Comprehensive Optimization for Thermoelectric Refrigeration Devices _______________________ A Thesis presented to the Graduate School Faculty University of Missouri – Columbia ________________________ In Partial Fulfillment of the Requirements for a Master of Science - Mechanical Engineering __________________________ By Robert A. Gary Solbrekken Thesis Supervisor December 2005 Acknowledgements This research would never have been completed without help and guidance from the people who deserve to be mentioned here. I truly appreciate the patience and advice of Dr. His knowledge of the topic and his willingness to answer (many) questions was indispensable.
My gratitude is also owed to Kasey Scheel for building an experimental set-up and doing the ‘grunt’ work of taking thermal resistance data. The MAE department secretaries were also instrumental in coordinating all the paperwork and ancillary tasks required in any research project. Thanks are also in order to family and friends who supported my efforts. They were a major driving force to my progress in these endeavors.
Thanks to everyone for all the encouragement… ii Comprehensive Optimization for Thermoelectric Refrigeration Devices Robert A. Gary Solbrekken Thesis Supervisor Abstract R. Smalley, 1996 recipient of the Nobel Prize in chemistry, stated that energy is the number one problem facing humanity for the next 50 years [Smalley, 1996]. If this projection comes to fruition, as it most probably will, proper implementation of technologies that generate and convert energy will be of immense importance.
A large market is currently in place for which thermoelectric (TE) technology can provide diverse energy solutions. This market should continue to grow as improvements are made to TE materials. In the last 10-15 years, researchers have developed TE materials that promise to double the current performance of currently available materials. The semi-conductor industry and an enormous amount of study are fueling this improvement.
The current study is directed to develop and analyze system level optimization schemes that make the best use of those new materials, in addition to currently available materials. To fully realize the benefits of TE refrigeration, system level optimization is critical. This study takes an in-depth look at how the electric current and TE geometry can be optimized. In both cases, it is possible to optimize the overall system to maximize the coefficient of performance or to minimize the heat source temperature.
A comparison between the two optimization techniques demonstrates conditions under which one approach would be chosen over the other. An interesting finding from the comparison is that there is an electric current and TE geometry that will provide the minimum heat source temperature AND the maximum COP. One may consider this point to be a true optimum that has not been previously published to the knowledge of the author. The models used to study the optimization strategies were validated experimentally.
The validation measurements were conducted using a test bed built by an undergraduate researcher. The measurements reinforced the expected trends from the optimization iii study and corroborated the point where the COP is maximized at the same current and geometry that the heat source temperature is minimized. Finally, one of the trends observed with the optimization study is that when the heat flow from the source increases, the TE geometry optimization process suggests that a thinner TE element is needed. However it is known that micro-scale/interfacial effects will become dominant as the geometry shrinks.
A survey of micro-scale thermal and electrical effects is briefly reviewed. The survey suggests that micro-scale effects will need to be accounted for when the TE geometry shrinks below 10 µm. iv Table of Contents Acknowledgements. iii List of Tables.
vii List of Illustrations. Thermoelectric Cooling/Heating. Generation of Electricity. Improving TE Material Performance.
Using Current Materials. Basic Thermoelectric Phenomena. Thermoelectric Cooling Optimization. Maximum Coefficient of Performance.
Operating Current Comparison. Heat Sink Analysis. Apparatus Set-Up. Heat Sink Characterization.
Micro-Scale Effects. Range of Applicability. Phonon Radiative Transfer. Acoustic Mismatch Model……………………………………………….
Diffuse Mismatch Model………………………………………………. Electrical Contact Resistance…………………………………………….- 101 - vi List of Tables Table 5. Optimization potential for the various parameters. Optimization approach comparison.
Decision process for using figure V.1 Type E thermocouple data [Omega, 2005]. Uncertainty in measurements. Specifications for commercially available modules. Experimental test for module 81036.
Experimental test for module 81460. Experimental test for module 81085. Experimental test for module 81026. Polynomials for computing temperature dependent properties [Rowe, 2003].
Reproducability study results, day 1. Reproducability study results, day 2. Reproducability study results, day 3. The values of specific heat and phonon velocity used in the EPRT.- 110 - vii List of Illustrations Fig.
Top: Number of transistors in Intel chips, Bottom: Power density comparison for the same components (units in W/cm2) [SIA, 2004]. Components of a TE module: Left: metallized connection bars on a ceramic, Right: P-N thermoelectric elements ready to be connected in series [Melcor, 2003]- 3 - Fig. Components of a TE module: Left: Ferrotec Single-stage TE module, Right: Two-stage TE cooling. TE COP as it varies with ∆T.
A comparison of TE to conventional electricity generation technology. The Seebeck coefficient along with thermal and electrical conductivity as functions of free carrier concentration (S is used as the Seebeck coefficient, α, and β is used for the thermal conductivity, k, in the figure). Maximum TE thermal efficiency versus ∆T (Th-Tc) with Z =. A Hi-Z employee installing thermoelectric modules in a class 8 diesel truck exhaust system [Hi-Z, 2003].
Left: A sample quantum dot structure, Right: A Si/SiGe superlatice structure [Shakouri, 2003]. Absolute cooling of a p-BiTe/SbTe superlattice as compared to the bulk material [Venkatasubramanian, 2001]. Top curves: Figure of merit for Bismuth Telluride materials. Bottom points: approximate measured figure of merit for single-walled carbon nano-tubes [Shi, 2003].
Improvement in figure of merit over the last few decades [Darpa, 2002]. Cross-section of a TE generator/thermocouple showing the p-n junction. A simple Peltier cooling/heating design. A typical TE module assembly [Melcor, 2003].
Thomson heat addition to a thermocouple. The baseline model diagram. Baseline model thermal resistance network. Sketch of a TE Refrigeration System.
Thermal Resistance Network for TE Refrigeration. An iteration technique for finding optimizing the COP. The iteration scheme for getting a minimum junction temperature. COP as a Function on Geometry for Both Methods.
COP and junction temperature as a function of current (Tj,min: Q = 21 W, ψha = 0. COP and junction temperature as a function of current for both methods (Tj,min: Q = 21 W, ψha = 0. COP and junction temperature as a function of current for both methods (Tj,min: Q = 21 W, ψha = 0. Junction temperature alignment as a function of current for both methods (Tj,min: Q = 80,100,120 W, ψha = 0.
Junction temperature alignment as a function of current for both methods (Tj,min: Q = 80,100,120 W, ψha = 0. ∆T = 20 K, I = Iopt, Tc = 340 K, γ = independent variable. Current optimization for N=71, ψha = 0.4 K/W, ICOPopt=ITj,min, γ = independent variable. Junction temperature plotted against Nγ; Qc = 75 W ψha = 0.
Junction temperature as a function of geometry for both approaches. Junction Temperature versus Qc. (COP and Nγ, for TE cooling, are also shown at each point, ψha = 0. Optimization for Q = variable, Tj,min = 85oC, I=ITj,min, and γ= γmin.
The COP and junction temperature as it varies with geometry (Tj,min: Q = 100 W, ψha =0.4 K/W I= Imin COPopt: Tc = 340 K, ∆T = 21.245 Amps; For both: N=71 and γ = independent variable). Junction temperature alignment as a function of current for both methods (Tj,min: Q = 80,100,120 W, ψha = 0. COP alignment as a function of current for both methods (Tj,min: Q = 80,100,120 W, ψha = 0. The airflow test chamber purchased from Airflow Measurement Systems, Inc.
Schematic of the airflow test chamber. The plexi-glass wind tunnel set-up. The baseline model diagram. Measured thermal resistance as a function of pressure drop.
The thermoelectric module test-bed. Plot of the material property variation as a function of temperature [Rowe, 2003]. Junction temperature versus current for the 81026 module. Junction temperature versus current for the 81460 module.
The variation in minimum junction temperature for the different modules. Junction temperature versus current for the 81036 module. Junction temperature versus current for the 81085 module. COP versus current for the 81026 module.
COP versus current for the 81460 module. The change in the COPopt point as geometry changes. COP versus current for the 81036 module. COP versus current for the 81085 module.
Testing plan for a reproducibility study. Junction temperature reproducibility results for the different days. Thermal resistance reproducibility study for the different days. The variation in junction temperature as it changes measurement trials.
The variation in thermal resistance as it changes measurement trials. EPRT prediction of non-dimensional heat flux vs. EPRT prediction of thermal conductivity for BiTe as compared to constant bulk conductivity. Specular phonon boundary scattering.
Diffusive boundary scattering. Boundary resistance ratio between the diffuse mismatch and the acoustic mismatch models [Swartz and Pohl, 1989]. The ratio of effective thermal conductivity to the bulk thermal conductivity for Bismuth Telluride. Ratio of bulk resistivity to the effective resistivity.
Reliability data for a selected thermoelectric module [Ferrotec, 2005]. Change in electrical resistivity with doping concentration [Heremans, 2003]. Topographical map of a mountainous region.006 m, ψha = independent variable.- 105 - xi Nomenclature COP Coefficient of Performance I Electrical current (Amps) K Thermal Conductance (W/°C) L TE element length (thickness) (m) L’ Fin length (m) N Number of TEC thermocouples (#) Q Heat load (W) Q’ Flow Rate (CFM) R Electrical resistance (Ohms) T Temperature (°C) W TE Input power (W) Z TE Figure of Merit (1/K) Z’ Acoustic Impedance (kg/m2-s) Greek Letters α Seebeck coefficient (V/K) α’ Transmission probability (dimensionless) ∆ Change in value k Thermal conductivity (W/mK) kb Boltzmann’s Constant (J/K-molecule) Ψ Thermal resistance (°C/W) γ TE element geometry metric (m) xii ρ Electrical resistively (Ohm-cm) Subscripts c TEC cold side h TEC hot side ha TE hot side to ambient hs TE hot side to heat sink j Junction jc Junction to case max Based on the maximum of given quantity min Based on the minimum of given quantity n N-type semi-conducting material p P-type semi-conducting material sa Sink to Ambient TE Thermoelectric xiii 1. Introduction Improvements in manufacturing methods, driven by the electronics industry, have made TE devices effective in numerous applications [Peltier Device Info Directory, 2005].
Their compact size and light weight make TE modules especially well-suited for portable and dimensionally constrained applications. Since TE devices are very sensitive to boundary and operating conditions, proper choice of materials, geometry, and operating conditions play a critical role in creating the optimum TE technology for a specific need. Blind application of thermoelectric technology will most likely be more costly and less effective than an optimized approach. Thus, it is important to study these devices to derive their maximum performance.
Since the bulk of the study is related to finding optimum cooling solutions, it is worth while to note the need for such designs. Currently the electronics industry is a large possible market for TE refrigeration applications.1 shows the increasing trend in the number of transistors and the power density in microprocessors. The corresponding thermal solution must become more effective since the microprocessor temperature must be still kept at 85oC or lower in spite of the power density increase [SIA, 2004]. Although TE performance is limited, new materials and module designs (discussed in later chapters) have potential to excel under these conditions.
-1- 1000000000 10000 100000000 10000000 1000 1000000 Heat Flux (W/cm2) # of Transistors 100000 Transistors 100 Heat Flux 10000 1000 10 100 10 1 1 1975 1980 1985 1990 1995 2000 2005 2010 2015 Year Fig.