Mathematical Analysis of Roll Coating Process by Using Couple Stress Fluid

2019 ◽  
Vol 8 (8) ◽  
pp. 1683-1691 ◽  
Author(s):  
M. Zafar ◽  
M.A. Rana ◽  
M. Zahid ◽  
M.A. Malik ◽  
M.S. Lodhi
Keyword(s):  
Coating Thickness ◽  
Couple Stress ◽  
Flow Parameter ◽  
Couple Stress Fluid ◽  
Lubrication Approximation ◽  
Isothermal Model ◽  
Roll Coating ◽  
Flow Equations ◽  
Pressure Profiles ◽  
Controlling Parameter

In this article, an incompressible isothermal model of a couple stress fluid between two rotating rolls is developed. Lubrication approximation theory is applied to simplify the flow equations. Exact solutions for velocity and pressure profiles are derived. Parameters of an industrial interest like pressure, separating force, coating thickness, detachment point and power transmitted by the rolls to the fluid are computed numerically. It is observed that the flow parameter is a controlling parameter for an exiting coating thickness. As the problem is symmetric, only one half of the geometry is considered.

scholarly journals Investigation of blood flow through an artery in the presence of overlapping stenosis

2017 ◽  
Vol 14 (1) ◽  
pp. 39-46 ◽  
Author(s):  
K. Maruthi Prasad ◽  
S. Thulluri ◽  
M. V. Phanikumari
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Pressure Drop ◽  
Wall Shear Stress ◽  
Couple Stress ◽  
Flow Characteristics ◽  
Couple Stress Fluid ◽  
Flow Equations ◽  
Wall Shear ◽  
Fluid Parameters

The effects of an overlapping stenosis on blood flow characteristics in an artery have been studied. Blood has been represented by a couple stress fluid. The flow equations have been linearised and the expressions for pressure drop, resistance to the flow and wall shear stress have been derived. The results are shown graphically. It is observed that the resistance to the flow, pressure drop and wall shear stress increases with height and length of the stenosis. And it is noticed that the resistance to the flow and pressure drop decreases with couple stress fluid parameters. But wall shear stress increases with couple stress fluid parameters.

scholarly journals Study of Slip Effects in Reverse Roll Coating Process Using Non-Isothermal Couple Stress Fluid

Coatings ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 1249
Author(s):  
Hasan Shahzad ◽  
Xinhua Wang ◽  
Muhammad Bilal Hafeez ◽  
Zahir Shah ◽  
Ahmed Mohammed Alshehri
Keyword(s):  
Pressure Gradient ◽  
Flow Rate ◽  
Couple Stress ◽  
Velocity Ratio ◽  
Closed Form Solution ◽  
Couple Stress Fluid ◽  
Slip Parameter ◽  
Roll Coating ◽  
Stress Parameter ◽  
The Impact

The non-isothermal couple stress fluid inside a reverse roll coating geometry is considered. The slip condition is considered at the surfaces of the rolls. To develop the flow equations, the mathematical modelling is performed using conservation of momentum, mass, and energy. The LAT (lubrication approximation theory) is employed to simplify the equations. The closed form solution for velocity, temperature, and pressure gradient is obtained. While the pressure and flow rate are obtained numerically. The impact of involved parameters on important physical quantities such as temperature, pressure, and pressure gradient are elaborated through graphs and in tabular form. The pressure and pressure gradient decreases for variation of the couple stress parameter and velocity ratio parameter K. While the variation of the slip parameter increases the pressure and pressure gradient inside the flow geometry. Additionally, flow rate decreases for the variation of the slip parameter as fluid starts moving rapidly along the roller surface. The most important physical quantity which is responsible for maintaining the quality of the coating and thickness is flow rate. For variation of both the couple stress parameter and the slip parameter, the flow rate decreases compared to the Newtonian case, consequently the coating thickness decreases for the variation of the discussed parameter.

Non-isothermal analysis of calendering using couple stress fluid

2017 ◽  
Vol 34 (4) ◽  
pp. 358-381 ◽  
Author(s):  
Nasir Ali ◽  
Muhammad Asif Javed ◽  
Hafiz Muhammad Atif
Keyword(s):  
Pressure Gradient ◽  
Couple Stress ◽  
Sheet Thickness ◽  
Power Input ◽  
Momentum Equation ◽  
Exact Expression ◽  
Couple Stress Fluid ◽  
Flow Equations ◽  
Stress Effects ◽  
Order Of Magnitude

The non-isothermal flow inside a calender is modeled and analyzed for a couple stress fluid. The governing flow equations are developed using conservation laws of mass, momentum and energy. An order of magnitude analysis is performed and leading terms in momentum and energy equations are retained. The reduced momentum equation is solved to obtain the exact expression for velocity and pressure gradient. The reduced energy equation is solved numerically using a hybrid numerical method. The significant effects of the involved parameters on the pressure, pressure gradient velocity profile, roll-separating force, power input, exiting sheet thickness and temperature are examined through various plots. The pressure inside the calender significantly increases with increased couple stress effects. For larger couple stress parameters, the power function and roll-separating function show steady state behavior. The two maxima are distinctly observed in temperature distribution near the roll surfaces for small couple stress effects [Formula: see text]. In contrast, the temperature achieves maximum at center for strong couple stress effects [Formula: see text]

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.

Chemically reactive species of time-dependent natural convection couple stress fluid flow past an isothermal vertical flat plate

2019 ◽  
Vol 97 (2) ◽  
pp. 166-175 ◽  
Author(s):  
Hussain Basha ◽  
G. Janardhana Reddy ◽  
M. Gnaneswara Reddy
Keyword(s):  
Fluid Flow ◽  
Flat Plate ◽  
Chemical Reaction ◽  
Couple Stress ◽  
Skin Friction Coefficient ◽  
Couple Stress Fluid ◽  
Physical Parameters ◽  
Flow Equations ◽  
Flow Past ◽  
Vertical Flat Plate

The transient two-dimensional natural convective couple stress fluid flow past a semi-infinite vertical flat plate in the presence of first-order homogenous chemical reaction is investigated. The analysis has been carried out by considering the effects of skin-friction coefficient and Nusselt and Sherwood numbers. The unsteady coupled nonlinear governing flow equations have been solved by applying the Crank–Nicolson implicit finite difference scheme. For the different set physical parameters, graphs are shown and examined. A relevant study with existing results is made in a limiting sense. The transient and steady-state velocity profiles decrease as the chemical reaction parameter, Schmidt number, and couple stress parameter increase. The deviations of concentration, temperature, and velocity contours of the couple stress fluid flow are considerably varied in comparison with the Newtonian fluid flow.

STABILITY OF COUPLE STRESS FLUID FLOW THROUGH A HORIZONTAL POROUS LAYER

2016 ◽  
Vol 19 (5) ◽  
pp. 391-404 ◽  
Author(s):  
B. M. Shankar ◽  
I. S. Shivakumara ◽  
Chiu-On Ng
Keyword(s):  
Fluid Flow ◽  
Porous Layer ◽  
Couple Stress ◽  
Couple Stress Fluid ◽  
Flow Through
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