Modeling the flash-heat experiment on porous domains
Authors:
H. T. Banks, D. Cioranescu, A. K. Criner and W. P. Winfree
Journal:
Quart. Appl. Math. 70 (2012), 53-67
MSC (2000):
Primary 35B27, 76R50, 78M40
DOI:
https://doi.org/10.1090/S0033-569X-2011-01230-8
Published electronically:
September 16, 2011
MathSciNet review:
2920615
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: We discuss a mathematical model for the flash-heat experiment in homogeneous isotropic media. We then use this model to investigate the use of homogenization techniques in approximating models for interrogation via flash-heating in porous materials. We represent porous materials as both randomly perforated domains and periodically perforated domains.
References
- H.T. Banks, B. Boudreaux, A. K. Criner, K. Foster, C. Uttal, T. Vogel, A.K. Criner and W.P. Winfree, Thermal based damage detection in porous materials, Tech. Rep. CRSC-TR08-11, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, September, 2008; Inverse Probl. Sci. Engr., 18 (2009), 835–851.
- H.T. Banks, D. Cioranescu, A.K. Criner and W.P. Winfree, Modeling the flash-heat experiment on porous domains, Tech. Rep. CRSC-TR10-06, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, May, 2010.
- H. T. Banks, N. L. Gibson and W. P. Winfree, Void detection in complex geometries, Tech. Rep. CRSC-TR08-09, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, May, 2008.
- H. T. Banks, Michele L. Joyner, Buzz Wincheski, and William P. Winfree, Nondestructive evaluation using a reduced-order computational methodology, Inverse Problems 16 (2000), no. 4, 929–945. MR 1776475, DOI https://doi.org/10.1088/0266-5611/16/4/304
- H. T. Banks and Fumio Kojima, Boundary shape identification problems in two-dimensional domains related to thermal testing of materials, Quart. Appl. Math. 47 (1989), no. 2, 273–293. MR 998101, DOI https://doi.org/10.1090/S0033-569X-1989-0998101-8
- H. T. Banks and F. Kojima, Identification of material damage in two-dimensional domains using the SQUID-based nondestructive evaluation system, Inverse Problems 18 (2002), no. 6, 1831–1855. Special section on electromagnetic and ultrasonic nondestructive evaluation. MR 1955921, DOI https://doi.org/10.1088/0266-5611/18/6/324
- H. T. Banks, Fumio Kojima, and W. P. Winfree, Boundary estimation problems arising in thermal tomography, Inverse Problems 6 (1990), no. 6, 897–921. MR 1082231
- D. Cioranescu, A. Damlamian and G. Griso, The periodic unfolding method in domains with holes, to appear.
- Doina Cioranescu and Jeannine Saint Jean Paulin, Homogenization of reticulated structures, Applied Mathematical Sciences, vol. 136, Springer-Verlag, New York, 1999. MR 1676922
- Doina Cioranescu and Patrizia Donato, An introduction to homogenization, Oxford Lecture Series in Mathematics and its Applications, vol. 17, The Clarendon Press, Oxford University Press, New York, 1999. MR 1765047
- Patrizia Donato and Aïssam Nabil, Homogenization and correctors for the heat equation in perforated domains, Ricerche Mat. 50 (2001), no. 1, 115–144. MR 1941824
- The Mathworks, Inc., Partial Differential Equation Toolbox 1: User’s Guide, The Mathworks, Inc., Natick, MA, 2008.
- W. J. Parker, R. J. Jenkins, C. P. Butler and G. L. Abbott, Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity, J. Appl. Phys. 32 (9):1679–1684, 1961.
- Pavel Šolín, Partial differential equations and the finite element method, Pure and Applied Mathematics (New York), Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 2006. MR 2180081
- Wenping Wang, Jiaye Wang, and Myung-Soo Kim, An algebraic condition for the separation of two ellipsoids, Comput. Aided Geom. Design 18 (2001), no. 6, 531–539. MR 1843064, DOI https://doi.org/10.1016/S0167-8396%2801%2900049-8
References
- H.T. Banks, B. Boudreaux, A. K. Criner, K. Foster, C. Uttal, T. Vogel, A.K. Criner and W.P. Winfree, Thermal based damage detection in porous materials, Tech. Rep. CRSC-TR08-11, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, September, 2008; Inverse Probl. Sci. Engr., 18 (2009), 835–851.
- H.T. Banks, D. Cioranescu, A.K. Criner and W.P. Winfree, Modeling the flash-heat experiment on porous domains, Tech. Rep. CRSC-TR10-06, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, May, 2010.
- H. T. Banks, N. L. Gibson and W. P. Winfree, Void detection in complex geometries, Tech. Rep. CRSC-TR08-09, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, May, 2008.
- H. T. Banks, M. L. Joyner, B. Wincheski and W. P. Winfree, Nondestructive evaluation using a reduced-order computational methodology, Inverse Probl. 16(4):929–945, 2000. MR 1776475 (2001e:78022)
- H.T. Banks and F. Kojima, Boundary shape identification problems in two-dimensional domains related to thermal testing of materials, Quart. Appl. Math. 47 (2):273–293, 1989. MR 0998101 (90f:65168)
- H. T. Banks and F. Kojima, Identification of material damage in two-dimensional domains using the SQUID-based nondestructive evaluation system, Inverse Probl. 18 (6):1831–1855, 2002. MR 1955921
- H. T. Banks, F. Kojima and W. P. Winfree, Boundary estimation problems arising in thermal tomography, Inverse Probl. 6 (6):897–921, 1990. MR 1082231 (91k:80003)
- D. Cioranescu, A. Damlamian and G. Griso, The periodic unfolding method in domains with holes, to appear.
- D. Cioranescu and J. Saint Jean Paulin. Homogenization of Reticulated Structures, Volume 136 of Applied Mathematical Sciences, Springer–Verlag, New York, 1999. MR 1676922 (2000d:74064)
- D. Cioranescu and P. Donato, An Introduction to Homogenization, Oxford Lecture Series in Mathematics and Its Applications Volume 27, Oxford University Press, New York, 1999. MR 1765047 (2001j:35019)
- P. Donato and A. Nabil, Homogenization and correctors for the heat equation in perforated domains, Ric. Mat., 50(1):115–144, 2001. MR 1941824 (2003i:35017)
- The Mathworks, Inc., Partial Differential Equation Toolbox 1: User’s Guide, The Mathworks, Inc., Natick, MA, 2008.
- W. J. Parker, R. J. Jenkins, C. P. Butler and G. L. Abbott, Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity, J. Appl. Phys. 32 (9):1679–1684, 1961.
- Pavel S̆olin, Partial Differential Equations and the Finite Element Method, John Wiley & Sons, Inc., Hoboken, NJ, 2006. MR 2180081 (2006f:35004)
- Wenping Wang, Jiaye Wang and Myung-Soo Kim, An algebraic condition for the separation of two ellipsoids, Comput. Aided Geom. Design, 18(6):531–539, 2001. MR 1843064 (2002c:65030)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC (2000):
35B27,
76R50,
78M40
Retrieve articles in all journals
with MSC (2000):
35B27,
76R50,
78M40
Additional Information
H. T. Banks
Affiliation:
Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University, Raleigh, North Carolina 27695-8212
MR Author ID:
194993
D. Cioranescu
Affiliation:
Laboratoire J. L. Lions, Université Pierre et Marie Curie, 175 rue du Chevaleret, 75013 Paris, France
MR Author ID:
49540
A. K. Criner
Affiliation:
Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University, Raleigh, North Carolina 27695-8212
W. P. Winfree
Affiliation:
Nondestructive Evaluation Science Branch, NASA Langley Research Center, MS 231, Hampton, Virginia 23681
Keywords:
Modeling porous media,
thermal diffusion,
homogenization
Received by editor(s):
May 16, 2010
Published electronically:
September 16, 2011
Article copyright:
© Copyright 2011
Brown University
