Discussion: "Sensitivity Analysis for Nonlinear Heat Condition," (Dowding, K. J., and Blackwell, B. F., 2001, ASME J. of Heat Transfer, 123(1), pp. 1–10)

Dowding and Blackwell derived sensitivity equations for general nonlinear heat conduction. What is surprising is that they chose to write these equations in dimensional form. One would expect that such a study must begin with writing the equations in nondimensional form and using Pi Theorem [2], p. 93 to find dimensionless groups of parameters on which the solution really depends. By failing to do this, the authors left undetected the fact that some of their sensitivity coefficients are linear dependent. In a practical calculation, this would unnecessarily increase the number of equations to solve. We agree completely with the analysis of Professor Shusser that the sensitivity coefficients for our verification problem are correlated. From our considerable experience in parameter estimation, this is something we are very familiar with. Perhaps in our article we failed to make it clear that we are attempting to address parameter sensitivity for multidimensional transient heat conduction problems in complex geometries. These problems may have tens to hundreds of parameters and it will be difficult to ascertain which parameters are correlated or pertinent dimensionless groups. By their nature, these problems require large computer codes and putting the equations in dimensionless form is not a realistic option. Our interest in the rather simple one-dimensional steady state problem with two linear conductivity segments was purely as a verification problem for our software implementation and the correlation of the sensitivity coefficients was not thought to be a significant issue in our work.