A New Viscosity Constitutive Model for Generalized Newtonian Fluids Using Theory of Micropolar Continuum

Abstract

In this paper, a new viscosity constitutive relation for the analysis of generalized Newtonian fluids is presented and analyzed. The theory of micropolar continuum is considered for the derivation of constitutive relations where the kinematics at the macroscopic level leads to incorporate the micro-rotational effects in existing rheology of Carreau Yasuda model. It provides a more realistic approach to analyze the flow behavior of generalized Newtonian fluids. To the best of the author's knowledge, such generalization of the existing rheology of Carreau-Yasuda is not present in literature. In order to show the effects of micro-rotations on the viscosity of generalized fluids, different computational experiments are performed using finite volume method (FVM). The method is implemented and validated for accuracy by comparison with existing literature in the limiting case through graphs and tables and a good agreement is achieved. It is observed that with the increase of micro-rotations the shear thinning phenomena slower down whereas the shear thickening is enhanced. Moreover, the effects of various model parameters on horizontal and vertical velocities as well as on boundary layer thickness are shown through graphs and contour plots. It is worth mentioning that the proposed constitutive model can be utilized to analyze the generalized Newtonian fluids and has wider applications in blood rheology.