Analytic couple modeling introducingdevice design factor fin factor th - PDF document

1 Analytic couple modeling introducingdevi
Analytic couple modeling introducingdevice design factor, fin factor, thermal diffusivity factor, and inductance factor Jon MackeyMechanical Engineering, University of AkronMaterials Science and Engineering, Case Western Reserve UniversityFred DynysNASA Glenn Research CenterNASA Cooperative Agreement: NNX08AB43ANASA/USRA Contract: 04555-004 Analytic Couple Modeling Classic Model Classic Parameters ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ Electrical-System- ൌܫܴ ൫ͳ൅ܻ݋݌ݐܼ൫ܺ ൅à

2 µ«Í³àµ…ܻ݋݌ݐ ͳ൅ሺ

µ«Í³àµ…ܻ݋݌ݐ ͳ൅ሺ Classic Solution Geometric- Materials- ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ of 7 Co u c c a m e t e r s e ec tri cal y AnalticCopleModeling assic So l u G e o m e t r i c L oa d - ateria ls - Objectives Investigate couple configurations analytically:RectangularCylindricalInvestigate additional physics from classic case:Thermal resistance of shoe materialLateral heat transferVariable material propertiesTransient operationEstablish a set of simple desi

3 gn guidelines, for lab couple demonstrat
gn guidelines, for lab couple demonstration purposesApplicable to automotive, power, electronic, and other industries Analytic Couple Modeling Classic Model Classic Parameters ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ Electrical-System- ൌܫܴ ൫ͳ൅ܻ݋݌ݐܼ൫ܺ ൅൫ͳ൅ܻ݋݌ݐ ͳ൅ሺ Classic Solution Geometric- Materials- ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ Analytic Couple Modeling Classic Model Classic Parameters ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣ

4 ǡܤ ܣǡܤܣǡܤܣǡܤ Electrical-Syste
ǡܤ ܣǡܤܣǡܤܣǡܤ Electrical-System- ൌܫܴ ൫ͳ൅ܻ݋݌ݐܼ൫ܺ ൅൫ͳ൅ܻ݋݌ݐ ͳ൅ሺ Classic Solution Geometric- Materials- ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ Four Assumptions Analytic Couple Modeling Classic Model Classic Parameters ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ Electrical-System- ൌܫܴ ൫ͳ൅ܻ݋݌ݐܼ൫ܺ ൅൫ͳ൅ܻ݋݌ݐ ͳ൅ሺ Classic Solution Geometric- Materials- ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣ

5 ǡܤܣǡܤܣǡܤ Analytic Couple Model
ǡܤܣǡܤܣǡܤ Analytic Couple Modeling Classic Model Classic Parameters ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ Electrical-System- ൌܫܴ ൫ͳ൅ܻ݋݌ݐܼ൫ܺ ൅൫ͳ൅ܻ݋݌ݐ ͳ൅ሺ Classic Solution Geometric- Materials- ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ Analytic Couple Modeling Classic Model Classic Parameters ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ Electrical-System- ൌܫܴ ൫ͳ൅ܻ݋݌ݐܼ൫ܺ ൅൫ͳ൅ܻ݋݌ݐ ͳ

6 ൅ሺ Classic Solutio
൅ሺ Classic Solution Geometric- Materials- ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ Analytic Couple Modeling Classic Model Classic Parameters ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ Electrical-System- ൌܫܴ ൫ͳ൅ܻ݋݌ݐܼ൫ܺ ൅൫ͳ൅ܻ݋݌ݐ ͳ൅ሺ Classic Solution Geometric- Materials- ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ Analytic Couple Modeling Classic Model Classic Parameters ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ

7 ܣǡܤܣǡܤܣǡܤ Electrical-System- àµ
ܣǡܤܣǡܤܣǡܤ Electrical-System- ൌܫܴ ൫ͳ൅ܻ݋݌ݐܼ൫ܺ ൅൫ͳ൅ܻ݋݌ݐ ͳ൅ሺ Classic Solution Geometric- Materials- ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ Analytic Couple Modeling Classic Model Classic Parameters ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ Electrical-System- ൌܫܴ ൫ͳ൅ܻ݋݌ݐܼ൫ܺ ൅൫ͳ൅ܻ݋݌ݐ ͳ൅ሺ Classic Solution Geometric- Materials- ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ Ana

8 lytic Couple Modeling Classic Model Clas
lytic Couple Modeling Classic Model Classic Parameters ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ Electrical-System- ൌܫܴ ൫ͳ൅ܻ݋݌ݐܼ൫ܺ ൅൫ͳ൅ܻ݋݌ݐ ͳ൅ሺ Classic Solution Geometric- Materials- ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ Analytic Couple Modeling Classic Model Classic Parameters ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ Electrical-System- ൌܫܴ Geometric- ൫ͳ൅ܻ݋݌ݐܼ൫ܺ ൅൫ͳ൅ܻ݋݌ݐ ͳ൅

9 ሺ Classic Solution Materia
ሺ Classic Solution Materials- ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ Analytic Couple Modeling Classic Model Classic Parameters ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ Electrical-System- ൌܫܴ Geometric- ൫ͳ൅ܻ݋݌ݐܼ൫ܺ ൅൫ͳ൅ܻ݋݌ݐ ͳ൅ሺ Classic Solution Materials- ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ Four Assumptions 2 of 7 Analytic Couple Modeling c e ec tri cal y assic So l utio Four Assum p Cylindrical Model

10 ൌܫܴ ܣǡܤݎܣǡܤ Ü
ൌܫܴ ܣǡܤݎܣǡܤ ܣǡܤܣǡܤʹߨݓܣǡܤ ܣǡܤ ܣǡܤܣǡܤݎߪܣǡܤ ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤʹߨݓܣǡܤܣǡܤ Electrical-System- c a m e t e r s Geo m e tri c - L oa d - ateria ls - Cylindrical Parameters Žàµ¬Ý‹Ç¡Ü£Žàµ¬Ý‹Ç¡Ü¤ Žàµ¬Í²Ç¡Ü¤Í´ß¨ßª Žàµ¬Ý‹Ç¡Ü£Í´ß¨ßª Geometric-Materials- Analytic Couple Modeling B.C. Model Boundary Conditions (B.C.)- ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤሺͲሻൌ݄ܽÇ

11 ¡Ü¾ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡÜ
¡Ü¾ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤܣǡܤ ݄∞ܿ B.C. Parameters Geometric- Materials- ܣǡܤܣǡܤܣǡܤ Device Design- B.C. Solution ͳ൅ሺሻ൤ ൫ͳെƒ˜‰ Analytic Couple Modeling B.C. Model Boundary Conditions (B.C.)- ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤሺͲሻൌ݄ܽǡܾ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤܣǡܤ ݄∞ܿ B.C. Parameters Geometric- Materials- ܣǡܤܣǡܤܣǡܤ Devic

12 e Design- B.C. Solution ͳ൅
e Design- B.C. Solution ͳ൅ሺሻ൤ ൫ͳെƒ˜‰ B.C. Solution ͳ൅ሺሻ൤ ൫ͳെƒ˜‰ Analytic Couple Modeling B.C. Model ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤሺͲሻൌ݄ܽǡܾ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤܣǡܤ ݄∞ܿ Boundary Conditions (B.C.)- B .C. Solutio n of 7 tic Cou pl e Mode l in Conditions (B.C. ) - B.C. M odel Classic Parameters Geometr

13 ic- Materials- B.C. Parameters Geome
ic- Materials- B.C. Parameters Geometric- Materials- ܣǡܤܣǡܤܣǡܤ Device Design- B.C. Solution ͳ൅ሺሻ൤ ൫ͳെƒ˜‰ Analytic Couple Modeling B.C. Model ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤሺͲሻൌ݄ܽǡܾ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤܣǡܤ ݄∞ܿ Boundary Conditions (B.C.)- B .C. Solutio n of 7 tic Cou pl e Mode l in B.C. M odel Classic Parameters Geometric- Materials- onditions (B.C.) - B.C. Pa

14 rameters Geometric- Materials- ܣǡÜ
rameters Geometric- Materials- ܣǡܤܣǡܤܣǡܤ Device Design- B.C. Parameters Geometric- Materials- ܣǡܤܣǡܤܣǡܤ Device Design- B.C. Solution ͳ൅ሺሻ൤ ൫ͳെƒ˜‰ Analytic Couple Modeling B.C. Model Boundary Conditions (B.C.)- ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤሺͲሻൌ݄ܽǡܾ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤܣǡܤ ݄∞ܿ B.C. P a r a m e t e r s eometri c d ce Des i gn of 7 Analytic Couple Mo

15 deling B.C. M odel Boundar Conditions (
deling B.C. M odel Boundar Conditions (B.C.) - ൫ͳ൅ܻܼ൫ܺ ൅൫ͳ൅ܻ ͳ൅ሺ Classic Solution 3of7 oupleModeling c e ri a l s - B .C. Solutio n B.C. Solution ͳ൅ሺሻ൤ ൫ͳെƒ˜‰ ݋݌ݐ൫ͳ൅ܻ݋݌ݐܼሺܺ݋݌ݐ ൫ͳ൅ܻ݋݌ݐ ቂͳെ ൛ͳെܦܽݒ݃ൟቃെ Ü¿λ B.C. Parameters Geometric- Materials- ܣǡܤܣǡܤܣǡܤ Device Design- B.C. Solution ͳ൅ሺሻ൤

16 ; ൫ͳെƒ˜
; ൫ͳെƒ˜‰ Analytic Couple Modeling B.C. Model Boundary Conditions (B.C.)- ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤሺͲሻൌ݄ܽǡܾ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤܣǡܤ ݄∞ܿ B.C. Parameters eometri c d ce Des i gn of 7 Analytic Couple Modeling B.C. M odel ൫ͳ൅ܻܼ൫ܺ ൅൫ͳ൅ܻ ͳ൅ሺ Classic Solution 3of7 oupleModeling c 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 o o o o o o o o o o o o o o f f f f f f f f f f f

17 f f f f f f f f 7 7 7 7 7 7 7 7 7 7 7 7
f f f f f f f f 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C o o o o o o o o o o o o o o u u u u u u u u u u u u u u p p p p p p p p p p p p p p l l l l l l l l l l l l l l l l l l l e e e e e e e e e e e e e e M M M M M M M M M M M M M M M M M M M o o o o o o o o o o o o o o d d d d d d d d d d d d d d d d d d d e e e e e e e e e e e e e e l l l l l l l l l l l l l l l l l l l i i i i i i i i i i i i i i i i i i i n n n n n n n n n n n n n n

18 g g g g g g g g g g g g g g B.C. So
g g g g g g g g g g g g g g B.C. Solution ͳ൅ሺሻ൤ ൫ͳെƒ˜‰ ݋݌ݐ൫ͳ൅ܻ݋݌ݐܼሺܺ݋݌ݐ ൫ͳ൅ܻ݋݌ݐ ቂͳെ ൛ͳെܦܽݒ݃ൟቃെ Ü¿λ m m m m m m m m m m m m Example Calculation Convection (W/m-K) Factor Max Efficiency Max Power Density (W/m 2 ) 1.006.1517,73350,0000.986.0517,1185000.382.282,300 B.C. Parameters Geometric- Materials- ܣǡܤܣǡܤܣǡܤ Device Design- B.C. Solution ͳ൅ሺ

19 ;ሻ൤ ൫ͳെƒ
;ሻ൤ ൫ͳെƒ˜‰ Analytic Couple Modeling B.C. Model Boundary Conditions (B.C.)- ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤሺͲሻൌ݄ܽǡܾ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤܣǡܤ ݄∞ܿ B.C. P a r a m e t e r s c i gn of 7 Analytic Couple Modeling B.C. Model ൫ͳ൅ܻܼ൫ܺ ൅൫ͳ൅ܻ ͳ൅ሺ Classic Solution 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 o o o o o o o o o o o o f f f f f f f f f f f f f f f 7 7 7 7 7 7 7 7 7 7

20 7 7 7 7 7 C C C C C C C C C C C C C C C
7 7 7 7 7 C C C C C C C C C C C C C C C C C C C C C C o o o o o o o o o o o o u u u u u u u u u u u u p p p p p p p p p p p p l l l l l l l l l l l l l l l e e e e e e e e e e e e M M M M M M M M M M M M M M M o o o o o o o o o o o o d d d d d d d d d d d d d d d e e e e e e e e e e e e l l l l l l l l l l l l l l l i i i i i i i i i i i i i i i n n n n n n n n n n n n g g g g g g g g g g g g B.C. Solution ͳ൅ሺሻ൤ ൫ͳെƒ˜‰ ݋݌ݐ൫ͳ൅ܻÝ

21 ‹ÝŒÝÜ¼áˆºÜºÝ‹ÝŒÝ ൫ͳ൅ܻ݋݌ݐ ቂÍ
‹ÝŒÝÜ¼áˆºÜºÝ‹ÝŒÝ ൫ͳ൅ܻ݋݌ݐ ቂͳെ ൛ͳെܦܽݒ݃ൟቃെ Ü¿λ G eom e L oa d - D e Design Guideline Analytic Couple Modeling Fin Model Fin Solution ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤ Thermal Governing Equation- ݋݌ݐ ͳ൅ሺÇ¡ ሻ Ç¡ ൯ൌ Fin Parameters ܣǡܤܣǡܤܣǡܤܣǡܤܣǡܤܣǡܤ ܺǡܩ Fin Factor-Geometric Fin-Materials- Analytic Couple Modeling Fin Model Fin Solution

22 ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ
ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤ Thermal Governing Equation- ݋݌ݐ ͳ൅ሺǡ ሻ ǡ ൯ൌ Fin Parameters ܣǡܤܣǡܤܣǡܤܣǡܤܣǡܤܣǡܤ ܺǡܩ Fin Factor-Geometric Fin-Materials- Analytic Couple Modeling Fin Model Fin Solution ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤ Thermal Governing Equation- ݋݌ݐ ͳ൅ሺǡ ሻ

23 ǡ ൯ൌ 4 of 7 tic Cou pl e Mo
ǡ ൯ൌ 4 of 7 tic Cou pl e Mode l in Fin Solutio n Thermal Governin g Equatio n - Fin M odel Classic Parameters Geometric- Materials- Fin Parameters ܣǡܤܣǡܤܣǡܤܣǡܤܣǡܤܣǡܤ ܺǡܩ Fin Factor-Geometric Fin-Materials- Analytic Couple Modeling Fin Model Fin Solution ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤ Thermal Governing Equation- ݋݌ݐ ͳ൅ሺǡ ሻ ǡ ൯ൌ 4 of 7 tic Cou pl e M

24 ode l in Fin Solutio n Thermal Fin M od
ode l in Fin Solutio n Thermal Fin M odel Classic Parameters Geometric- Materials- vernin Equatio n - Fin Parameters ܣǡܤܣǡܤܣǡܤܣǡܤܣǡܤܣǡܤ ܺǡܩ Fin Factor-Geometric Fin-Materials- Fin Parameters ܣǡܤܣǡܤܣǡܤܣǡܤܣǡܤܣǡܤ ܺǡܩ Fin Factor-Geometric Fin-Materials-Analytic Couple Modeling Fin Model ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤ Thermal Governing Equation- Fi n P a r a m e t e r s in F ac t or e

25 tri c Fi n d C Fin M odel A A A l l l l
tri c Fi n d C Fin M odel A A A l l l l t i i i C C C hermal Governin g Equatio n - ൫ͳ൅ܻܼ൫ܺ ൅൫ͳ൅ܻ ͳ൅ሺ Classic Solution M a t e r i a l s - 4 4 4 4 4 4 4 4 4 4 o o o o o o o o o o f f f f f f f f f f 7 7 7 7 7 7 7 7 7 7 C C C C C C C o o o o o o o o o o o o o o o o o o o u u u u u u u u u u p p p p p p p p p p p p p p p l l l l l l l l l l e e e e e e e e e e M M M M M M M M M M o o o o o o o o o o d d d d d d d d d d e e e e e e e e e e l l l l l l l l l l i i

26 i i i i i i i i n n n n n n n n n n g g
i i i i i i i i n n n n n n n n n n g g g g g g g g g g g g g g g C Fin Solution ݋݌ݐ ͳ൅ሺÇ¡ ሻ Ç¡ ൯ൌ ൫ͳ൅ܻ ܼሺܺǡܩሻ ൅൫ͳ൅ܻ݋݌ݐ൯െߟ–ƒŠá‰€ Fin Parameters ܣǡܤܣǡܤܣǡܤܣǡܤܣǡܤܣǡܤ ܺǡܩ Fin Factor-Geometric Fin-Materials-Analytic Couple Modeling Fin Model ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤ Thermal Governing Equation- Fin Parameters in

27 F ac t or e tri c Fi n d C Fin M odel
F ac t or e tri c Fi n d C Fin M odel A A A l l l l t i i i C C C ൫ͳ൅ܻܼ൫ܺ ൅൫ͳ൅ܻ ͳ൅ሺ Classic Solution 4 4 4 4 4 4 4 4 4 4 o o o o o o o o o o f f f f f f f f f f 7 7 7 7 7 7 7 7 7 7 C C C C C C C o o o o o o o o o o o o o o o o o o o u u u u u u u u u u p p p p p p p p p p p p p p p l l l l l l l l e e e e e e e e e e M M M M M M M M o o o o o o o o o o d d d d d d d d d e e e e e e e e e e l l l l l l l l i i i i i i i i n n n n n n n n n n g g g g g g g g g g

28 g g g g g C Fin Solution ݋݌ݐ ͳ൅&
g g g g g C Fin Solution ݋݌ݐ ͳ൅ሺÇ¡ ሻ Ç¡ ൯ൌ ൫ͳ൅ܻ ܼሺܺǡܩሻ ൅൫ͳ൅ܻ݋݌ݐ൯െߟ–ƒŠá‰€ m m m m m m m m m m m Example Calculation Convection (W/m-K) Factor Max Efficiency Max Power Density (W/m 2 ) 00.006.1517,73350.326.0517,7335000.382.7017,733 Fin Parameters ܣǡܤܣǡܤܣǡܤܣǡܤܣǡܤܣǡܤ ܺǡܩ Fin Factor-Geometric Fin-Materials-Analytic Couple Modeling Fin Model ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ Ü

29 £Ç¡Ü¤Ü£Ç¡Ü¤Ü£Ç¡Ü¤ ܣǡܤܣǡܤܣǡܤܣǡ
£Ç¡Ü¤Ü£Ç¡Ü¤Ü£Ç¡Ü¤ ܣǡܤܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤ Thermal Governing Equation- Fi n P a r a m e t e r s c Fi n C Fin Model hermal Governin g Equatio n - ൫ͳ൅ܻܼ൫ܺ ൅൫ͳ൅ܻ ͳ൅ሺ Classic Solution M a t e r i a l s - 4 4 4 4 4 4 4 4 4 4 o o o o o o o o o o f f f f f f f f f f 7 7 7 7 7 7 7 7 7 7 C C C C C C C o o o o o o o o o o o o o o o o o o o u u u u u u u u u u p p p p p p p p p p p p p p p l l l l l l l l l l e e e e e e e e e e M M M M M M M M M M o o o o

30 o o o o o o d d d d d d d d d d e e e e
o o o o o o d d d d d d d d d d e e e e e e e e e e l l l l l l l l l l i i i i i i i i i i n n n n n n n n n n g g g g g g g g g g g g g g g C Fin Solution ݋݌ݐ ͳ൅ሺÇ¡ ሻ Ç¡ ൯ൌ ൫ͳ൅ܻ ܼሺܺǡܩሻ ൅൫ͳ൅ܻ݋݌ݐ൯െߟ–ƒŠá‰€ F in F ac Geo m e L oa d - Design Guideline Analytic Couple Modeling Variable Model Asymptotic Expansion Material Properties by Asymptotic Expansion- Variable Solution ܵሺܶሻ ൅߳ܵ ൅߳ܶ ොàµ

31 Œß®àµ…߳߮ ߪሺܶሻ ൅߳ߪ ݇ሺܶá
Œß®àµ…߳߮ ߪሺܶሻ ൅߳ߪ ݇ሺܶሻ ൅߳݇ οܵοܶ οܵοܶ Analytic Couple Modeling Variable Model Asymptotic Expansion Material Properties by Asymptotic Expansion- Variable Solution ܵሺܶሻ ൅߳ܵ ൅߳ܶ ොൌ߮൅߳߮ ߪሺܶሻ ൅߳ߪ ݇ሺܶሻ ൅߳݇ οܵοܶ οܵοܶ Analytic Couple Modeling Variable Model Material Properties by Asymptotic Expansion- ܵሺܶሻ ൅߳ܵ ߪሺܶሻ ൅߳ߪ ݇ሺܶሻ ൅߳݇ Asymptotic Expansion ൅߳ܶ ොൌ߮൅߳߮ οܵοܶ οܵοܶ

32 5 of 7 Analytic Couple Modeling
5 of 7 Analytic Couple Modeling Material Properties by Asymptotic Expansion S Conversion Efficiency 6.00% Asymptotic Expansion ypp p tot c Ex p ans i Asymptotic Expansion n TS Conversion Efficiency 6.30% Variable Solution ThTc S Conversion Efficiency 6.15% Analytic Couple Modeling Transient Model Greens Function Solution Electrical-System- Transient Parameters ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ൌܫܴ൅ܪ

33 ݔǡߦൌߜሺݔെߦሻ ݔÇ
ݔǡߦൌߜሺݔെߦሻ ݔǡߦ ܣǡܤܽݒ݃ܣǡܤܣǡܤܽݒ݃ ܽݒ݃ܽݒ݃ Thermal diffusivity factor-Inductance factor- Analytic Couple Modeling Transient Model Greens Function Solution Electrical-System- Transient Parameters ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ൌܫܴ൅ܪ ݔǡߦൌߜሺݔെߦሻ ݔǡߦ ܣǡܤܽݒ݃ܣǡܤܣǡܤܽݒ݃ ܽݒ݃ܽݒ݃ Thermal diffusivity factor-Inductance

34 factor- Analytic Couple Modeling Trans
factor- Analytic Couple Modeling Transient Model Greens Function Solution Electrical-System- ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ൌܫܴ൅ܪ ݔǡߦൌߜሺݔെߦሻ ݔǡߦ of 7 Analytic Couple Modeling s i e nt M odel Greens Function Solution Th e ec tri cal System Transient Parameters ܣǡܤܽݒ݃ܣǡܤܣǡܤܽݒ݃ ܽݒ݃ܽݒ݃ Thermal diffusivity factor-Inductance factor- t t t t t t t t t t e e

35 m Periodic On/Off Operation F u n c t
m Periodic On/Off Operation F u n c t i o Design Guideline ʹܽെͳ ܽൌͳ൅ Acknowledgements Tom Sabo, Ray Babuder, Ben Kowalski, Clayton Cross NASA Glenn Research CenterDr. Sabah Bux, Dr. Jean-Pierre NASA Cooperative Agreement: NASA/USRA Contract:Several new design factors can have a large influence on couple behaviorDevice Design FactorFin FactorThermal Diffusivity FactorInductance FactorThe introduced design guidelines must be considered in couple design Analytic Couple Modeling Appendix Analytic

36 Couple Modeling Transient Model Greens
Couple Modeling Transient Model Greens Function Solution Electrical-System- ܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ܣǡܤ ൌെܵܣǡܤܣǡܤ ܣǡܤܣǡܤܣǡܤ ൌܫܴ൅ܪ ݔǡߦൌߜሺݔെߦሻ ݔǡߦ Analytic Couple Modeling ee n F u n c ti o n So l u ti on e r m ec t r y Transient Parameters ܣǡܤܽݒ݃ܣǡܤܣǡܤܽݒ݃ ܽݒ݃ܽݒ݃ Thermal diffusivity factor-Inductance factor- Tr s i e nt M ode l m m m m m m m m m m a l - r i i i i i c c c