Specific shear-dependent viscoelastic third-grade fluid model

This paper numerically solves the third-order fluid flow during calendering with slip condition at the rolls. The basic equations are transformed into dimensionless forms and simplified by adopting LAT (Lubrication Approximation Theory). The flow equations are then solved with the perturbation technique. Whereas a finite difference scheme along with TDMA (Tridiagonal Matrix Algorithm) is implemented to solve the energy equation. Engineering parameters like power input, exit distance, and roll separating force are computed. The impact of slip parameter [Formula: see text] and material parameter [Formula: see text] on the velocity profile, pressure, pressure gradient, temperature profile, power input, detachment point, and roll separating force is portrayed through graphs and discussed. It is noticed that both the parameters [Formula: see text] and [Formula: see text] exhibit opposite behaviors and give insight to the mechanisms that control the physical and engineering parameters.

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“…Using these approximations into equations ( 30), (32), (34), and ( 35) and looking at b 0 and b 1 , we get the sub-problems as follows.…”

Section: Perturbation Analysismentioning

confidence: 99%

Analysis of calendering process of non-isothermal flow of non-Newtonian fluid: A perturbative and numerical study

Khaliq

Abbas

2021

Journal of Plastic Film & Sheeting

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“…While polymer suspensions exhibit viscoelastic properties, a single model does not easily represent their stress-deformation relationship. We are using a constitutive model for thirdgrade fluid in this analysis as defined by Carapau et al [14]. A higher-order differential equation is produced by the constitutive equation describing the relationship between the shear stress and the strain rate of a non-Newtonian fluid than in the classic Navier-Stokes equation.…”

Section: Introductionmentioning

confidence: 99%

A Theoretical Study of Reverse Roll Coating for a Non-Isothermal Third-Grade Fluid under Lubrication Approximation Theory

Ali

Zahid

Hou

et al. 2022

Mathematical Problems in Engineering

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The flow of non-Newtonian fluids is extremely important in a variety of industrial applications and processes, including painting, printing, and coating. The goal of this paper is to develop a mathematical model for an incompressible, non-isothermal third-grade fluid as it travels through a minor gap between two heated rolls that are revolving in the opposite direction. Using appropriate dimensionless parameters, the dimensionless version of the governing equations is constructed. To simplify the nondimensional form of the governing equations, the LAT (lubrication approximation theory) is applied. It is mentioned that the perturbation approach should be used. It is a very important tool in modern mathematical physics and practical fluid mechanics, and it is used a lot. Through perturbation techniques, exact solutions for velocity distribution, flow rate, temperature distribution, and pressure gradient are offered. To observe the flow pattern, streamlines are also drawn. Numerical outcomes of some substantial engineering quantities like flow rate, roll separation force, power input, and pressure distribution are found. Some outcomes are displayed graphically although others are presented in tabular form. We have observed that the third-grade parameters give a way to control velocity, pressure gradients, flow rate, and coating thickness. Further, increasing the velocities ratio values lowers the coating thickness on the web. Furthermore, the Brickman number has a significant influence on the temperature profile and has increased with the increase in the Brickman number. Both the model and the numerical calculations are in agreement with the viscous fluid model that is already present in the literature.

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“…Some readings about research work in coating efficaciously indulge the non-linear work and their comparisons in leading TGF [8][9][10][11][12][13][14][15][16][17][18]. Sullivan et al [12] premeditated the coating depth in surface coating size/width of TGF by implementing lubrication estimates with numerical and investigational outcomes for NNF.…”

Section: Introductionmentioning

confidence: 99%

“…Hwang [15] and Dien et al [16] also premeditated NNF in the blade thin film and projected estimated stream studies, Maxwellian flow model in surface protection layer, and studied the fragile viscoelastic performance. This investigation articulates the statement that viscoelastic characteristics of TGF may affect pressure [17,18] so they espoused LAT and associated the modelling and investigational outcomes.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Thin Layer Formation of Third-Grade Fluid

et al. 2019

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In present learning, surface protection layer progression of a third-grade fluid (TGF) is examined. Fluid transport within the micro passage made by the firm bladehas beenpresented. Main system of equations of fluidity have been narrated and streamlined by means of lubrication approximation theory (LAT). Here, approximate solutions of velocity, pressure gradient, and coating depth have been presented. Results of coating and layer forming have been tabulated and discussed as well. It is observed that the transport properties of third-order fluid delivers an instrument to regulate flow velocity, pressure, and affect the final coated region.

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Specific shear-dependent viscoelastic third-grade fluid model

Cited by 4 publications

References 7 publications

Analysis of calendering process of non-isothermal flow of non-Newtonian fluid: A perturbative and numerical study

Analysis of calendering process of non-isothermal flow of non-Newtonian fluid: A perturbative and numerical study

A Theoretical Study of Reverse Roll Coating for a Non-Isothermal Third-Grade Fluid under Lubrication Approximation Theory

Analysis of a Thin Layer Formation of Third-Grade Fluid

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