Distributed parameter thermal controllability: A numerical method for solving the inverse heat conduction problem

International Journal for Numerical Methods in Engineering

Volumn 59, Issue 7, 2004, Pages 945-961

  Alaeddine, Marios ^a   Doumanidis, Charalabos C ^b  

^a Tufts University   (United States)

^b NATIONAL SCIENCE FOUNDATION   (United States)

Author keywords

Distributed parameter; Numerical method; Thermal control

Indexed keywords

ALGORITHMS; GREEN'S FUNCTION; HEAT CONDUCTION; INVERSE PROBLEMS; ITERATIVE METHODS; NUMERICAL METHODS; OPTIMIZATION;

INVERSE HEAT CONDUCTION PROBLEMS; THERMAL MANUFACTURING PROCESSES;

THERMAL VARIABLES CONTROL;

HEAT CONDUCTION; MATHEMATICAL METHOD; TEMPERATURE CONTROL;

EID: 1442289297     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.898     Document Type: Article

References (26)

1. Alifanov OM. Inverse Heat Transfer Problems. Springer: Berlin, 1994.
2. Beck JV, Blackwell B, Haji-Sheikh A. Comparison of some inverse heat conduction methods using experimental data. International Journal of Heat and Mass Transfer 1996; 39(17):3649-3657.
3. Shumakov NV. A method for the experimental study of the process of heating a solid body. Soviet Physics Technical Physics 1957; 2:771-781 (Translated by American Institute of Physics).
4. Stolz Jr G. Numerical solutions to an inverse problem of heat conduction for simple shapes. Journal of Heat Transfer 1960; 82:20-26.
5. Kailath T. Linear Systems. Prentice-Hall: Englewood Cliffs, NJ. 1980.
6. Doumanidis CC, Fourligkas N. Infinite-dimensional modeling and control of thermal manufacturing processes. IEEE 4th Mediterranean Conference on New Directions in Control and Automation, Maleme GR, 1996; 632-636.
7. Armaou A, Christofides PD. Dynamic optimization of dissipative PDE systems using nonlinear order reduction. Chemical Engineering Science 2002; 57:5083-5114.
8. Bendersky E, Christofides PD. Optimization of transport-reaction processes using nonlinear model reduction. Chemical Engineering Science 2000; 55:4349-4366.
9. Baker J, Christofides PD. Finite-dimensional approximation and control of nonlinear parabolic PDE systems. International Journal of Control 2000; 73:439-456.
10. Christofides PD, Daoutidis P. Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds. Journal of Mathematical Analysis and Applications 1997; 216:398-420.
11. Antoniades C, Christofides PD. Integrating nonlinear output feedback control and optimal actuator/sensor placement for transport-reaction processes. Chemical Engineering Science 2001; 56:4517-4535.
12. Tzafestas SG (ed). Distributed Parameter Control Systems. Pergamon Press: Oxford, 1982.
13. Ray WH, Lainiotis DG. Distributed Parameter systems: Identification, Estimation, and Control. Marcel Dekker: New York, 1978.
14. Beck JV, Blackwell B, St. Clair Jr AR. Inverse Heat Conduction: III-Posed Problems. Wiley: New York, 1985.
15. Burggraf OR. An exact solution of the inverse problem in heat conduction theory and application. Journal of Heat Transfer 1964; 86:373-382.
16. Sparrow EM, Haji-Sheikh A, Lundgren TS. The inverse problem in transient heat conduction. Journal of Heat Transfer 1964; 86:369-375.
17. Shoji M. Study of inverse problems of heat conduction. Transactions of the Japan Society of Mechanical Engineers 1978; 44(381):1633-1643 (in Japanese).
18. Shoji M, Ono N. Application of the boundary element to the inverse problem of heat conduction. Transactions of the Japan Society of Mechanical Engineers 1988; 54(506B):2893-2900 (in Japanese).
19. Imber M, Khan J. Prediction of transient temperature distributions with embedded thermocouples. AIAA Journal 1972; 10(6):784-789.
20. Imber M. Temperature extrapolation mechanism for two-dimensional heat flow. AIAA Journal 1974; 12(8): 1089-1093.
21. Monde M. Analytical method in inverse heat transfer problem using Laplace transform technique. International Journal of Heat and Mass Transfer 2000; 43(21):3965-3975.
22. Lesnic D, Elliott L, Ingham DB. Application of the boundary element method to inverse heat conduction problems. International Journal of Heat and Mass Transfer 1996; 39(7):1503-1517.
23. Chen HT, Lin SY, Fang LC. Estimation of surface temperature in two-dimensional inverse heat conduction problems. International Journal of Heat and Mass Transfer 2001; 44(8):1455-1463.
24. Mills AF. Basic Heat and Mass Transfer. Irwin Professional Publishing: Burr Ridge, 1995.
25. Carslaw HS, Jaeger JC. Conduction of Heat in Solids (2nd edn). Clarendon Press: Oxford, 1959.
26. Beck JV, Cole KD, Haji-Sheikh A, Litkouhi B. Heat Conduction Using Green's Functions. Hemisphere Publishing Corporation: London, Washington DC, 1992.