A closed-form solution to estimate space-dependent parameters in heat and mass transport

Heat and particle transport play an important part in the performance of fusion reactors. This can be studied by modelling and by perturbative experiments. In case of perturbative experiments, the trans-port modelling can be simplified to a one-dimensional diffusion-transport-reaction equation. Currently, the spatially varying parameters are estimated using simplifying assumptions, e.g. piecewise constant parameters, or only diffusivity and convectivity are considered. In this work, we present a method to simultaneous estimate all four space-dependent transport parameter: diffusivity, convectivity, reactivity and the power deposition prole. Moreover, the proposed method has a closed-form solution, avoiding the commonly used computational expensive optimization methods. The closed-form solution is obtained by transforming the problem into the frequency and using a spatial discretization. The functioning of the proposed methodology to simultaneous estimate the spatially varying transport parameters is illustrated by means of simulation examples.