Mathematical Analysis of Pseudoplastic Polymers during Reverse Roll-Coating

Ali, Fateh; Hou, Yanren; Zahid, Muhammad; Rana, M. A.

doi:10.3390/polym12102285

Cited by 19 publications

(11 citation statements)

References 24 publications

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“…The solution of equation 17 ð Þ by utilizing the boundary conditions defined in equation 19 ð Þ becomes…”

Section: Mathematical Resultsmentioning

confidence: 99%

“…where dp dx is defined in equation 23 ð Þ. Solving equation 27 ð Þ subject to boundary conditions in equation 19 ð Þ, we get where…”

Section: Temperature Distributionmentioning

confidence: 99%

“…Analytical expressions for velocity profile, flow rate and pressure gradient have been demonstrated. Williamson fluid was studied by Ali et al 19 and some engineering parameters, such as coating thickness, power input, separation points, pressure distribution and roll separation force were discussed.…”

Section: Introductionmentioning

confidence: 99%

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Influence of magnetohydrodynamics and heat transfer on the reverse roll coating of a Jeffrey fluid: A theoretical study

Ali¹,

Hou²,

Zahid³

et al. 2021

Journal of Plastic Film & Sheeting

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The purpose of this article is to provide a mathematical model of magnetohydrodynamic (MHD) non-isothermal flow of an incompressible Jeffrey fluid as it goes through a minimal gap between the two counter rotating rolls. The dimensionless forms of governing equations are obtained by using appropriate dimensionless parameters. The LAT (lubrication approximation theory) is utilized to simplify the dimensionless form of governing equations. Analytical solutions for the velocity, pressure gradient, flow rate, Nusselt number and temperature distribution are presented. How the Jeffrey parameters, MHD and velocities ratio influence on the flow patterns and heat transfer rate are explored. Outcomes of some significant engineering quantities such as flow rate, power input, pressure distribution and roll separation force are obtained numerically in tabular form and some are displayed graphically. We found that the MHD parameter served as a controlling parameter for different engineering quantities like velocity, temperature, flow rate, and coating thickness. Moreover, the coating thickness on the web decreases by increasing the values of velocities ratio.

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“…The solution of equation 17 ð Þ by utilizing the boundary conditions defined in equation 19 ð Þ becomes…”

Section: Mathematical Resultsmentioning

confidence: 99%

“…where dp dx is defined in equation 23 ð Þ. Solving equation 27 ð Þ subject to boundary conditions in equation 19 ð Þ, we get where…”

Section: Temperature Distributionmentioning

confidence: 99%

See 1 more Smart Citation

Influence of magnetohydrodynamics and heat transfer on the reverse roll coating of a Jeffrey fluid: A theoretical study

Ali¹,

Hou²,

Zahid³

et al. 2021

Journal of Plastic Film & Sheeting

Self Cite

View full text Add to dashboard Cite

show abstract

“…The results reveal the strong efficiency of the velocities ratio and viscoplastic parameter for pressure and velocity. The theoretical investigation of pseudoplastic polymer was carried out by Ali et al [42] by considering reverse roll coating. They used LAT for simplification of flow equations and obtained the required results through perturbation technique.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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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.

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“…Studies of pseudoplastic fluids have gained excessive attention for their utmost utility in industrial processes like extruding of polymer films, melts, and solutions with high molecular weight polymers and films coated with emulsion such as photographic films. Due to the pseudoplastic nature of Williamson fluid [10][11][12], its model is being focused on. However, less consideration has been paid to the Williamson fluid model, which describes the properties of pseudoplastic fluids.…”

Section: Introductionmentioning

confidence: 99%

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

Zahid

Siddique

Saleem

et al. 2021

Mathematical Problems in Engineering

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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.

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Mathematical Analysis of Pseudoplastic Polymers during Reverse Roll-Coating

Cited by 19 publications

References 24 publications

Influence of magnetohydrodynamics and heat transfer on the reverse roll coating of a Jeffrey fluid: A theoretical study

Influence of magnetohydrodynamics and heat transfer on the reverse roll coating of a Jeffrey fluid: A theoretical study

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

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

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