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Thermoelectric cooling with Peltier cells

Peltier effect was discovered by Jean-Charles Peltier, a french physicist (1785 - 1845), in 1834. The opposite phenomenon is called the Seebeck effect, discovered in 1821 by the Estonian physicist Thomas Seebeck. Because both phenomena are reversible, some people refer to them as the Seebeck-Peltier effect.

Seebeck effect is the direct conversion of heat energy into electrical energy. When an electrical loop is made up with two different metals (A and B), two junctions exist (1 and 2). If the temperature of the junctions (T1 and T2) is different, an EMF is produced and a current flows. SA and SB are the Seebeck coefficients of the materials (equation below is simplified as Seebeck coefficients depend on temperature).

Peltier effect is the heat pumping (moving heat energy from a cold place to a hotter one) by using electrical energy. If we insert a voltage source and force a current into the two-metal loop, we will find that one junction cools down while the other heats up. A similar equation applies and the cooling power (Q) is proportional to the difference of Peltier coefficients of the metals (ΠA and ΠB) and the current I.

Modern integrated Peltier cells have many junctions connected electrically in series and thermally in parallel. They usually come square-shaped, with ceramic sides, ranging in size from 5 mm to 60 or more, according to power, and from 3 to 5 mm thick. There is no real need for large cells as a number of them can be parallelled to obtain the desired power.

When operating a Peltier cell, an amount of heat is absorbed at the cool side (Pc) and another amount of heat (Ph) is released at the hot side. Because the cell absorbs electrical power that is converted into heat, Ph is greater than Pc.

Some people have a confusion with heat and temperature. Heat is thermal energy contained in matter. Temperature measures the tendency of a body to accept heat from or to release heat to another body. Heat will always flow from high temperature places to low temperature places.

Heat contained in a body depends on its temperature, mass and the specific heat (cs). Specific heat is a  constant for each substance. For water is 4186 J/(kg·K) To obtain the energy necessary to heat up a body from T1 to T2, we use:

Q = m·cs·(T1-T2)

This equation tells us we need 10 times more energy to heat up 10 kg than 1 kg of water (which is understandable) and also that we need more energy to heat up 1 kg of water than 1 kg of anything else (because water has the largest specific heat of all substances known). The conclusion is that temperature is not a direct measure of energy.

Peltier cell manufacturers use to provide in their datasheets a working voltage, a maximum current and the maximum cooling power obtained for that current. Actually, the cooling power also depends on the temperature difference between the hot and cold side. Picture below ilustrates how the obtained cooling power drops with temperature difference and device current.

Heat transfer between two solid bodies depend on the temperature difference and the contact area. If one of the bodies is a fluid (a liquid or a gas) then it also depends on fluid speed at the contact surface (for this reason we feel it's colder when it's windy even at the same temperature).
Heat transfer is physically and mathematically similar to electric current flow. The driving force is the temperature difference, similar to voltage and heat flow is similar to current.

The dot over any letter means the flow of that magnitude per unit time, so the dotted Q stands for heat flow per second, in J/s or W. Temperature in S.I. is measured in Kelvin, and is Celsius temperature plus 273. When we talk about temperature differences, Kelvin and Celsius degrees are equivalent. Thermal resistance units are then K/W.

Thermal resistances as low as possible allow a large heat flow with a small ΔT. In case of a solid-solid union flat, polished surfaces and conductive grease (to avoid air bubbles) give the best results. In the cases of solid-fluid, finned metal heatsinks, maybe with an attached fan are used. For solid-fluid unions we can obtain a very low resistance with a very large and ventilated heat sink if its bulkiness it's not a problem.

When cooling down with Peltier cells we usually have a cold temperature to achieve, a heat power to remove and an exhaust temperature where the heat is released to, usually the atmosphere, with its summer/winter and day/night variations. The scheme below graphically shows all data (temperatures, heat powers and resistances) and equations. The process has an iterative nature.

As an example, let's design a cooling system with the following goals:
 

Cool temperature TCB  5 ºC  
Cooling power PC  6 W  
Exhaust temperature TE 45 ºC  (worst case)

We can choose 3 ºC cold side drop, then TC will be 2 ºC and the cold side thermal resistance is 0,5 K/W.
If we suppose a 15 W cell, the released power will be 21 W. Assuming 10 ºC drop at the hot side (Thermal resistance is again 0,5 K/W) TH equals 55 ºC.
The cell ΔT equals 55 - 2 = 53 K. The cooling power (6 W) represents 40 % of the cell power.
Last step is to check on the cell diagram (% power vs ΔT) if this is possible, that is, if the point is below the line.
 

  •  If the point is well below the line, a smaller (less power) cell can be tried.

  •  If the point is well over the line, a bigger (more power) cell must be tried.

  •  If the point is a little above the line, better (lower resistance) heat sinks can be tried, if allowed.

  •  If the point is a little below the line, smaller (higher resistance) heat sinks can be tried.

When designing Peltier cooling systems, it must be taken into account that thermal resistances either calculated or empirically found have an important tolerance (up to 20 %) because they depend on mechanical and manufacturing factors. This is even more important (up to 80 %) when natural convection is used, specially with gases. Forced convection gives better tolerances (about 40 %). It is also important, specially in gas forced convection, the build-up of dust in the fan blades and heat sink fins, raising the thermal resistance. Ageing also degrades the conductive grease in solid-solid unions and the mechanical fittings.
When the cool temperature must be guaranteed, the safest advice is to oversize the design. If it's allowed that the cool temperature is not achieved at extreme conditions or for a short time, a more economical system can be used.

When a cooling system with Peltier cells starts up, both cold and hot sides are at the same temperature, so ΔT is zero and the cell develops its maximum power. As temperature difference across the cell increases, cooling power decreases and temperatures stabilize. When temperature rates have to be controlled, computer models and simulations are highly effective.
 

This graph shows the start-up transient simulation using a MatLab model developed by us.
This system uses a 15 W cell that cools down a closed air space and releases the heat to the atmosphere at 35 ºC. The starting temperature is 25 ºC.
The lines are the cell sides temperatures (upper is the hot one and lower is the cold one).
Note the sudden rise in the hot side temperature while it takes more than 3 minutes for the cold side to reach 0 ºC. High power cells can present a temperature overshoot at the hot side.
 

To the right there is an animation that shows tem-perature profile transient (from 0 to 1000 seconds in 50 sec steps).
Only upper half is shown because of symmetry.
Fluid to be cooled (bottom) is a glycol-water mixture. Hot side of Peltier cell (above white rectangle) is refrigerated by the finned heat sink inside an air duct with forced air flow (transversal to the picture). Isolating wall surrounds both cold and hot ducts. Heat leaks to atmosphere are also simulated in this model.

Driving a Peltier cell is easy. It behaves very much like a resistor, with practically negligible capacitance and inductance. A low-voltage medium-current BJT or MOSFET can be used as a switch. Nevertheless, in a good system it is wise to monitor the four temperatures (cooled body, exhaust environment and cell sides) as well as the current through the cell(s). High temperature drops in the cold or hot side are indications of a higher thermal resistance and can be used to warn the user. Temperature rates can be controlled to avoid thermomechanical stress in the ceramic plates of the cell or because physical requirements. Pulse width modulation is a common method of driving Peltier cells. Frequencies as low as 10 Hz can be used. Control algorithm doesn't pose special problems, although temperature control is always slow. A good cooling system should have: