TY - JOUR

T1 - Analytical Solution of Slow Squeeze Flow of Slightly Viscoelastic Fluid Film between Two Circular Disks Using Recursive Approach

AU - Memon, Muhammad

AU - Shaikh, Asif Ali

AU - Siddiqui, Abdul Majeed

AU - Kumar, Laveet

N1 - Publisher Copyright:
© 2022 Muhammad Memon et al.

PY - 2022

Y1 - 2022

N2 - This research investigates an analytical solution for the slow squeeze flow of the slightly viscoelastic fluid film between two circular disks in which the upper disk approaches the lower disk with a constant velocity, and the lower disk is kept stationary. The determination of the study is to identify the behavior of the differential type fluid on the steady squeezing flow using Langlois recursive approach. The governing equations for the axisymmetric flow are expressed in cylindrical coordinates and yield the nonlinear system of partial differential equations. The analytical solution of the resulting equations with nonhomogeneous boundary conditions is obtained by the Langlois recursive approach. Flow variables such as stream function, velocity profiles, pressure distribution, shear, normal stresses, and normal force acting on the disk are determined. These flow variables are nondimensionalized by using suitable dimensional quantities. The influence of slightly viscoelastic parameter β, radial distance r, and aspect ratio on velocity components, pressure distribution, and normal squeeze force is examined mathematically and portrayed graphically. The results illustrate that the axial and radial velocities increase at the higher values of the slightly viscoelastic parameter β, which confirms the shear thickening behavior. The obtained solutions of the flow variables satisfied the existing solutions on squeeze flow of viscous fluid upon vanishing the slightly viscoelastic parameters. This solution could elucidate the classical lubrication problems, particularly in load and thrust bearing characteristics of the human body joints, the compression molding process of materials, etc.

AB - This research investigates an analytical solution for the slow squeeze flow of the slightly viscoelastic fluid film between two circular disks in which the upper disk approaches the lower disk with a constant velocity, and the lower disk is kept stationary. The determination of the study is to identify the behavior of the differential type fluid on the steady squeezing flow using Langlois recursive approach. The governing equations for the axisymmetric flow are expressed in cylindrical coordinates and yield the nonlinear system of partial differential equations. The analytical solution of the resulting equations with nonhomogeneous boundary conditions is obtained by the Langlois recursive approach. Flow variables such as stream function, velocity profiles, pressure distribution, shear, normal stresses, and normal force acting on the disk are determined. These flow variables are nondimensionalized by using suitable dimensional quantities. The influence of slightly viscoelastic parameter β, radial distance r, and aspect ratio on velocity components, pressure distribution, and normal squeeze force is examined mathematically and portrayed graphically. The results illustrate that the axial and radial velocities increase at the higher values of the slightly viscoelastic parameter β, which confirms the shear thickening behavior. The obtained solutions of the flow variables satisfied the existing solutions on squeeze flow of viscous fluid upon vanishing the slightly viscoelastic parameters. This solution could elucidate the classical lubrication problems, particularly in load and thrust bearing characteristics of the human body joints, the compression molding process of materials, etc.

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U2 - 10.1155/2022/4043909

DO - 10.1155/2022/4043909

M3 - Article

AN - SCOPUS:85132524741

SN - 1024-123X

VL - 2022

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

M1 - 4043909

ER -