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.

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 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.

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.

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.

scholarly journals Asymptotic Behavior of a Viscoelastic Fluid in a Closed Loop Thermosyphon: Physical Derivation, Asymptotic Analysis, and Numerical Experiments

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Justine Yasappan ◽  
Ángela Jiménez-Casas ◽  
Mario Castro
Keyword(s):  
Asymptotic Behavior ◽  
Viscoelastic Fluid ◽  
Closed Loop ◽  
Theoretical Study ◽  
Equations Of Motion ◽  
Asymptotic Properties ◽  
Inertial Manifold ◽  
Thermal Gradients ◽  
External Temperature ◽  
First Time

Fluids subject to thermal gradients produce complex behaviors that arise from the competition with gravitational effects. Although such sort of systems have been widely studied in the literature for simple (Newtonian) fluids, the behavior of viscoelastic fluids has not been explored thus far. We present a theoretical study of the dynamics of a Maxwell viscoelastic fluid in a closed-loop thermosyphon. This sort of fluid presents elastic-like behavior and memory effects. We study the asymptotic properties of the fluid inside the thermosyphon and the exact equations of motion in the inertial manifold that characterizes the asymptotic behavior. We derive, for the first time, the mathematical derivations of the motion of a viscoelastic fluid in the interior of a closed-loop thermosyphon under the effects of natural convection and a given external temperature gradient.

Dynamic Analysis of the Rotating Composite Thin-Walled Cantilever Beams with Shear Deformation

2013 ◽  
Vol 690-693 ◽  
pp. 309-313
Author(s):  
Yong Sheng Ren ◽  
Qi Yi Dai
Keyword(s):  
Shear Deformation ◽  
Cross Section ◽  
Fiber Orientation ◽  
Model Comparison ◽  
Natural Frequencies ◽  
Theoretical Study ◽  
Equations Of Motion ◽  
Cantilever Beams ◽  
The Finite Element Method ◽  
Rotating Speed

This paper presents a theoretical study of the dynamic characteristics of rotating composite cantilever beams. Considering shear deformation and cross section warping, the equations of motion of the rotating cantilever beams are derived using Hamilton’s principle. The Galerkin’s method is used in order to analysis the free vibration behaviors of the model. Comparison of the theoretical solutions has been made with the results obtained from the finite element method, which prove the validity of the model presented in this paper. Natural frequencies are obtained for circular tubular composite beams. The effects of fiber orientation, rotating speed and structure parameters on modal frequencies are investigated.

scholarly journals Inertia and Couple-Stress Effects in a Curvilinear Thrust Hydrostatic Bearing

2017 ◽  
Vol 22 (3) ◽  
pp. 759-767 ◽  
Author(s):  
A. Walicka ◽  
P. Jurczak ◽  
J. Falicki
Keyword(s):  
Couple Stress ◽  
Equations Of Motion ◽  
Inertia Effects ◽  
Numerical Examples ◽  
Thrust Bearings ◽  
Hydrostatic Bearing ◽  
Stress Effects ◽  
Pressure Distributions ◽  
Radial Thrust ◽  
Inertia Forces

AbstractThe flow of a couple-stress lubricant in a clearance of a curvilinear thrust hydrostatic bearing with impermeable walls is considered. The flow in the bearing clearance is considered with inertia forces. The equations of motion are solved by an averaged inertia method. As a result, the formulae for pressure distributions without and with inertia effects were obtained. Radial thrust bearings and spherical bearings are discussed as numerical examples. It is shown that inertia effects influence the bearing performance considerably.

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