Parameters identification for the unsteady helical flows of a generalized Oldroyd-B fluid model based on its numerical solution

Abstract

In this paper, we mainly consider the problem of parameter identification for the unsteady helical flows of a generalized Oldroyd-B fluid between two infinitely long coaxial circular cylinders. The implicit finite difference method is employed to obtain the numerical solution for the direct problem. By means of the Levenberg–Marquardt method, the numerical inversion for identifying the three parameters of the model is implemented simultaneously, that is, the Riemann–Liouville time-fractional derivative α, relaxation time λ, and retardation time λr. To test the validity of the proposed numerical method, varied initial guesses and the observed data, whether or not they involve random error, have been used to verify the reliability of the estimation. This paper provides an efficient method to obtain the estimated value of the unknown parameters for the generalized non-Newtonian fluids model.