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The effect of material parameters on three rate-type constitutive equations (White-Metzner, Oldroyd 3-constant and Kopaç-Arıkol) used successfully according to the literature was investigated. The flow along the symetry axis of a converging-diverging flow channel was considered. In order to determine the effect of material parameters appearing in constitutive equations, the tensorial expressions of the models were reduced to the axis of symmetry, using derivative operators of models and flow kinematics. Arıkol's values (1976, 1985) were used for the velocity and initial viscosity values appearing in reduced nonlinear ordinary differantial equations. The reduced constituve equations were solved numerically using the 4th order Runge-Kutta method. In these calculations, velocity and the 1st and 2nd derivatives of velocity were used as input in the equations. Solving the constitutive equations for 3 different values of the material parameters, the normal stress differences were determined along the axis of symmetry. The sum of squares between the calculated normal stress values and Arıkol's(1976, 1985) experimental values were determined. As a result, the material parameters, sensitive and non-sensitive, were determined in each of the constitutive equations.

In this study using some existing constitutive equations, a modified Jeffreys type model with retardation time is developed which is successful with the experimental data for simple shear flow and shear free flow. Nonlinear regression analysis based on Marquardt Algorithm is used for determination of material parameters for simple shear flow. The general form of the modified model is reduced by using the simple shear flow conditions and Oldroyd derivative for cartesian coordinates. In the determination of material parameters of the modified model is used experimental data of Leider and Lilleleht(1973) for viscometric functions. When viscometric functions of the modified model is compared with viscometric functions of the existing constitutive equations which use the material parameters of Leider and Lilleleht(1973), viscometric functions of the modified model is found to be more successful.

The effect of material parameters on three rate-type constitutive equations (White-Metzner, Oldroyd 3-constant and Kopac-Arikol) used successfully according to the literature was investigated. The flow along the symetry axis of a converging-diverging flow channel was considered. In order to determine the effect of material parameters appearing in constitutive equations, the tensorial expressions of the models were reduced to the axis of symmetry, using derivative operators of models and flow kinematics. Arikol's values (1976, 1985) were used for the velocity and initial viscosity values appearing in reduced nonlinear ordinary differantial equations. The reduced constituve equations were solved numerically using the 4th order Runge-Kutta method. In these calculations, velocity and the 1st and 2nd derivatives of velocity were used as input in the equations. Solving the constitutive equations for 3 different values of the material parameters, the normal stress differences were determined along the axis of symmetry. The sum of squares between the calculated normal stress values and Arikol's(1976, 1985) experimental values were determined. As a result, the material parameters, sensitive and non-sensitive, were determined in each of the constitutive equations.The effect of material parameters on three rate-type constitutive equations (White-Metzner, Oldroyd 3-constant and Kopac-Arikol) used successfully according to the literature was investigated. The flow along the symmetry axis of a converging-diverging flow channel was considered. In order to determine the effect of material parameters appearing in constitutive equations, the tensorial expressions of the models were reduced to the axis of symmetry, using derivative operators of models and flow kinematics. Arikol's values (1976, 1985) were used for the velocity and initial viscosity values appearing in reduced nonlinear ordinary differential equations. The reduced constitutive equations were solved numerically using the 4th order Runge-Kutta method. In these calculations, velocity and the 1st and 2nd derivatives of velocity were used as input in the equations. Solving the constitutive equations for 3 different values of the material parameters, the normal stress differences were determined along the axis of symmetry. The sum of squares between the calculated normal stress values and Arikol's (1976, 1985) experimental values were determined. As a result, the material parameters, sensitive and non-sensitive, were determined in each of the constitutive equations.

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.