Parameters in the heat conduction equation are frequently modeled as temperature dependent. Thermal conductivity, volumetric heat capacity, convection coefficients, emissivity, and volumetric source terms are parameters that may depend on temperature. Many applications, such as parameter estimation, optimal experimental design, optimization, and uncertainty analysis, require sensitivity to the parameters describing temperature-dependent properties. A general procedure to compute the sensitivity of the temperature field to model parameters for nonlinear heat conduction is studied. Parameters are modeled as arbitrary functions of temperature. Sensitivity equations are implemented in an unstructured grid, element-based numerical solver. The objectives of this study are to describe the methodology to derive sensitivity equations for the temperature-dependent parameters and present demonstration calculations. In addition to a verification problem, the design of an experiment to estimate temperature variable thermal properties is discussed.
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e-mail: kjdowdi@sandia.gov
e-mail: bfblack@sandia.gov
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Sensitivity Analysis for Nonlinear Heat Conduction
Kevin J. Dowding,
e-mail: kjdowdi@sandia.gov
Kevin J. Dowding
Sandia National Laboratories, P.O. box 5800, Mail Stop 0828, Albuquerque, NM 87185-0828
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Bennie F. Blackwell
e-mail: bfblack@sandia.gov
Bennie F. Blackwell
Sandia National Laboratories, P.O. box 5800, Mail Stop 0828, Albuquerque, NM 87185-0828
Search for other works by this author on:
Kevin J. Dowding
Sandia National Laboratories, P.O. box 5800, Mail Stop 0828, Albuquerque, NM 87185-0828
e-mail: kjdowdi@sandia.gov
Bennie F. Blackwell
Sandia National Laboratories, P.O. box 5800, Mail Stop 0828, Albuquerque, NM 87185-0828
e-mail: bfblack@sandia.gov
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division October 5, 1999; revision received August 23, 2000. Associate Editor: S. Sadhal.
J. Heat Transfer. Feb 2001, 123(1): 1-10 (10 pages)
Published Online: August 23, 2000
Article history
Received:
October 5, 1999
Revised:
August 23, 2000
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Dowding, K. J., and Blackwell, B. F. (August 23, 2000). "Sensitivity Analysis for Nonlinear Heat Conduction ." ASME. J. Heat Transfer. February 2001; 123(1): 1–10. https://doi.org/10.1115/1.1332780
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