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.

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 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.

A comparative study of heat transfer analysis of fractional Maxwell fluid by using Caputo and Caputo–Fabrizio derivatives

2020 ◽  
Vol 98 (1) ◽  
pp. 89-101 ◽  
Author(s):  
Nauman Raza ◽  
Muhammad Asad Ullah
Keyword(s):  
Exact Solutions ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Maxwell Fluid ◽  
Heat Transfer Analysis ◽  
Flow Parameters ◽  
Fluid Parameter ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Temperature And Velocity Fields

A comparative analysis is carried out to study the unsteady flow of a Maxwell fluid in the presence of Newtonian heating near a vertical flat plate. The fractional derivatives presented by Caputo and Caputo–Fabrizio are applied to make a physical model for a Maxwell fluid. Exact solutions of the non-dimensional temperature and velocity fields for Caputo and Caputo–Fabrizio time-fractional derivatives are determined via the Laplace transform technique. Numerical solutions of partial differential equations are obtained by employing Tzou’s and Stehfest’s algorithms to compare the results of both models. Exact solutions with integer-order derivative (fractional parameter α = 1) are also obtained for both temperature and velocity distributions as a special case. A graphical illustration is made to discuss the effect of Prandtl number Pr and time t on the temperature field. Similarly, the effects of Maxwell fluid parameter λ and other flow parameters on the velocity field are presented graphically, as well as in tabular form.

scholarly journals A New Numerical Solution of Maxwell Fluid over a Shrinking Sheet in the Region of a Stagnation Point

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
S. S. Motsa ◽  
Y. Khan ◽  
S. Shateyi
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Nonlinear Partial Differential Equations ◽  
Maxwell Fluid ◽  
Shrinking Sheet ◽  
Two Dimensional ◽  
Similarity Transformations ◽  
The Mathematical Model ◽  
Successive Linearisation Method ◽  
Fluid Parameters

The mathematical model for the incompressible two-dimensional stagnation flow of a Maxwell fluid towards a shrinking sheet is proposed. The developed equations are used to discuss the problem of being two dimensional in the region of stagnation point over a shrinking sheet. The nonlinear partial differential equations are transformed to ordinary differential equations by first-taking boundary-layer approximations into account and then using the similarity transformations. The obtained equations are then solved by using a successive linearisation method. The influence of the pertinent fluid parameters on the velocity is discussed through the help of graphs.

A theoretical analysis of the calendering of Ellis fluid

2016 ◽  
Vol 33 (2) ◽  
pp. 207-226 ◽  
Author(s):  
Muhammad Asif Javed ◽  
Nasir Ali ◽  
Muhammad Sajid
Keyword(s):  
Theoretical Analysis ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Pressure Distribution ◽  
Sheet Thickness ◽  
Power Input ◽  
Lubrication Approximation ◽  
Material Parameters ◽  
Operating Variables ◽  
Roll Separating Force

We present a theoretical analysis of calendering of Ellis fluid based on lubrication approximation. The equations governing the flow are nondimensionalized and solved to get closed form expressions of velocity and pressure gradient. Runge–Kutta algorithm is employed to compute the pressure distribution. The operating variables which are used in the calendering process, i.e. roll-separating force, power input to the rolls and exiting sheet thickness are calculated. The influence of the material parameters on the velocity profile, pressure gradient, pressure distribution and operating variables is shown graphically and discussed in detail.

scholarly journals Phase Behavior Analysis of CO2 and Formation Oil System

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Lei Tang ◽  
Tongyao Zhang ◽  
Baogang Li ◽  
Lu Zhang ◽  
Dong Han
Keyword(s):  
Molecular Weight ◽  
Liquid Phase ◽  
Expansion Coefficient ◽  
Volume Expansion ◽  
Average Molecular Weight ◽  
Injection Rate ◽  
Co2 Injection ◽  
Bubble Point Pressure ◽  
Volume Expansion Coefficient ◽  
Point Pressure

In this paper, there are nine oil samples to explore the characteristics of formation oil at different CO2 injection rate, and the characteristics include bubble point pressure, volume expansion coefficient, viscosity, density, and average molecular weight, composition of gas and liquid phase, and asphalt sediment. According to the experimental results of early nine oil samples of swelling tests, in high temperature and high pressure conditions, characteristics and changing rules of properties of formation oil, including bubble point pressure, volume expansion coefficient, viscosity, density, and average molecular weight, composition of gas and liquid phase, and asphalt sediment, were evaluated and analyzed at different CO2 injection rate systematically. The research not only can provide guides for petroleum engineers when they need to adjust the injection and production programs, but also can provide comparatively comprehensive experimental rules for researches on enhanced oil recovery (EOR) mechanisms of gas miscible and nonmiscible flooding. Moreover, phase parameters of different formation oil system can be extracted for reservoir numerical simulation.

18.—The Isotropic Turbulent Dynamics of a Maxwell Fluid

1975 ◽  
Vol 72 (3) ◽  
pp. 225-237 ◽  
Author(s):  
W. D. McComb
Keyword(s):  
Time Domain ◽  
Isotropic Turbulence ◽  
Equations Of Motion ◽  
Maxwell Fluid ◽  
Turbulent Energy ◽  
Decay Rates ◽  
Normal Direction ◽  
Constitutive Relationship ◽  
Newtonian Case ◽  
Key Factor

SynopsisUsing the constitutive relationship for a Maxwell body, as an example of a viscoelastic fluid, the equations of motion are derived in the Fourier wavenumber-time domain, and specialised to the case of isotropic turbulence. It is shown that, for grid-generated turbulence, the model predicts increased spectral intensity levels, reduced decay rates and steepening of the spectrum in wavenumber, relative to the Newtonian case. These forms of behaviour have been observed in dilute solutions of drag reducing polymers. The key factor in this is found to be the presence of an ‘elastic’ non-linear term in the equations of motion: this term reverses the normal direction of turbulent energy transfer in wavenumber.

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.

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