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

Zafar, Muhammad; Rana, M. A.; Zahid, Muhammad; Ahmad, Babar

doi:10.3390/coatings9070458

Cited by 13 publications

(12 citation statements)

References 10 publications

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“…On the other hand, the reverse trend of temperature is found in the second solution. It is worth to notice that all plots (2)(3)(4)(5)(6)(7)(8) satisfy asymptotically the far-field boundary conditions for both solutions which show the validity of the shooting methods and generated numerical results. The variation of Eckert number on the non-dimensional fluid temperature profiles is revealed in Figure 8, indicating that both temperature and thickness of thermal boundary layer increase in the first solution.…”

Section: Resultsmentioning

confidence: 59%

“…It is not possible that one fluid model keeps all characteristics of the non-Newtonian fluid. Therefore, researchers introduced many non-Newtonian models such as model of Casson [3,4], Micropolar [5,6], Maxwell [7,8]; Jeffrey [9,10]; Burgers [11,12], etc. The micropolar model was introduced by Eringen in 1966 [13] in which he added the microrotation effect in the equation of Navier Stokes as the equation of Navier Stokes fails to interpret the behavior of such fluids.…”

Section: Introductionmentioning

confidence: 99%

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Effect of Viscous Dissipation in Heat Transfer of MHD Flow of Micropolar Fluid Partial Slip Conditions: Dual Solutions and Stability Analysis

et al. 2019

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In this study, first-order slip effect with viscous dissipation and thermal radiation in micropolar fluid on a linear shrinking sheet is considered. Mathematical formulations of the governing equations of the problem have been derived by employing the fundamental laws of conservations which then converted into highly non-linear coupled partial differential equations (PDEs) of boundary layers. Linear transformations are employed to change PDEs into non-dimensional ordinary differential equations (ODEs). The solutions of the resultant ODEs have been obtained by using of numerical method which is presented in the form of shootlib package in MAPLE 2018. The results reveal that there is more than one solution depending upon the values of suction and material parameters. The ranges of dual solutions are S ≥ S c i , i = 0 , 1 , 2 and no solution is S < S c i where S c i is the critical values of S . Critical values have been obtained in the presence of dual solutions and the stability analysis is carried out to identify more stable solutions. Variations of numerous parameters have been also examined by giving tables and graphs. The numerical values have been obtained for the skin friction and local Nusselt number and presented graphically. Further, it is observed that the temperature and thickness of the thermal boundary layer increase when thermal radiation parameter is increased in both solutions. In addition, it is also noticed that the fluid velocity increases in the case of strong magnetic field effect in the second solution.

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Section: Resultsmentioning

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Effect of Viscous Dissipation in Heat Transfer of MHD Flow of Micropolar Fluid Partial Slip Conditions: Dual Solutions and Stability Analysis

et al. 2019

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“…ey manipulated the Herschel-Bulkley model of viscoplasticity, thereby reducing it to the Newtonian models under suitable modifications, Bingham, and power-law. Recently, Zahid et al [20,21] undertook the same situation with the viscoelastic fluid being incompressible in which the roll, as well as web, was assumed to move with the same rates. To simplify expressions for motion, they performed the above-mentioned theory.…”

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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“…The forward roll coating was of vital significance amongst these and was the commonly discussed. Experimental investigation has been conducted on this by many scientists, whereas the theoretical research have been offered by Benkreira et al, 7 Greener and Middleman et at., 8 Zafar et al, 9 Zahid et al…”

Section: Introductionmentioning

confidence: 99%

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

Cited by 13 publications

References 10 publications

Effect of Viscous Dissipation in Heat Transfer of MHD Flow of Micropolar Fluid Partial Slip Conditions: Dual Solutions and Stability Analysis

Effect of Viscous Dissipation in Heat Transfer of MHD Flow of Micropolar Fluid Partial Slip Conditions: Dual Solutions and Stability Analysis

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

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

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