Dowding and Blackwell 1 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.

The simple problem of steady one-dimensional heat conduction with temperature-dependent thermal conductivity used in 1 as a verification problem provides a good example to illustrate this point. Defining
one can re-write...
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