Diffusion processes identification in cylindrical geometry using fractional models

The fractional differentiation operator is used in order to model the heat transfer at the diffusion interface in homogeneous material. Commensurate and non-commensurate models of different fractional orders are obtained for thermal processes in cylindrical geometry. The parameters of a state space fractional model, including the fractional orders, are identified with an iterative nonlinear programming algorithm, as a result of a quadratic parameter optimization problem in output error formulation. A novel fractional multivariable sensitivity functions model is used to compute the gradient and Hessian expressions needed in the parameter update of the algorithm. The suggested method is applied to numerical simulation data of the heat transfer problem obtained using finite differences. Fractional commensurate and non-commensurate order models of the thermal process are identified. The results are consistent with known mathematical models of interface diffusion processes. It is also shown in the simulation that non-commensurate low order models represent heat transfer data with good accuracy.