Parameter Estimation of a Thermal Fluid System

In this paper we consider the problems of parameter estimation for a counter flow heat exchanger. The problem is complicated when convection dominates the heat transfer so that the diffusion coefficient is small compared to the convection coefficient. We employ the full flux physics model, which means the model is defined by convection-diffusion equations and the parabolic equations are viewed as a perturbation of the zero diffusion model. We show that by proper formulation of the boundary conditions and employing combined finite element-finite volume schemes one can estimate the small diffusion term. Moreover, by employing constrained optimization one can obtain physically meaningful results. We compare constrained and unconstrained nonlinear least squares approaches. Numerical results are presented to illustrate the ideas and some open questions are discussed.