APPLICATION OF SENSITIVITY COEFFICIENTS FOR HEAT CONDUCTION PROBLEMS

In parameter estimation, considerable insight is provided by examining sensitivity coefficients. This article focuses on the use of sensitivity coefficients in connection with estimating thermal properties in the heat conduction equation. It is demonstrated how sensitivity coefficients are used in the design analysis of parameter estimation experiments. A general methodology for computing sensitivity coefficients can be an important design tool in many other regards also. A control-volume, finite-element program is used to implement numerical sensitivity coefficient calculations. In this approach, general problems can be studied. Several example cases are presented to demonstrate the insight gained from sensitivity coefficients. The cases are selected from experimental studies to characterize the thermal properties of carbon carbon composite. However, no experimental data are reported. Sensitivity coefficients show that in an experiment that is not well designed, additional materials in the experimental configuration can have a larger impact on the temperature than the material of interest. Two-dimensional configurations demonstrate that there can be isolated areas of insensitivity and the difficulty of estimating multiple parameters.