????????? - Inverse heat transfer

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?????????- Inverse heat transfer

• ?????
• ??????? ???

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Introduction

• ?????????,??????(Initial condition)?????(Boundary
  condition)?????(Material Properties)?????????,????
  ??????????????????,?????????????????(Direct Heat
  Conduction Problem DHCP )

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Introduction

• ??????????????????????????,???????????,???????????
  ???????,???????????????,?????????????????(Inverse
  Heat Conduction Problem IHCP),??????????????,?????
  ?????????1-5?

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????

• Estimation of Surface Absorptivity and Surface
  Temperature1(???????)

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????

• ?1950????,?????????????????????????? 4
  ????,??????????,??????????????????????????????????
  ?????????????????????????????????

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Inverse??---??????5

• ???????????????
• ??????????????????
• ?????????????????????
• ??????????????????????????
• ???????????????????
• ?????????????
• ??????????????

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????

• Direct Problem
• Known a1?a2?b1?b2?Q?R
• Unknown X?Y

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????

• Inverse Problem
• Known a1?a2?b1?b2?Y?R
• Unknown X?Q

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????---????6

• Finite Difference Equation

???6
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????---Direct

• Known T1 T12
• Unknown TA1 TA4
• ??Finite Difference
• Equation?????

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• T2T12TA3TA2-4TA10 1
• T3T5TA1TA4-4TA20 2
• T11T9TA1TA4-4TA30 3
• T6T8TA2TA3-4TA40 4
• -4T1T2T120 5
• T1-4T2T3TA10 6
• T2-4T3T4TA20 7
• T3-4T4T50 8
• T4-4T5T6TA20 9
• T5-4T6T7TA40 10
• T6-4T7T80 11
• T7-4T8T9TA40 12
• T8-4T9T10TA30 13
• T9-4T10T110 14
• T10-4T11T12TA30 15
• T1T11-4T12TA10 16

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????---Inverse

• Known T3 T12? TA1? TA2
• Unknown T1 ?T2? TA3 ?TA4
• ??Finite Difference
• Equation?????

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Inverse method

• ???(sensitivity)??????(the least square method)
• ?????(Conjugate Gradient Method)
• Modified Conjugate Gradient Method
• B-Spline Method
• ?????????,??????????,????????????????

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?????(Sensitivity coefficient)

• ?????????????????,??????(superposition)???????????
  ????????????????????

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?????(the least square method)

• ?????(???????)?????????,?????????????????????????
  7
• ????

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?????(the least square method)

• ???????(??????)??
• ??,?????(associate)

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?? for COMSOL
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• ??????1?????????2?3?4,???2?B1???????????,?????????
  3?B2???????????,?????????4?????????????,??????????
  ?????????(A)?

gt
(A)
22

• ???(A)??????,????????,?????????????????????????

(A)
?????
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COMSOL ??

• ??
• ??20m
• ??20m
• ????steel AISI4340
• Mesh???, 20x10(??????????)

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COMSOL ???(Direct)

• ???????
• ???
• ??373.15K
• ??473.15K
• ???

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(No Transcript)
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COMSOL ?????

• P3463.15K
• P4 463.15K
• P5 463.15K

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(No Transcript)
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COMSOL ???(Inverse)
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COMSOL ???(Inverse)

• ??????
• P30.52307 K
• P40.073444 K
• P50.016213 K

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COMSOL ???(Inverse)
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COMSOL ???(Inverse)

• ??????
• P30.073444 K
• P40.49132 K
• P50.065743 K

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COMSOL ???(Inverse)
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COMSOL ???(Inverse)

• ??
• P3180.909078 K
• P4195.931548 K
• P5424.372615 K

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??MATLAB??

• gtgt A0.52307,0.0734440.073444,0.491320.016213,0
  .065743
• gtgt F463.15463.15463.15
• gtgt D180.909078195.931548424.372615
• gtgt xinv(A'A)A'(F-D)
• x
• 473.1505
• 473.1506
• gt???? 473.15????(OK)

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COMSOL step by step

• STEP1????
• ??COMSOL(??????????)
• ??????
• ??????
• ??

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Step2????

• ??????
• ?????????

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• 3.???????,??????,????,???
• 4.????,? ??????????

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Step3?????

• ?? ???gt?????
• ?????????
• ???? STEEL AISI4340
• ??

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Step4????

• ?? ???gt????
• ????????
• ????
• ??

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Step5????

• ?? ?? gt ??????
• ??????????
• gt????gt??????
• gt20x10

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Step6????

• ????gt????
• ???gt????
• gt???
• (????P3?P4?P5??)

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(No Transcript)
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Step7MATLAB

• ?????????????,??MATLAB??

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Reference

• Yann-Shouh Sun, Cheng-I Weng, Tei-Chen CHEN, and
  Wang-Long LI, Estimation of Surface Absorptivity
  and Surface Temperature, JAPANESE JOURNAL OF
  APPLIED PHYSICS PART 1-REGULAR PAPERS SHORT NOTES
  REVIEW PAPERS 35 (6A) 3658-3664 JUN 1996
• ???,???????????????????????,?????????????????,1995
  
• Tai-Sheng Chen, Horng-Yuan Jang, Tsung-Chien
  Chen,and Pan-Chio Tuan, Adaptive Input
  Estimation Method Combining Finite Element Scheme
  for Inverse Jet Flow Heat Flux Estimating,
  JOURNAL OF C.C.I.T., VOL.34, NO.2, May., 2006
• ???,????????????????????????,?????????????????????
  ?,2002
• ???????,?????????????,????B,????,???,2000
• Introduction to Heat Transfer, THIRD EDITION,
  WILEY
• Wikipadia (http//zh.wikipedia.org/wiki/E7B981
  E4BD93E4B8ADE69687)