Hi Keith,

I'm glad you fond the posting of interest.

I do not know what sort of mixtures you are proposing. With a previous power generation algorithm, I have modeled elements composed of up to three layers of different TE materials along with interface materials such as connecting tabs, substrates, and gap fillers. I am hoping to incorporate my new algorithm into a similar program in the future. It is possible to add additional layers of TE material, as well, it just adds computing time. This could also be done with cooling elements, I just haven't gotten around to it and I'm not sure whether anyone else has. If you are talking about non-layered 'mixtures', I'm not sure what you might have in mind.

Be aware, too, that there are issues with the way data is gathered for temperature dependency and things aren't quite as apecific as they may appear on the surface. While modeling for temperature dependency is still useful for exploring the interaction of phenomena associated with bulk properties, the variability within a 'population' of material is seldom captured. Typically, few samples are examined. Furthermore, differences between the way data is tested and the way material is employed, can lead to errors in generalization. These matters are discussed in the book.

Michael Spry

Keith,

This kind of scenario is very challenging to capture in a model.  If the shape of the enclosed conductor was such that it could be captured in some type of mathematical representation or three-dimensional array, one had bulk property information on both materials, and there was a defined volume and current level for the main conductor, it should be possible to do an analysis with a custom computer model.  If the conductors were doped-semiconductor material, the bulk property testing would have to be consistent with the orientation of the crystals for majority charge carrier flow.

I would go with finite element analysis dividing the overall volume into many segments and treating the enclosed material as though it is in parallel with the enveloping material.  The more simple the shape of the enclosed material, the easier it would be to approach the problem.  There might have to be some convergence algorithms to cope with the irregularities(?).  Just like with parallel electrical circuits, one would come to terms with the parallel portion and use the knowledge to understand each ‘leg’.  It might be possible to get relative indications of Seebeck voltage for the two materials in that area and resistance levels.  A complex shape would really make matters difficult, however.

Of course, with the second material being entirely enclosed, depending on how you look at it, there is either one junction or an infinite number of them.  Eddy currents are produced because there would be different Seebeck voltages developed across the entirety of the enclosed material with the same thermal gradient for both materials.  The difference in voltages would cause current flow all around the frontier between the two materials.  The potential differences would tend to resolve themselves locally.

If the shape of the enclosed material is at all complex, I think the most accurate assessments might well come out of an empirical approach, but as I’ve outlined, that takes a lot of sample testing.  You would need some way to assess the distribution of the particles, too.  As I often shared with my testing colleagues, “Nothing is easy.”

Michael Spry

Keith,

The key phrase is "great enough," especially if there is minimal dT across the material.

I don't see any big issues with measuring samples for bulk properties.  The tough part is correlating the results with distributions of the non-homogenous materials which would be unknown.

Michael Spry

Here is the basic criticism of Thomson's assertion of a "third effect":

1. Thomson starts with the notion that there will be a different energy level in a conductor with a ΔT depending on whether current flows from cold to hot versus hot to cold. This is true.
2. In "On The Dynamical Theory Of Heat", Thomson builds a long case on parallels with a mechanical engine using principals from Joule and Carnot. He ramps his argument to demonstrating that when electrical current moves from one temperature to another, heat must be absorbed or evolved in the process. He presents a good argument.
3. Thomson, however, presumes that this absorption and evolution must occur in a process outside of Peltier Effect or any other of the known bulk properties involved with conductors. Thus he proposes a second current-dependent effect which creates thermal responses (absorption and evolution of heat) as it interacts with increasing or decreasing temperature.
4. In fact, modern solid state theory shows us that Peltier Effect with its temperature dependency, would lead to absorption and release of heat along the length of a conductor and not just at the junctions. As charge carriers move through the band structure and increase or decrease in temperature, heat must be absorbed or evolved along the way. This would be consistent with changes in the Peltier coefficient as the temperature increases or decreases along the gradient. Similar absorption and evolution to a lesser degree also results due to temperature dependencies of Seebeck coefficient which effect charge carrier/energy level interaction related to Seebeck voltage.  Thus, there is no need for the second current-dependent effect to produce the kind of action which Thomson describes in "On The Dynamical Theory Of Heat". Bulk-property-related phenomena already provide the expected absorption and evolution as current moves among temperature levels.  Thomson's engine model is satisfied.
5. There was an alternative thesis to account for the energy differences which concerned Thomson. He was aware that Seebeck Effect and thermal conduction could either aid or oppose Peltier Effect, yet within his collected writings, there is no indication that he contemplated the thesis based upon these realities. When charge carriers flow from cold to hot (classic uphill cooling), Seebeck Effect and thermal conduction are in opposition to Peltier Effect and this tends to decrease the overall energy level within the conductor. On the other hand, when charge carriers move from hot to cold (downhill cooling), all three of those phenomena are aiding and this tends to heighten the energy level in the conductor. This has been clearly demonstrated with my own computer models which take temperature dependencies of all bulk properties into account. A thermal gradient results for each condition consisting of the temperatures which bring energy balance to every point along the length of the conductor. There are small differences between the gradients regardless of the nature of the operating points.
6. In "On The Dynamical Theory Of Heat" (page 319 of Volume I of the collected Mathematical and Physical Papers), Thomson presents an argument which actually just demonstrates the existence of the energy disparity between the two conditions of current polarity with respect to a ΔT. Because he has not considered the alternative thesis, however, he labors under the belief that his "third effect" (which is the second current-dependent effect he proposes) is the only explanation for this manifestation. He thus concludes that he has proven the existence of the effect when he has not.
7. Thomson's paired two-conductor experiments, which were detailed in "The Electrodynamical Quality Of Metals", only demonstrate the existence of disparities between the two conditions, and not always in the direction anticipated by Thomson. These experiments never did more than prove that energy disparities can result from the conditions; they did not in any way prove the existence of Thomson's proposed effect. They certainly provided no evidence favoring Thomson's hypothesis over any other theses that might explain the results.
8. The only suggestion of a mechanism to support Thomson Effect, was the elevation or lowering of energy levels with temperature--which is precisely what impacts upon charge carriers in Peltier transport.  This makes the amount transported at each point along the length, the product of the Peltier coefficient and the current level.

Based on these considerations, it is quite clear that there are logical flaws in Thomson's arguments supporting the existence of his eponymous effect, though some of those flaws may have only become apparent in the light of later understanding. Thomson did, however, possess adequate knowledge to entertain the alternative thesis at a conceptual level, though a lack of mathematical understanding on thermal conduction would have prevented more detailed analysis.

Inasmuch as the energy differences can be easily explained and modeled using only the four basic bulk properties, and the actions of those properties meet Thomson's concerns about the properties of engines, it would appear that there is no need for the concept of Thomson Effect and that its existence has never been proven.  Without clear indication of a distinct mechanism to support it—one that is clearly apart from the other bulk properties—I would say there is no reason to conclude that Thomson Effect exists.

Michael Spry

3/27/2015

Updated 10/27/2015