A two-stage Lie-group shooting method (TSLGSM) to identify time-dependent thermal diffusivity

International Journal of Heat and Mass Transfer

Volumn 53, Issue 21-22, 2010, Pages 4876-4884

  Liu, Chein Shan ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

Inverse problem; Parameter identification; Time dependent thermal diffusivity; Two stage Lie group shooting method

Indexed keywords

EFFICIENT METHOD; ESTIMATION ERRORS; HEAT CONDUCTION EQUATIONS; INTERNAL POINTS; MEASUREMENT OF TEMPERATURE; NUMERICAL TESTS; TIME-DEPENDENT THERMAL DIFFUSIVITY; TWO-STAGE LIE-GROUP SHOOTING METHOD;

INVERSE PROBLEMS; THERMAL DIFFUSION; THERMAL DIFFUSIVITY;

PARAMETER ESTIMATION;

EID: 77955519254     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2010.06.005     Document Type: Article

References (25)

1. Beck J.V., Blackwell B., St.Clair C.R. Inverse Heat Conduction: Ill-Posed Problems 1985, Wiley-Interscience Publication, New York.
2. Jurkowski T., Jarny Y., Delaunay D. Estimation of thermal conductivity of thermoplastics under moulding conditions: an apparatus and an inverse algorithm. Int. J. Heat Mass Transfer 1997, 40:4169-4181.
3. Zueco J., Alhama F., Gonz ález-Fernández C.F. An inverse problem to estimate temperature dependent heat capacity under convection processes. Heat Mass Transfer 2003, 39:599-604.
4. Kim T., Lee Z. Time-varying heat transfer coefficients between tube-shaped casting and metal mold. Int. J. Heat Mass Transfer 1997, 40:3513-3525.
5. Su J., Hewitt G.F. Inverse heat conduction problem of estimating time-varying heat transfer coefficient. Num. Heat Transfer, Part A 2004, 45:777-789.
6. Dehghan M. Identification of a time dependent coefficient in a partial differential equation subject to an extra measurement. Numer. Meth. Partial Diff. Eq. 2005, 21:611-622.
7. Shamsi M., Dehghan M. Recovering a time-dependent coefficient in a parabolic equation from overspecified boundary data using the pseudospectral Legendre method. Numer. Meth. Partial Diff. Eq. 2007, 23:196-210.
8. Dehghan M., Tatari M. The radial basis functions method for identifying an unknown parameter in a parabolic equation with overspecified data. Numer. Meth. Partial Diff. Eq. 2007, 23:984-997.
9. Liu C.-S. An LGEM to identify time-dependent heat conductivity function by an extra measurement of temperature gradient. CMC: Comput. Mater. Continua 2008, 7:81-95.
10. Liu C.-S. An LGSM to identify nonhomogeneous heat conductivity functions by an extra measurement of temperature. Int. J. Heat Mass Transfer 2008, 51:2603-2613.
11. Liu C.-S. Cone of non-linear dynamical system and group preserving schemes. Int. J. Non-Linear Mech. 2001, 36:1047-1068.
12. Liu C.-S. The Lie-group shooting method for nonlinear two-point boundary value problems exhibiting multiple solutions. CMES: Comput. Model. Eng. Sci. 2006, 13:149-163.
13. Liu C.-S. Efficient shooting methods for the second order ordinary differential equations. CMES: Comput. Model. Eng. Sci. 2006, 15:69-86.
14. Liu C.-S. The Lie-group shooting method for singularly perturbed two-point boundary value problems. CMES: Comput. Model. Eng. Sci. 2006, 15:179-196.
15. Chang J.R., Liu C.-S., Chang C.W. A new shooting method for quasi-boundary regularization of backward heat conduction problems. Int. J. Heat Mass Transfer 2007, 50:2325-2332.
16. Chang C.W., Liu C.-S., Chang J.R. The Lie-group shooting method for quasi-boundary regularization of backward heat conduction problems. ICCES Online J. 2007, 3:69-79.
17. Liu C.-S. One-step GPS for the estimation of temperature-dependent thermal conductivity. Int. J. Heat Mass Transfer 2006, 49:3084-3093.
18. Liu C.-S. An efficient simultaneous estimation of temperature-dependent thermophysical properties. CMES: Comput. Model. Eng. Sci. 2006, 14:77-90.
19. Liu C.-S. Identification of temperature-dependent thermophysical properties in a partial differential equation subject to extra final measurement data. Numer. Meth. Partial Diff. Eq. 2007, 23:1083-1109.
20. Liu C.-S. Solving an inverse Sturm-Liouville problem by a Lie-group method. Boundary Value Prob. 2008, 2008. (Article ID 749865).
21. Liu C.-S. Identifying time-dependent damping and stiffness functions by a simple and yet accurate method. J. Sound Vib. 2008, 318:148-165.
22. Liu C.-S. A two-stage LGSM for three-point BVPs of second-order ODEs. Boundary Value Prob. 2008, 2008. (Article ID 963753).
23. Liu C.-S. A two-stage LGSM to identify time-dependent heat source through an internal measurement of temperature. Int. J. Heat Mass Transfer 2009, 52:1635-1642.
24. Yeih W., Liu C.-S. A three-point BVP of time-dependent inverse heat source problems solving by a TSLGSM. CMES: Comput. Model. Eng. Sci. 2009, 46:107-127.
25. Liu C.-S. An efficient backward group preserving scheme for the backward in time Burgers equation. CMES: Comput. Model. Eng. Sci. 2006, 12:55-65.