauss.

An entirely different set of tests were performed on solid steel cores where higher frequencies were used to confine the cyclic magnetization to surface layers of the test specimen. These were based on the eddy current effects affecting the phase angle of the magnetizing current in relation to voltage. The action is tantamount to a time-lag effect which affects that phase angle. The hypothesis I was exploring was that hysteresis loss involves transient adjustment of magnetic flux as domain boundary walls move in abrupt steps when there is instability. I reasoned that, if the magnetizing current were to increase so fast that those transient adjustments did not occur at the trigger level of that current, as applied to the zero-frequency B-H magnetization cycle, then there would be added loss. It would, in effect, be a dynamic hysteresis loss, and I wondered if this could be the true cause of the eddy current anomaly.

So I did experiments with that in mind and the results are to be found in my paper Magnetic Time-Lag Effects in Solid Steel Cores, Proc. I.E.E., vol. 103C, pp. 272-278 (1956). Note that the measurements of such a time-lag effect do not tell us whether there is, in fact, a retardation in the magnetization process or whether there is an increase of eddy-currents owing to a reduction of electrical resistivity. Certainly, the thermoelectric effect discussed above should still be of consequence in tests using solid cylindrical steel cores, because the heat escapes radially and the currents flow circumferentially, with magnetic flux polarization being longitudinal. There was no doubt that the time-lags recorded were commensurate with those applicable to laminar core tests, but one vital fact did emerge. The time-lag reduced virtually to the minimal no-anomaly level when the core was polarized close to saturation, though still subject to sufficient oscillatory flux change for eddy-currents to be measurable and of significance.

In summary, my experimental research on the eddy-current anomaly gave results all of which were consistent with the thermoelectric regeneration interpretation, the interpretation which goes against the Second Law of Thermodynamics as having an governing influence upon the heat to electricity conversion.


With such knowledge the question now confronting me is how I can exploit the action I see at work in the standard power transformer core to tap into that Nernst Effect power before the energy is lost in those eddy currents.

At this stage it helps to do some quantitative evaluation. The suggestion is that the EMF set up across a flow path equal to the thickness of a sheet steel lamination (0.3mm) is sufficient to overwhelm the EMF set up around the whole eddy current circuital flow path in that transformer. The latter can easily be of the order of 0.05 volt in a moderately large power transformer. One then sees that the Nernst EMF per cm induced in that lamination has to be of the order of volts per cm and, taking the Nernst coefficient of iron at 10,000 gauss as 10.5 volts per cm, per degree C per cm, this really tells us that a temperature gradient of 0.1oC/cm will suffice to account for the eddy current anomaly factors observed. The magnetization loss need only be a few milliwatts per cc to sustain such a temperature gradient, which is consistent with the specification of loss properties of electrical sheet steel. Accordingly the theory does have quantitative support.

Before proceeding I will here comment on my objective in drawing attention to this topic. I believe one could build a solid-state device which will tap the thermal energy of the background environment and provide cooling in combination with electrical power generation. If we can do this we have breached the Second Law of Thermodynamics.

We are in these Web pages exclusively concerned with the physics which has eluded the scientific community at large. If what is presented here were merely a repetition of accepted knowledge as taught in academic institutions, the author would be enjoying his retirement in other ways, rather than striving to attract attention to what is here disclosed. It is a very daring pursuit to try to convince scientists in general that the Second Law of Thermodynamics can be breached to our advantage, but it is even more daring to declare that we can derive our power needs from the energy of the environment or that of the aether.

I am all too aware of the words of Sir Arthur Eddington which I have seen quoted on page 639 of the book 'The Anthropic Cosmological Principle' by John D. Barrow and Frank J. Tipler, as first published by Oxford University Press in 1986 and reissued in 1996:

"The law that entropy always increases - the Second Law of Thermodynamics - holds, I think, the supreme position among the laws of physics. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things from time to time. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation."

I am now going to show why these words of Eddington should be ignored, but first I will quote one other item from that book just mentioned. It appears in the Introduction on page 5:

"The Holy Grail of modern physics is to explain why these numerical constants - quantities like the ratio of the proton and electron masses for example - have the particular numerical values they do. Although there has been significant progress towards this goal during the last few years we still have far to go in this quest."

Let me now ask you, the reader, a question. Suppose you set off in search of that Holy Grail. How do you proceed? There are only two routes to follow. Either you say that all the protons in the universe were created in the early phases of the hypothetical Big Bang which marked the beginning of time or you can imagine that protons are being created even now throughout the universe, but only where energy has been shed by proton decay. This presumes that there is a regenerative process, involving, as ever, conservation of energy, but nevertheless a process that can be regulated by physical principles based on what can be measured in the laboratory. You see, you need to understand how a proton is created before you can deduce its mass. All protons are the same. It is as if they come from a common mould and understanding that mould is the secret of that Holy Grail.

If you read that book by Barrow and Tipler, you will learn nothing about Creation, because, as they declare in that quotation from page 5, they do not know how protons are created and yet protons account for 99.9% of the mass of the universe. On the other hand if you read my 1980 book Physics Unified, published six years before that book by Barrow and Tipler, you will see how protons are created and be able to calculate the proton/electron mass ratio. You will see that the theoretical value is slightly greater than 1836.152, which is also its measured value. Further you will see that this explanation of the creation of matter in the form of the proton, was published in the scientific literature five years before that, in 1975. So if you go in search of that Holy Grail all you need to do is to obtain a copy of my book or just look elsewhere in these Web pages, starting with the Tutorial section.

My point in saying this is to stress that it is illogical for physicists to try to understand how matter is created unless they are prepared to accept the regenerative energy process. Energy shed into space in that ever-increasing entropy process has a way of joining in a quantum dance and packaging itself into a form that can materialize to produce protons.

From this position it seems a trivial exercise to argue against the Eddington proposition that the Second Law of Thermodynamics is sacrosanct. Let us therefore now come back to that lesser task, the prospect of building a solid-state device that can cool and generate electricity by tapping the energy of heat in our environment.


Consider what happens when an electric current flows around a circuit formed by connecting two wires, each of a different metal, say nickel and aluminium, with the two junctions maintained at different temperatures. We do not need an electrical power supply to set up this current flow. That temperature difference is sufficient.

It is found that the current will flow from the nickel wire to the aluminium wire at the hot junction and from the aluminium wire to the nickel wire at the cold junction. This phenomenon is known as the Seebeck Effect, discovered in 1826, though at that early date the nickel-aluminium combination was not in Seebeck's list. The heat drives the current. In other words heat is converted into electricity. Now, how efficient is this process?

Well, here we have a problem, because what is happening at the hot junction is a cooling process and that means that the temperature over the restricted interface where the current crosses the junction is substantially reduced. Indeed, it must be well below the temperature of the heat source applied to that junction, because with reduction of temperature these two metals develop an increased conductivity and this can become confined to spot regions owing to the current flow escalating its concentration into those regions. However, whatever the actual spot temperature at the point of junction crossing, it is heat at that temperature that is converted into electricity.

Now, quite obviously, this has to be conversion at 100% efficiency. Heat becomes electricity and if this process were inefficient all that would mean is that there would be some heat produced to augment the heat supplied. Conservation of energy means 100% conservation as between heat and electricity.

There is, of course, something happening at the cold junction, but my concern here is the part of the circuit on the left hand side of Fig. 4.

Fig. 4.
Here I show two metal interfaces or junctions and ask you to look at that left portion of the circuit, the hot junction, from the viewpoint of those two different metals. Owing to the local temperature at that junction there is a voltage V across the interface and a current I flows. It is d.c. current and so the electrical power flow across that interface is VI. I say that VI is 100% of the heat extracted from the thermal state of that hot junction between the two metals.

I well realize that an overall assessment of the energy conversion efficiency of the circuit needs to allow for some heat loss owing to thermal conduction through the metal, but that need not be too great. What is important is the fact that that voltage generated cannot supply its energy to a normal load such as a resistor. It must, owing to the configuration using two metals, pass that current through the junction from aluminium to nickel, where it converts electricity back into heat and does so with 100% efficiency.

In that process the cold junction will not demand as much electricity as is generated at the hot junction, because it has a lower temperature. Its V value is lower, lower in proportion to absolute temperature. Now, if the EMF acting between the different metals is proportional to the absolute temperature of the junction temperature then the Seebeck Effect cannot convert heat to electricity with an efficiency exceeding the Carnot factor, namely the difference of the two temperatures as divided by the one of higher value, the latter being expressed in absolute units.

With the Nernst Effect that we discussed with our transformer eddy-current anomaly in mind there is no opposing EMF in the circuit other than that attributable to the load. In other words, apart from a little loss owing to circuit resistance, the heat deployed is all active in generating useful electrical power. It is just that in the context of eddy currents in the power transformer there is no 'load' as such other than that circuit resistance, which is why the regenerative feature presents itself as the enhanced loss which is known as 'the eddy current anomaly'.

Now at this point I shall conclude this Lecture. I have contended that there is in every electrical power transformer a manifestation of an anomalous energy phenomenon which, if properly interpreted, tells us that low grade heat, meaning heat at ambient temperatures driven by a temperature differential of 10 or so degrees C, is being converted back into electricity with remarkable efficiency. That efficiency is such that one can contemplate harnessing the phenomenon to advantage, By building a conventional reverse heat engine, a heat pump, and running it back-to-back with an energy converter harnessing such principles it seems economically feasible, indeed highly feasible, to expect to be able to harness heat extracted from our environment at its ambient temperature and generate useful electrical power.

My hope is that those having the resources needed to fabricate laminar metal assemblies based on bonded core structures for use in a modified type of transformer will show interest in this prospect and take up this proposition. I shall enlarge on this theme as I add to these Web pages.

Harold Aspden
May 9, 1998