Modeling and Sizing a Thermoelectric Cooler Within a Thermal Analyzer Jane Baumann C&R Technologies, Inc. Littleton, Colorado

Thermoelectric Device l Thermoelectric coolers are solid-state devices capable of generating electrical power from a temperature gradient - Seebeck effect or converting electrical energy into a temperature gradient - Peltier effect l The ability to use TECs to heat as well as cool makes them suitable for applications requiring temperature control of a device over a specified temperature range l Although these devices have been around for years, they are gaining popularity in the aerospace industry for providing temperature control within optical systems and loop heat pipe temperature control

Thermoelectric Cooler l A typical thermoelectric module is composed of P-type and N-type elements between ceramic substrates typically Bismuth Telluride several couples connected electrically in series and thermally in parallel l When current is applied to the device, heat is moved from the cold side to the hot side where the heat is typically removed by a conduction or a cooling loop

Modeling TECs l Historically, modeling of a TEC device was left up to the analyst Hand calculations were performed external to a model using sizing charts Simplified modeling in SINDA/FLUINT using a heater node, user defined array lookups, or user defined logic l New methods for TEC modeling Built into SINDA/FLUINT and Thermal Desktop Steady state and transient simulations Enable sizing studies and parametric runs Proportional or thermostatic control options

SINDA/FLUINT Methods l SINDA/FLUINT definition User defines cold side/hot side nodes Define conductors between the cold and hot sides Define arrays containing above node and conductor IDs Define an array of areas associated with conductors Define input mode (power, current, or voltage) Define aspect ratio (area/thickness ration of a couple) Define number of couples l Thermal Desktop simplifies the input Define surfaces for substrate Define TEC contact between the surfaces Define input mode, aspect ratio, and number of couples

SINDA/FLUINT Methods l SINDA/FLUINT calculates cooling capacity and electrical power required l Heat pumped at cold side l Maximum temperature differential l Can define several independent TEC devices l Can stack multiple devices for additional cooling capacity or create multistage coolers

An Example l Sample Application* Device to be cooled is inch x inch Estimated heat load of 22 watts Maximum ambient temperature of 25°C Device needs to be maintained 5+2°C Convection heat sink with a thermal resistance of 0.15°C/watt * An Introduction to Thermoelectric Coolers, Sara Godfrey, Melcor Corporation

Thermal Desktop Model Device to be cooled Ceramic substrates Heat sink l Model development Use surfaces or solids for ceramic substrates, device and mounting plate Convection off mounting plate at 0.15°C/watt Create TEC contact between substrates l Optional inputs Can model core fill in TEC if desired

TEC Input l Simple user interface Provide input mode Current Voltage Power Aspect ratio Number of couples Select cold side Select hot side l Optional inputs Generate conductors Temperature control Non-bismuth telluride devices

TEC Sizing Study l Key input parameters for cooler definition Maximum heat load of device to be cooled, 22 watts Maximum allowable temperature of device being cooled, 7C Maximum environment for cooling hot side, 25C Thermal Desktop can handle complex thermal/fluid connections Minimum current, voltage, or power, 4 amps (max 6 amps) l Key output parameters Temperature of hot and colds substrates Aspect ratio Number of couples Optimum input current, voltage and power

TEC Sizing Study l Setup design sweeps on key parameters Aspect ratio range Looking at TEC specifications, aspect ratios range from 0.1 to 0.4 cm Number of couples Single stage coolers typically have between 17 to 127 couples l Preliminary selection of the TEC device l Run a parametric on input current

Aspect Ratio/No. of Couples l Design point of 5C for device couples 127 couples standard l Wish to minimize aspect ratio to reduce heat path through the device Aspect ratio less than.25 Design Point Aspect ratio=0.1 Aspect ratio=0.15 Aspect ratio=0.2 Aspect ratio=0.3 Aspect ratio=0.25

TEC Selection l Need to be able to generate a 40C temperature differential DTmax > 40C Design Point l Maximum cooling capacity Qmax between watts

TEC Selection l The Melcor CP L meets the requirements and footprint required for our example l CP L specifications Number of couples = 127 Geometry factor (aspect ratio) = cm I max = 6.0 amps Q max = 51.4 watts V max = 15.4 volts T max = 67°C

Steady State Results

Parametric Sweep Input Current Design point

Transient Simulation l Applied a time varying environment l Set proportional control in on cold side at 5+2C

Transient Response l For this sample we can demonstrate full control of the TEC device when exposed to the defined environment (3C<cooler.T115<7C)

Conclusion l New capabilities have been added to existing software tools allowing the steady state and transient modeling of thermoelectric devices l Access to built-in parametric and optimization methods in SINDA/FLUINT aid in design sizing and device selection l New features in Thermal Desktop allow the device to reside in an overall system model for system-level steady state and transient modeling l SINDA/FLUINT methods have been validated against published examples and sizing tools provided by TEC suppliers