Stabilization of ill-posed problems through thermal rate sensors

Journal of Thermophysics and Heat Transfer

Volumn 20, Issue 2, 2006, Pages 238-246

  Frankel, J I ^a,c,d   Osborne, G E ^a,c,d   Taira, K ^b,d,e  

^a UNIVERSITY OF TENNESSEE   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c Mechanical Aerospace and Biomedical Engineering Department   (United States)

^d AIAA   (United States)

^e Mechanical Engineering Department   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DATA PROCESSING; HEAT FLUX; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PRODUCT DESIGN; REAL TIME SYSTEMS;

DATA DIFFERENTIATION; HIERARCHY; MATHEMATICAL FORMULATION; THERMAL RATE SENSORS;

SENSORS;

DATA PROCESSING; HEAT FLUX; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PRODUCT DESIGN; REAL TIME SYSTEMS; SENSORS;

EID: 33744508936     PISSN: 08878722     EISSN: 15336808     Source Type: Journal    
DOI: 10.2514/1.9136     Document Type: Article

References (32)

1. Doebelin, E. O., Measurement Systems, McGraw-Hill, New York, 1975, Chap. 8.
2. Diller, T. E., "Advances in Heat Flux Measurements," Advances in Heat Transfer, Vol. 23, Academic Press, New York, 1993, pp. 279-368.
3. Lu, F. K., and Marren, D. E. (eds.), Advanced Hypersonic Test Facilities, Progress in Astronautics and Aeronautics, Vol. 198, AIAA, Reston, VA, 2002, pp. 279-314.
4. Neumann, R. D., Erbland, P. J., and Kretz, L. O., "Instrumentation of Hypersonic Structures," AIAA Thermophysics, Plasmadynamics and Lasers Conf., June 1988.
5. Kress, R., Linear Integral Equations, Springer-Verlag, Berlin, 1989, Chap. 15.
6. Wing, G. M., A Primer on Integral Equations of the First Kind, Society for Industrial and Applied Mathematies, Philadelphia, 1991, Chap. 2.
7. Beck, J. V., Blackwell, B., and St. Clair, C. R., Jr., Inverse Heat Conduction, Wiley, New York, 1985, Chap. 1.
8. Kurpisz, K., and Nowak, A. J., Inverse Thermal Problems, Computational Mechanics, Southampton, U.K., 1995, Chap. 1.
9. Hanke, M., and Scherzer, O., "Inverse Problems Light: Numerical Differentiation," American Mathematical Monthly, Vol. 108, June/July 2001, pp. 512-520.
10. Groetsch, T., "Differentiation of Approximately Specified Functions," American Mathematical Monthly, Vol. 98, No. 9, 1991, pp. 847-850.
11. Frankel, J. I., Keyhani, M., and Taira, K., "In-Phase Error Estimation of Experimental Data and Optimal First Derivatives," AIAA Journal, Vol. 42, No. 5, 2004, pp. 1017-1024.
12. Frankel, J. I., and Keyhani, M., "Inverse Heat Conduction: The Need of ∂T/∂t Data for Design and Diagnostic Purposes," Paper 113, International Conference on Modeling, Identification and Controls, International Association of Science and Technology for Development, Feb. 1999.
13. Frankel, J. I., "Inverse Heat Conduction and Data-Type Issues," Boundary Element Communications, Vol. 11, No. 4, 2000, pp. 37-42.
14. Frankel, J. I., and Osborne, G. E., "The Development of Heating/Cooling Rate, dT/dt and Heat Flux Rate, dq"/dt Sensors for Aerospace Applications," Propulsion Measurement Sensor Development Workshop, Paper 1.2.4, NASA, Huntsville, AL, May 2003.
15. Frankel, J. I., and Osborne, G. E., "The Prediction of Heating/Cooling Rates in Material Science Investigations," 4th International Conference on Quenching and Control of Distortion, Paper 86, Chinese Heat Treatment Society, Beijing, PRC, Nov. 2003.
16. Frankel, J. I., and Osborne, G. E., "Motivation for the Development of Heating/Cooling Rate dT/dt and Heat Flux Rate dq"/dt Sensors for Engineering Applications," AIAA Paper 2004-0823, Jan. 2004.
17. Lu, F. K., and Kinnear, K. M., "Characterization of Thin Film Heat-Flux Gauges," 20th Advanced Measurement and Ground Testing Technology Conf., AIAA Paper 98-2504, June 1998.
18. Hodge, J. K., Chen, A. L., and Hayes, J. R., "Unsteady Heat Transfer Coefficient Estimation for Long Duration," Journal of Thermophysics and Heat Transfer, Vol. 2, No. 3, 1988, pp. 218-226.
19. Cook, W. J., and Felderman, E. J., "Reduction of Data from Thin-Film Heat Transfer Gauges: A Concise Numerical Technique," AIAA Journal, Vol. 4, March 1966, pp. 561-562.
20. Cook, W. J., "Determination of Heat Transfer Rates from Transient Surface Temperature Measurements," AIAA Journal, Vol. 8, No. 7, 1970, pp. 1366-1368.
21. Linz, P., Analytical and Numerical Methods for Volterra Equations, Society for Industrial and Applied Mathematics, Philadelphia, 1985, Chap. 8.
22. Baker, C. T. H., The Numerical Treatment of Integral Equations, Clarendon Press, Oxford, England, U.K., 1978, Chap. 6.
23. Golberg, M. A. (ed.), Solution Methods for Integral Equations, Plenum, New York, 1979, Chap. 1.
24. Ozisik, M. N., Heat Conduction, Wiley, New York, 1980, Chap. 1.
25. Arpaci, V. S., Conduction Heat Transfer, Addison Wesley Longman, Reading, MA, 1966, Chap. 1.
26. Brebbia, C. A., Telles, J. C. F., and Wrobel, L. C., Boundary Element Techniques, Springer-Verlag, Berlin, 1984, Chap. 4.
27. Kaplan, W., Advanced Calculus, 2nd ed. Addison Wesley Longman, Reading, MA, 1973, p. 439.
28. Frankel, J. I., and Keyhani, M., "A Global Time Treatment for Inverse Heat Conduction Problems," Journal of Heat Transfer, Vol. 119, Nov. 1997, pp. 673-683.
29. Frankel, J. I., Vick, B., and Ozisik, M. N., "Flux Formulation in Hyperbolic Heat Conduction," Journal of Applied Physics, Vol. 58, No. 9, 1985, pp. 3340-3345.
30. Hardy, R. L., "Theory and Applications of the Multiquadric Biharmonic Method," Computers in Mathematics with Applications, Vol. 19, No. 8, 9, 1990, pp. 163-208.
31. Boley, B. A., and Weiner, J. H., Theory of Thermal Stresses, Dover, New York, 1997, Chap. 6.
32. Penner, S. S., and Olfe, D. B., Radiation and Reentry, Inst. for Defense Analysis, Washington, DC, 1968, Chap. 7.