Authors: Mehmet KOPAÇ, Mahir ARIKOL
Abstract: In this study using some constitutive equations present in the literature, a rate-type constitutive equation is developed which is successful with the experimental results. The method being used is a nonlinear regression method that is known as Marquardt Method. Studies were done considering flow along the centerline of the flow channel. In this study the general form of the proposed constitutive equation was reduced on the centerline by using the flow kinematics and derivative operator for cartesian coordinates. Developing the difference of the normal stress components in the 1- and 2- directions a nonlinear ordinary differential equation was obtained for the normal stress difference. When this differential equation that was reduced on the centerline was solved by this nonlinear regression method, model parameters, normal stress difference values along the centerline and sum of squares were determined simultaneously. When the proposed constitutive equation was compared with the existing equations, the proposed equation was found to be more successful in the flow along the centerline.
Keywords: Non-Newtonian fluids; viscoelastic fluids; constitutive equations; non-linear regression