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Transient Thermoelectric Pulse Cooling – Presented at the 36th International Conference on Thermoelectrics (ICT)

The below (at the bottom) downloadable PDF slides were presented at the 2017 ICT (36th International Conference on Thermoelectrics) on August 1st by Alfred Piggott. The talk was well received and generated much interest in transient thermoelectric pulse cooling. Each section of the presentation is summarized below. The published paper is available for free download: thermoelectric pulse cooling. I look forward to seeing you at the 2018 ICT.

Importance of this Transient Thermoelectric Pulse Cooling Research

The work herein is important because it facilitates a way for short duration cooling applications like pulsed laser sensors and on-chip hot spot cooling to be optimized. Previously this optimization had not been accomplished. The same cooling can be achieved at lower cost or more cooling for the same cost. This fulfills the iNEMI roadmap goal of finding more effective and cost-efficient ways of removing heat from electronic systems.

Background of Transient Thermoelectric Pulse Cooling

All else being equal, the temperature of the cold side of a given thermoelectric cooler or couple is dependent on the magnitude of the electric current at which the device is operating. The steady state electric current that produces the lowest temperature, or maximum $\Delta T$ across the device is referred to as $I_{max}$. While operating a thermoelectric device at steady state $I_{max}$, a current pulse can be applied. This current pulse produces a temperature that is lower than the lowest possible temperature achievable with steady state current.

Figure 1: Cold side temperature vs. time with a current pulse

This instant lower temperature achieved with a current pulse is referred to as supercooling. The area encompassed by the supercooling shown in figure 1 is known as transient advantage. In the literature, it was found that this supercooling is followed by a period of heating that is larger in magnitude and duration than the supercooling. This heating period is called superheating. The area encompassed by the superheating is known as transient penalty. The reason this transient supercooling is followed by superheating is due to the time separation between Peltier cooling and Joule heating. Peltier cooling happens instantly at the surface of the thermoelement junction. The Joule heat takes place instantly and throughout the volume of the thermoelement. The temperature measurement is very close to the junction so the low temperature is measured first. The Joule heat takes time to diffuse throughout the thermoelement to the junction. This creates the time separation between the cooling and heating. The entire event is called transient thermoelectric pulse cooling.

Research Hypothesis about Transient Thermoelectric Pulse Cooling

In the transient thermoelectric pulse cooling literature, the predominantly studied current pulse shape is a square wave and the transient penalty was for the most part much larger than the transient advantage. One transient thermoelectric pulse cooling study used an isosceles shaped current pulse. In this study, it was found that a transient advantage can be larger than the transient penalty.

Figure 2: Pulse height and duration

Since the isosceles study only used one pulse duration and on pulse height, the hypothesis formed was that there likely existed a current pulse duration and height that could potentially increase the transient advantage further relative to the transient penalty.

Research Goal for Transient Thermoelectric Pulse Cooling

The goal of the transient thermoelectric pulse cooling work herein was to optimize the current pulse height and duration of an isosceles triangle pulse to maximize the transient advantage relative to the transient penalty.

Figure 3: Transient advantage and transient penalty

Transient Thermoelectric Pulse Cooling: Electric Currents of Interest

Transient thermoelectric pulse cooling is different from using a PWM module. PWM uses pulsed electrical current with a prescribed duty cycle to control the average current to the thermoelectric cooler. The PWM current pulses start from zero current. So far, the research for transient thermoelectric pulse cooling does not start current pulses from zero. Transient thermoelectric pulse cooling starts current pulses from steady state $I_{max}$. When a thermoelectric cooler is operating at steady state $I_{max}$, it produces the largest temperature difference between the hot side of the device and the cold side. This is referred to $\Delta T_{max}$.

Figure 4: $I_{opt}$ and $I_{max}$

For the work herein, there was also interest in what happens when a current pulse starts from $I_{opt}$. $I_{opt}$ is the current that produces maximum cooling power from a thermoelectric module. $I_{opt}$ is slightly higher than $I_{max}$. Note that in the thermoelectric literature, sometimes $I_{max}$ terminology is meant to be $I_{opt}$ and vice versa. To be clear of the meaning, the equations have been specified in figure 4.

Modeling Approach for Transient Thermoelectric Pulse Cooling

Many times, thermoelectric coolers are modeled with zero dimensional steady state equations. For transient thermoelectric pulse cooling, these zero-dimensional equations cannot be used. The model must be able to simulate the heat flow relative to the thermoelement length with time during a current pulse.

For the work herein, a SPICE model was used to model transient thermoelectric pulse cooling. SPICE stands for Simulation Program with Integrated Circuit Emphasis. SPICE is an electrical engineering software for numerically solving electrical circuit problems.

Figure 5: The SPICE Model

Electrical thermal analogies are used in combination with SPICE. With these analogies, capacitors are thermal mass, current sources are heat flow (Joule heat and Peltier cooling), resistors are the thermal resistance of the thermoelements.

Figure 6: Electrical-Thermal Analogies

Figure 5 shows the thermoelement was divided up into 50 “finite” elements. Each finite element contains the circuit represented in the dashed rectangle. This portion of the thermoelement thermal model simulates the distributed mass, thermal resistance and Joule heat generation. The electrical model uses distributed voltage sources and electrical resistance which are temperature dependent and reference the thermal model. In the electrical model, the voltage sources simulate the Seebeck effect in each of the 50 differential elements. This SPICE modeling approach makes for a fast and accurate model to simulate transient thermoelectric pulse cooling.

Transient Thermoelectric Pulse Cooling Model Validation

To validate the SPICE model, the output was compared with the output to other available models as well as with experimental data for transient thermoelectric pulse cooling. There was good agreement between the models and experimental data.

Figure 7: Transient thermoelectric pulse cooling model validation

Results of the Transient Thermoelectric Pulse Cooling Research Herein

In figure 8, the center of the image shows shows a typical plot that might be found in the literature for transient thermoelectric pulse cooling. Each of the characteristic parameters is listed on the plot. For the work herein, each of the characteristic parameters for transient thermoelectric pulse cooling was plotted on the z-axis of a three-dimensional plot. The independent variables on the x and y-axis were pulse height and duration. 2025 combinations of pulse height and duration were used to create the surfaces. (Also see: analysis of transient thermoelectric pulse cooling for each characteristic plot).

Figure 8: Results of transient thermoelectric pulse cooling response surfaces

The main focus of the research was transient advantage and transient penalty and if it was possible to optimize the pulse height and duration of an isosceles triangle shaped current pulse to maximize transient advantage relative to transient penalty. For this, it was decided to use a new term. The term “net transient advantage” was defined as the transient advantage minus the transient penalty. Anywhere net transient advantage is positive indicates the transient advantage is larger than the transient penalty. The transient penalty surface was subtracted from the transient advantage surface. The net transient advantage surface was plotted to visually see where the surface was positive and to see the shape of the surface.

Figure 9: Net transient advantage definition

Transient Thermoelectric Pulse Cooling Research Outcome

It was found that that a current pulse height and duration can be optimized to maximize net transient advantage. Furthermore, the other listed characteristic transient parameters in figure 8 can also be maximized or minimized by optimizing the current pulse height and duration.

Figure 10: Net transient advantage, zooming In

Future Transient Thermoelectric Pulse Cooling Research

Rather than focus on transient thermoelectric pulse cooling from the perspective of a freestanding couple and cold side temperature only,  transient thermoelectric pulse cooling from that of a thermoelectric module and from a system perspective will be studied. Specifically, a module attached to a heat generating object.

Some questions that will be answered are:

• Does transient thermoelectric pulse cooling work with a module?
• How does pulse cooling effect COP, power consumption, Qc and average cooled object temperature?
• What system variables are most sensitive to pulse cooling? (i.e. thermal interface resistance, heat spreader thermal conductivity etc.)
• What happens during continuous pulses?

• What happens to the temperature distribution inside the thermoelement during pulses?

Download our Transient Thermoelectric Pulse Cooling work Presented to the 36th International conference on thermoelectrics (ICT), August 1st, 2017 (below)

20170801-transient-thermoelectric-pulse-cooling-applied-thermoelectric-solutions-llc