Here, basic concepts of temperature and thermal energy are discussed, the general behavior of TEMs described, and a method for modeling device performance mathematically introduced. Subsequent pages show how this information can be used to make calculated system performance estimates, and highlight various other considerations relevant to the successful use and application of thermoelectric modules.
Introduction
Thermoelectric modules (TEMs) are solid-state devices that can directly convert an electrical input into a heat pumping effect, transferring thermal energy from a region of low temperature to one of higher temperature, opposite the direction in which it tends to flow naturally. The conversion of electrical energy directly to a heat-pumping phenomenon in this way is referred to as the Peltier effect, and devices employing it for heat transfer purposes are sometimes referred to as Peltier devices accordingly. When the phenomenon is run in the opposite direction by maintaining a temperature difference between junctions of dissimilar metals/semiconductors in order to produce an electric potential or current flow, it’s referred to as the Seebeck effect and forms the basis for thermocouple sensors used for temperature measurement. It can also be used to produce small amounts of electrical energy, the process of so doing being referred to as thermoelectric generation.
TEMs are commonly used for refrigeration and temperature control at small physical scales, when minimal size and weight are important, or when the amount of heat energy to be moved is too small for other refrigeration methods to be practical. Additionally, the heat pumping effect produced by a thermoelectric device can be reversed or modulated by reversing or varying the electrical input power applied, making them extremely useful for applications requiring repeated warming/cooling cycles or where maintenance of a very precise temperature is required. While this ability to produce a refrigeration effect by applying electricity to a solid-state device is certainly convenient, the use of thermoelectric devices for cooling is not as straightforward as it might appear at first glance, and is less efficacious than other common refrigeration techniques for reasons to be discussed.
Figure 1: A variety of thermoelectric modules with various options. (L-R) A standard unsealed TEM, one with potted (sealed) junctions, metallized mounting surfaces, and a 4-stage device with metallized cold-side surface.
Temperature: What Is It?
Before engaging any discussion of thermoelectric devices, it’s helpful to lay a foundation of ideas concerning what this concept of temperature actually is. In the totality of human consciousness, it seems that there are few ideas that are used so widely and are so universally understood at a subjective level, while at the same time being so sparsely understood in an objective sense. People have experienced “hot” and “cold” since the beginning, and the perception is similar across the board, regardless of language or culture. Temperature is mentioned in weather forecasts, in recipes for baking, as an indicator of one’s state of health. Ask Random Stranger what temperature is, what it’s actually measuring however, and the answer will likely be something along the lines of “how hot or cold something is.” Such a response seems ultimately to be an appeal to that shared, self-referencing human experience that’s been the same throughout recorded history; “hot” causes one to sweat, “cold” causes one to shiver.
Such a response however, does not offer an explanation for what physical processes are actually taking place, doesn’t offer a coherent explanation of what “coldness” or “hotness” fundamentally are . Such concepts did not emerge in forms resembling the present understanding until the early 1800s, and were not developed and demonstrated in currently understood forms until the mid to latter portion of that century, when humanity began developing molecular theory into something with some real utility. An explanation for what “hot” and “cold” are in a physical sense arose from the understanding that the atoms and molecules from which matter is composed are not stationary, but instead moving; vibrating, quivering, bouncing around off of each other. These small particles, like larger objects such as a rock or a baseball, carry energy by this fact of their being in motion, and we call energy in this form of molecular motion thermal energy . The faster the motion, the more energy is being carried.
Temperature, in effect, is a measure of the speed or intensity of this molecular motion. Imagine a room with a large number of rubber balls lying on the floor, stationary and not moving; this is an imperfect but useful way to visualize “absolute zero” temperature. If one adds a small amount of energy to the system by throwing one of the balls, it will bounce around and eventually impact another ball, causing it to move and eventually impact another, and so on, until most of the balls are rolling around gently; this represents a “low” temperature. If one adds a lot of energy to the system by using a rapid-fire pitching machine to throw a lot of the balls at high speed, the room will shortly be filled with a cloud of balls moving around like a swarm of angry insects; this would represent a “high” temperature.
The nature of the random collisions in the room-full-of-balls picture is that the speed of the balls tends to even out; fast-movers get slowed down upon impact, and stationary or slow ones are soon bumped into causing them to pick up speed, until some sort of stable average has been reached. Open a divider between adjacent rooms, one “hot” full of balls moving at high speed and one “cold” where they’re just gently rolling around, and a transfer of energy will occur from the “hot” side to the “cold” side. Fast-moving balls from the “hot” side will impact slower-moving ones on the “cold” side, causing the fast to move more slowly and the slow to gain speed. Never do they interact in a way that results in the slow/cold balls transferring their energy to the fast/hot ones on average, such that the cold become colder and the hot become hotter; energy is always transferred from a hot substance/object to a cold one when the two are exposed to each other.
We measure temperature, among other reasons, to understand how much energy is stored in an object/substance by virtue of molecular motion, and to determine the direction and rate at which energy is expected to transfer from one object/substance to another. Thermal energy will flow from something at a higher temperature to one at a lower temperature, like water runs downhill; it’s going to happen . Where there is a temperature difference, there will be a transfer of thermal energy; it’s only a question of how much and how fast.
The reason for starting this resource on thermoelectric devices with a discussion on this topic is the large proportion of support requests for TEM devices having some variant of “it’s not getting cold” as the chief complaint. The issue in the great majority of these cases is the users’ under-appreciation of the need to manage the energy flows that result from the temperature differential they’re trying to create. Those who don’t appear to recognize the connection between temperature and energy at all will often present an implementation that lacks essential components. Those who do understand the idea in a structural sense but lack the tools needed to make calculated estimates of system behavior will often present a system with one or more components improperly sized relative to each other, the end objective, or both. And those persons who both understand the concepts and have the conceptual tools needed to avoid raw guesswork in the design process? They generally don’t call tech support.
Thermoelectric Modules: Basic Ideas and Concepts
The basic idea behind a thermoelectric module is that application of an electrical input results in the transportation of thermal energy or ‘heat’ from one side of the device to the other. (How exactly it achieves this is a different topic for a different time.) This electrical input is itself a form of energy, which is being dumped into the TEM in order to power that heat pumping process. Putting energy into an object such as a TEM (or a rock, or a pizza, or…) will increase its temperature, if that same amount of energy is not extracted from it somehow. Similarly, moving thermal energy from one side of a device to the other will result in a temperature difference between the two. Something important to note here is that like any other pump, TEMs do not work very well with a plugged outlet; heat in the form of electricity is being put into the device and if it can’t escape out the “hot” side, the temperature of the TEM will increase until A) it does escape from the hot side B) it escapes out the cold side instead, or C) something breaks.
Quantities of thermal energy, measured in joules, are commonly represented using the symbol Q . The rate at which some quantity of energy is changed or transferred per unit of time is commonly measured in units of joules per second, which are equivalent to units of watts and are measure of power. In formal theoretical/analytical contexts where a person is at risk of running out of letters with which to do math, it’s common to represent those thermal power quantities using the same Q with an added dot over the top, to indicate a rate of change in the dotted quantity with respect to time. Such notation is a nuisance for publishing purposes however, so folks working from a more practical/applied perspective will often omit the dot and just use the Q symbol to represent thermal power. Particularly for students who get exposed to both conventions before gaining a level of comfort with either, it’s an understandable point of confusion.
The temperature difference between the two sides of a TEM resulting from the heat pumping effect it produces is commonly represented with the symbol ΔT. (The Greek letter Delta representing a difference, the T for temperature.) How much of a temperature difference is produced? It depends, both on the amount of electrical power applied to the device, and what’s done with all that thermal energy that’s being moved around. TEMs are quite leaky, thermally speaking; quite a lot of thermal energy can flow through them as a result of a small temperature difference between their two sides. The greatest temperature difference a TEM can produce results when it’s not actually moving any heat from its environment from one side to the other, but is rather only just able to keep up with the amount of leakage through itself that’s caused by the temperature difference it’s producing.
At the other extreme, where there is perfect external heat transfer between the hot and cold sides of the TEM (the thermal equivalent of a short circuit) the temperature difference is zero and the amount of thermal energy drawn through the cold side of the device is at a maximum. Neither extreme is perfectly achievable in practice, nor would either be especially useful were that possible; practical applications operate at some point along a continuum between the two extremes.
Characterization of Thermoelectric Devices
Exact practices vary somewhat, but it is common for better suppliers of TEMs to characterize them in terms of several inter-relating quantities:
- The temperatures of the hot and cold sides of the device
- The amount of thermal power transferred through the device’s cold-side plate
- The amount of electrical current passed through the thermoelectric device
- The voltage across it that develops as a result.
This information or its equivalent is necessary for making a calculated estimate of device behavior in a given scenario. Suppliers of a lesser standard are more likely to simply offer numerical “maximum” and/or “rated” electrical and thermal values for their products, often with limited supporting qualifications. Such limited information is better than none at all for purposes of making informed use of a thermoelectric device, though not by much.
Using CUI part number CP85438 as an example for this case study, the datasheet excerpt in figure 2 shows the limiting values for the device, along with that for several related part numbers. This information is fairly well qualified, with notes and annotations describing relevant conditions at which it applies; it’s not merely using numbers to describe the device, it’s also indicating specifically what those numbers mean. Information of a lesser standard will often just indicate “maximum” values for ΔTMax, , current and voltage, without indicating the conditions under which any of those values apply.
Figure 2: CP85438 datasheet excerpt.
While the tabular information provided for the CP85438 is quite good, the graphical information provided later in the datasheet and excerpted in figure 3 is a very significant addition, in that it provides information as to how the device behaves under a range of operating conditions. There’s some very important insights to be found therein. First, locating the points on the chart that are described by the maximum values given numerically earlier in the datasheet, it can be seen that these points are at the opposite extreme ends of the curve corresponding to maximum rated drive current; in other words, the maximum temperature difference and heat pumping values do NOT apply simultaneously. Instead, each one applies when the other is zero. Again, any practical application is likely to operate somewhere in between those two extreme points.
Second, there are significant operating efficiencies to be gained by operating the device below its listed electrical maximums. There are 5 lines plotted on each of the two (conjoined) charts, representing the operating curve at 20% increments of maximum rated current. The curves on the Q vs. ΔT plots grow significantly closer together as operating current increases, despite the corresponding voltage curves remaining more or less equally-spaced. A (thoughtful) glance here suggests that operating at 100% of maximum rated drive current might not be an optimal design decision. If one assumes a constant 20-watt cold-side thermal load for example as represented by the dotted line in figure 4, the first 1.7A of drive current buy about 4° of ΔT. That’s not much to write home about, but the second 1.7A drive current increment buys 29° of ΔT, a rather significant increase in thermal value for one’s electrical money. The next 1.7 amps buys 12°, the one after that 8°, and the final 20% increment in electrical input current buys only about 3° of additional ΔT. If maximum performance potential at any cost is the goal, then yes, operation at maximum electrical input produces that. If getting the best value for one’s electrical investment is the goal however, operating at about 30-40% of maximum is the better choice.
A third (and less obvious) observation that follows from the second is that these diminishing returns in cooling benefit obtained for (approximately) constant incremental increases in electrical input means that in practical systems, increasing the electrical input to a TEM does not necessarily yield increased cooling system performance, even though it might hold the potential to do so. Once the disposal costs (in thermal terms) of additional electrical input exceed the heat pumping benefit gained from it, maximum system performance has been reached and any further increases in electrical input will result in a reduction of net cooling effect. This is an issue of particular importance in temperature control applications, since it can cause a system to become unstable and lose regulation.
Figure 3: CP85438 datasheet excerpt with operating points referenced by tabulated “maximum” values highlighted. Note that the horizontal axis is plotted backwards from the usual convention.
Figure 4: CP85438 datasheet excerpt highlighting how incremental drive current increases yield differing incremental increases in cooling benefit.
For making a more detailed analysis, it’s helpful to condense this graphical information into a handful of equations to facilitate simulation. It’s apparent in this case that the operating curves are essentially straight lines, making it a fairly straightforward affair to use the X- and Y-axis crossings to find the slope and develop an equation, as shown in Figure 5. An alternative graphical technique in the era of digital documentation is to overlay an image captured from the datasheet onto a chart in a spreadsheet, as shown in figures 6 and 8. After scaling the axes in the chart and captured image to match, data series can be plotted on the chart that are coincident with the data contained in the spreadsheet image, and the spreadsheet’s trendline functionality used to derive an equation representing the datasheet information and verify its fit.
Using either approach, equations for both the required drive voltage and amount of cold-side heat pumping effect (Q) can be found quite easily for each of the 5 drive current levels characterized, as a function of temperature difference (ΔT) across the TEM. Equations for the voltage appearing across the TEM as a function of ΔT for a given drive current can be derived similarly. The resulting model, summarized in figure 7, of the thermoelectric device is fairly limited; it assumes a hot-side temperature equal to that for which the data was plotted, and must be solved separately for different electrical drive levels. As such, it’s a bit cumbersome and cannot be expected to produce perfectly accurate results. Better models based on the actual mechanisms at work in the device and allowing for arbitrary drive current and hot-side temperatures can certainly be developed. Information needed to do so however, is not commonly available in product datasheets nor is it generally available from TEM suppliers with anything resembling convenience. The advantage of the approach demonstrated here lies in its accessibility based on readily available information, and the relative benefit it offers compared to the typical alternative; physically constructing a system based on guesswork and testing it with fingers crossed in the hope that it will produce the desired result.
Figure 5: Use of tabulated QMax and ΔTMax values to form an equation for a TEM’s operating curve.
Figure 6: Image capture illustrating use of spreadsheet chart and trendline functions to develop equations describing graphical data in numeric form. Some manipulation of the image captured from a datasheet is generally necessary, including a horizontal flip in this case.
Figure 7 : Summary of graphical CP85438 performance data in mathematical form.
Figure 8: Use of spreadsheet chart and trendline functions to translate graphical voltage data into mathematical form.