Roll coating analysis of a third grade fluid

2016 ◽  
Vol 33 (1) ◽  
pp. 72-91 ◽  
Author(s):  
M Zahid ◽  
T Haroon ◽  
MA Rana ◽  
AM Siddiqui
Keyword(s):  
Equations Of Motion ◽  
Gradient Flow ◽  
Material Constant ◽  
Maximum Pressure ◽  
Lubrication Approximation ◽  
Third Grade Fluid ◽  
Regular Perturbation ◽  
Roll Coating ◽  
Grade Fluid ◽  
The Web

This paper studies the roll-coating process of an incompressible viscoelastic fluid, where the roll and the web have equal velocities. The lubrication approximation theory is used to simplify the equations of motion. Solutions for velocity profile, pressure gradient, flow rate per unit width, and shear stress at the roll surface are obtained by using a regular perturbation method. Integrated quantities of engineering interest are also calculated. These include the maximum pressure, separation point, roll/sheet separating force, power transmitted to the fluid by the roll, and coating thickness. It is found that these quantities increase substantially and monotonically as the fluid’s material constant increases.

scholarly journals Theoretical Study of the Reverse Roll Coating of Non-Isothermal Magnetohydrodynamics Viscoplastic Fluid

Coatings ◽  
2020 ◽  
Vol 10 (10) ◽  
pp. 940
Author(s):  
Fateh Ali ◽  
Yanren Hou ◽  
Muhammad Zahid ◽  
Muhammad Afzal Rana
Keyword(s):  
Theoretical Study ◽  
Equations Of Motion ◽  
Trapezoidal Rule ◽  
Viscoplastic Fluid ◽  
Lubrication Approximation ◽  
Roll Coating ◽  
Pressure Distributions ◽  
Temperature Distributions ◽  
False Position ◽  
The Web

This article describes the development of a mathematical model of the reverse roll coating of a thin film for an incompressible non-isothermal magnetohydrodynamics (MHD) viscoplastic fluid as it passes through a small gap between two rolls rotating reversely. The equations of motion required for the fluid added to the web are constructed and simplified using the lubrication approximation theory (LAT). Analytical results are obtained for the velocity profile, pressure gradient, and temperature distribution. The pressure distributions and flow rate are calculated numerically using the trapezoidal rule and regular false position method, respectively. Some of these results are presented graphically, while others are shown in a tabular form. From the present analysis, it has been observed that the magnitude of pressure distributions increases by increasing the value of the involved parameters. It is worth mentioning that the velocities ratio and Brickman’s number are controlling parameters for the temperature distributions. The results indicate the strong effectiveness of the viscoplastic parameter and velocities ratio for the velocity and pressure distributions. It is also concluded that the coating of Casson material has been remarkably affected by the magnetohydrodynamics effects.

scholarly journals Forward Roll Coating of a Williamson’s Material onto a Moving Web: A Theoretical Study

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
M. Zahid ◽  
I. Siddique ◽  
S. Saleem ◽  
A. Al-Zubaidi ◽  
M. A. Rana ◽  
...  
Keyword(s):  
Coating Thickness ◽  
Gradient Flow ◽  
Separation Point ◽  
Maximum Pressure ◽  
Perturbation Approach ◽  
Regular Perturbation ◽  
Roll Coating ◽  
Flow Equations ◽  
Operating Variables ◽  
Roll Separating Force

This paper presents a mathematical model for the thin film roll coating process of an incompressible Williamson material, passing through a closed passage between a rotating roll and a web. In light of lubrication approximation theory, the flow equations are nondimensionalized. The regular perturbation approach is used to provide solutions for the velocity profile, pressure gradient, flow rate per unit width, and shear stress at the roll surface. Important engineering quantities such as coating thickness, maximum pressure, separation point, roll/sheet separating force, and roll-transmitted power to the fluid are also obtained. The effects of several factors are graphically projected. The study shows that the material factors that are involved determine the operating variables. Coating thickness and separation point are controlled by Weissenberg’s number, therefore acting as a controlling parameter for the rate of flow, thickness in coating, power contribution, pressure, roll separating force, and separation point. In comparison to the existing results in the literature, the current results are broader and zero-order results are more accurate.

Applying Quasi-Linearization to the Problem of Steady Laminar Flow of a Second Grade Fluid Between Two Rotating Porous Disks

1984 ◽  
Vol 106 (4) ◽  
pp. 448-455 ◽  
Author(s):  
P. D. Verma ◽  
P. R. Sharma ◽  
P. D. Ariel
Keyword(s):  
Laminar Flow ◽  
Equations Of Motion ◽  
Elastic Parameter ◽  
Rotation Parameter ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Regular Perturbation ◽  
Injection Parameter ◽  
Grade Fluid ◽  
Steady Laminar

The problem of steady laminar flow of an incompressible second grade fluid between two rotating porous disks has been investigated. The equations of motion are solved by regular perturbation method for small suction/injection parameter and by the quasilinearization method for higher values of suction/injection parameter. The results from both the methods have been compared for both the Newtonian and Non-Newtonian fluids. The effects of suction/injection parameter, rotation parameter and visco-elastic parameter on the velocity components and skin friction have been discussed numerically and shown graphically.

scholarly journals Some Exact Solutions to Equations of Motion of an Incompressible Third Grade Fluid

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Saif Ullah
Keyword(s):  
Exact Solutions ◽  
Equations Of Motion ◽  
Third Grade ◽  
Solutions To Equations ◽  
Steady Flows ◽  
Third Grade Fluid ◽  
Complex Functions ◽  
Grade Fluid ◽  
Steady Plane ◽  
Transformation Methods

This investigation deals with some exact solutions of the equations governing the steady plane motions of an incompressible third grade fluid by using complex variables and complex functions. Some of the solutions admit, as particular cases, all the solutions of Moro et al. [1990, “Steady Flows of a Third Grade Fluid by Transformation Methods,” ZAMM, 70(3), pp. 189–198]

scholarly journals Mathematical Analysis of the Coating Process over a Porous Web Lubricated with Upper-Convected Maxwell Fluid

Coatings ◽  
2019 ◽  
Vol 9 (7) ◽  
pp. 458 ◽  
Author(s):  
Muhammad Zafar ◽  
Muhammad A. Rana ◽  
Muhammad Zahid ◽  
Babar Ahmad
Keyword(s):  
Equations Of Motion ◽  
Maxwell Fluid ◽  
Injection Rate ◽  
Lubrication Approximation ◽  
Roll Coating ◽  
Flow Parameters ◽  
Point Pressure ◽  
Coating Procedure ◽  
Roll Separating Force ◽  
Fluid Parameters

The present study offers mathematical calculations of the roll-coating procedure lubricated with an upper-convected Maxwell fluid. An incompressible isothermal viscoelastic fluid was considered, with both the roll and the porous web having uniform velocities. By using the lubrication approximation theory, the desired equations of motion for the fluid applied to the porous web were modelled and analyzed. The suction rate on the web and the injection rate at the roll surface were proportionately anticipated. Results for the velocity profile and pressure gradient were received analytically. Fluid parameters of industrial significance (i.e., detachment point, pressure, sheet/roll separating force, power contribution, and coating thickness) were also calculated numerically. A substantial and monotonic increase was witnessed in these quantities with the increase of flow parameters.

Numerical solution of hybrid method for third grade flow due to variable accelerated plate in a rotating frame

2018 ◽  
Vol 7 (2.15) ◽  
pp. 98 ◽  
Author(s):  
Shafaruniza Mahadi ◽  
Zainal Abdul Aziz ◽  
Yeak Su Hoe ◽  
Faisal Salah ◽  
Farah Suraya Md Nasrudin
Keyword(s):  
Finite Difference Method ◽  
Numerical Solution ◽  
Hybrid Method ◽  
Interpolation Method ◽  
Material Constant ◽  
Third Grade ◽  
Rotating Frame ◽  
Third Grade Fluid ◽  
Velocity Flow ◽  
Grade Fluid

The aim of this article is to obtain numerical solution for incompressible unsteady flow for third grade fluid induced by variable accelerated plate. Numerical solution is obtained by using Hybrid method which combine between finite difference method (FDM) and asymptotic interpolation method. The influence of difference values of material constant parameters on the velocity flow fluid are discussed and shown graphically. 

A theoretical analysis of roll-over-web coating assessment of viscous nanofluid containing Cu-water nanoparticles

2019 ◽  
Vol 36 (1) ◽  
pp. 55-75 ◽  
Author(s):  
Sabeeh Khaliq ◽  
Zaheer Abbas
Keyword(s):  
Pressure Gradient ◽  
Volume Fraction ◽  
Power Input ◽  
Lubrication Approximation ◽  
Nanoparticle Volume Fraction ◽  
Cu Nanoparticles ◽  
Roll Coating ◽  
Inverse Effect ◽  
Physical Quantities ◽  
The Web

The roll-coating analysis of viscous nanofluid using lubrication approximation theory over a flat porous sheet is investigated. We considered water-based copper ( Cu) nanoparticles to discuss the roll-coating analysis. The rate of fluid entering at the roll surface is assumed equal to the rate of fluid leaving on the web surface. The resulting differential equation developed under lubrication approximation and closed-form expressions is obtained for velocity and pressure gradient. The effects of entering velocity, Reynolds number, geometric parameter, and nanoparticle volume fraction with different models on physical quantities such as pressure, pressure gradient, velocity, force, power input are calculated. Some of these effects are presented graphically. It is noted that increasing nanoparticle volume fraction increases the pressure gradient, pressure distribution and has negligible effect on the velocity profile. Model II has a greater effect on pressure and pressure gradient than model I and has an inverse effect on force and power factor.

Couette - Poiseuille Two-Layer Flow of a Third Grade Fluid

2013 ◽  
Vol 390 ◽  
pp. 103-110
Author(s):  
Ali R. Ansari ◽  
Maya K. Mitkova ◽  
Abdul M. Siddiqui
Keyword(s):  
Nonlinear Differential Equations ◽  
Material Constant ◽  
Immiscible Fluids ◽  
Third Grade ◽  
Third Grade Fluid ◽  
The Third ◽  
Grade Fluid ◽  
Layer Flow ◽  
Grade Material ◽  
Different Thickness

The two-layer Couette-Poiseuille flow of a third grade fluid is examined. The problem is reduced to solving nonlinear differential equations governing the motion of the two immiscible fluids in case of different thickness of layers. The solutions are used to study the effect of the third grade material parameter on the velocity profiles. The investigation focuses especially on the location of the velocity maximum as function of the viscosity and third grade material constant.

Parallel Plate Flow of a Third-Grade Fluid and a Newtonian Fluid With Variable Viscosity

2016 ◽  
Vol 71 (7) ◽  
pp. 595-606
Author(s):  
Volkan Yıldız ◽  
Mehmet Pakdemirli ◽  
Yiğit Aksoy
Keyword(s):  
Newtonian Fluid ◽  
Parallel Plate ◽  
Numerical Solutions ◽  
Variable Viscosity ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Regular Perturbation ◽  
Approximate Analytical Solutions ◽  
Grade Fluid ◽  
Perturbation Solutions

AbstractSteady-state parallel plate flow of a third-grade fluid and a Newtonian fluid with temperature-dependent viscosity is considered. Approximate analytical solutions are constructed using the newly developed perturbation-iteration algorithms. Two different perturbation-iteration algorithms are used. The velocity and temperature profiles obtained by the iteration algorithms are contrasted with the numerical solutions as well as with the regular perturbation solutions. It is found that the perturbation-iteration solutions converge better to the numerical solutions than the regular perturbation solutions, in particular when the validity criteria of the regular perturbation solution are not satisfied. The new analytical approach produces promising results in solving complex fluid problems.

scholarly journals Mathematical Analysis of the Coating Process Over a Porous Web Lubricated with Upper Convected Maxwell Fluid

2019 ◽  
Author(s):  
Muhammad Zafar ◽  
Babar Ahmad ◽  
Muhammad Afzal Rana ◽  
Muhammad Zahid
Keyword(s):  
Equations Of Motion ◽  
Maxwell Fluid ◽  
Injection Rate ◽  
Lubrication Approximation ◽  
Roll Coating ◽  
Flow Parameters ◽  
Point Pressure ◽  
Coating Procedure ◽  
Roll Separating Force ◽  
Fluid Parameters

Present study offers mathematical calculations of the roll-coating procedure lubricated with upper Convected Maxwell Fluid. An incompressible isothermal viscoelastic fluid is considered with roll and the porous web having uniform velocities. By employing Lubrication Approximation Theory, the desired equations of motion for the fluid concerned over porous web are modelled and analyzed. The suction rate on the web and injection rate at the roll surface are anticipated proportionate. Results for velocity profile and pressure gradient are obtained analytically. Fluid parameters of industrial significance i.e. detachment point, pressure, sheet /roll separating force, power contribution and coating thickness are also calculated numerically. Substantial and monotonic increase is witnessed in these quantities with the increase of flow parameters.

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