A nonlinear indirect measurement problem for a multithermocouple probe immersed in a liquid

The problem described herein concerns the processing of the time-dependent, internal temperatures within a multithermocouple probe. These are used to compute the temperature of the surrounding fluid, as part of an inverse hea t conduction problem (IHCP). The novel achievement in this work is that the exchange coefficients do not have to be supplied a priori, but instead are an additional solution output. Consequently the IHCP is nonlinear and requires significant stabilization. Four methods are applied successively, until a satisfactory solution is fou nd: the parameterization of spatial variations in fluid temperatures and ex change coefficients; a functional specification method (using future time d ata) to address the noncausal nature of the solution; a lower bound on the exchange coefficient; and a maximum number of iterations at each time step (in accordance with the discrepancy principle).