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.
Sensitivity Analysis for Nonlinear Heat Conduction
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.
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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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