Insight Into the Dynamics of the Rabinowitsch Fluid Through an Elliptic Duct: Peristalsis Analysis

Abstract

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The current research is concerned with the mechanical characteristics of a Rabinowitsch fluid model that has been developed via an elliptic duct. If we study physiology or biomedicine, we will find that the Rabinowitsch fluid model in peristalsis is very useful because it is used to move blood around in the heart, lungs, sanitary fluid transport systems, transfer of corrosive fluids, and innovative pharmaceutical delivery systems. It is possible to get the elliptic domain for this duct model by using Cartesian coordinates, and in the boundary conditions for this duct, the equation of an ellipse is used to keep the elliptic cross-section for this duct in place. A mathematical model for an incompressible fluid is being created, and the mathematical issue is then transformed into its dimensionless form by using suitable transformations, including long-wavelength approximation. As soon as the problem is put into a dimensionless form, the partial differential equations for the velocity profile can be found. These partial differential equations are solved across elliptical cross-sections with the help of boundary conditions that are given, and accurate mathematical solutions are then found for them. This model is important because it shows three different types of flow: a dilatant fluid for γ<0, a Newtonian fluid for γ=0, and a pseudoplastic fluid for γ>0. The prime objective of our work is to obtain a novel solution to this problem as well. In the last section, we see and read about how the formulas for flow characteristics were made.

Keywords

• peristalsis
• elliptical duct
• Rabinowitsch fluid model
• polynomial solution
• exact solutions