G.E. Osborne, J.I. Frankel, and A.S. Sabau (USA)
Parameter estimation, inverse problems, Function Decomposition Method, DSC
A lumped heat transfer model and parameter estimation technique are proposed for determining key parameters associated with a heat flux Differential Scanning Calorimeter (DSC). Part I of this two-part paper focuses on developing the mathematical model and describing the proposed parameter estimation technique. Part II presents the numerical implementation using a conventional Runge-Kutta method with results indicating the merit of the proposed parameter estimation method. In this part, the physical model is derived, and simplifying assumptions are presented. The resulting heat transfer model requires the simultaneous resolution of two conduction and two radiation parameters, and one time-dependent function using two concurrent temperature data streams emanating from the container plates in the device. The unknown functions of interest include the furnace temperature which is expanded into a finite series involving predefined basis functions each having a corresponding unknown expansion coefficient. The resulting system of initial-value problems is linearized using quasilinearization. Each dependent variable is then decomposed into a series of baseline and sensitivity functions. A least-squares minimization method is introduced using the collected data streams to determine the parameters at the updated iterate. The iterative process is continued until convergence takes place for all system parameters. This paper highlights the modeling and algorithm aspects associated with resolving these parameters.
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