Calendering of non-isothermal Rabinowitsch fluid

2018 ◽  
Vol 38 (1) ◽  
pp. 83-92 ◽  
Author(s):  
Muhammad Sajid ◽  
Hira Siddique ◽  
Nasir Ali ◽  
Muhammad Asif Javed
Keyword(s):  
Temperature Distribution ◽  
Pressure Gradient ◽  
Energy Equation ◽  
Fluid Model ◽  
Sheet Thickness ◽  
Lubrication Approximation ◽  
Flow Equations ◽  
Hybrid Numerical Method ◽  
Isothermal Analysis ◽  
Roll Separating Force

Abstract: A non-isothermal analysis of calendering by using the Rabinowitsch fluid model is presented in this article. The flow equations are simplified by utilizing the lubrication approximation theory. The exact expressions of velocity and pressure gradient are obtained. The pressure distribution and engineering quantities are computed numerically by employing the Runge-Kutta algorithm. The temperature distribution is obtained by solving the energy equation numerically using the hybrid numerical method. The influence of the involved parameters on the velocity profile, pressure, pressure gradient and mechanical quantities such as roll-separating force, power function and exiting sheet thickness are shown graphically. The temperature distribution at various axial points is also shown through graphs.

Numerical analysis of the calendering process by using Giesekus fluid model

2019 ◽  
Vol 36 (2) ◽  
pp. 167-190 ◽  
Author(s):  
Muhammad Asif Javed ◽  
Nasir Ali ◽  
Sabeen Arshad
Keyword(s):  
Pressure Gradient ◽  
Power Function ◽  
Numerical Study ◽  
Fluid Model ◽  
Sheet Thickness ◽  
Deborah Number ◽  
Flow Equations ◽  
Giesekus Fluid ◽  
Engineering Parameters ◽  
Roll Separating Force

A numerical study of the calendering process is presented. The material to be calendered is modeled by using Giesekus constitutive equation. The flow equations are first presented in dimensionless forms and then simplified by incorporating the lubrication approximation theory. The resulting equations are analytically solved for the stream function. The pressure gradient, pressure, and other engineering parameters related to the calendering process, such as roll-separating force, power function, and entering sheet thickness, are numerically calculated by using Runge–Kutta algorithm. The influence of the Giesekus parameter and the Deborah number on the velocity profile, pressure gradient, pressure, power function, roll-separating force, and exiting sheet thickness are discussed in detail with the help of various graphs. The present analysis indicates that the pressure in the nip region decreases with increasing Giesekus parameter and Deborah number. The power function and the roll-separating force exhibit decreasing trends with increasing Deborah number. The exiting sheet thickness decreases up to a certain entering sheet thickness, as compared to the Newtonian case. Beyond this entering sheet thickness, the exiting sheet thickness increases with increasing entering sheet thickness.

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.

Analysis of the lubrication approximation theory in the calendering/sheeting process of upper convected Jeffery’s material

2020 ◽  
pp. 875608792096254
Author(s):  
M Zahid ◽  
NZ Khan ◽  
AM Siddiqui ◽  
S Iqbal ◽  
A Muhammad ◽  
...  
Keyword(s):  
Pressure Distribution ◽  
Flow Rate ◽  
Approximation Theory ◽  
Material Parameter ◽  
Sheet Thickness ◽  
Power Input ◽  
Lubrication Approximation ◽  
Flow Equations ◽  
Velocity Flow ◽  
Roll Separating Force

This paper analyses an isothermal calendering for an upper convected Jeffery’s Material. Lubrication Approximation Theory (LAT) is applied to simplify the flow equations. Analytical solutions of velocity, flow rate, and pressure gradient are carried out. Outcomes of sheet thickness, detachment point, roll separating force, power input to the roll, and pressure distribution are obtained. The effects of some involved parameters are displayed through graphs and tables. It is noted that the material parameter is a controlling device for sheet thickness, flow rate, detachment point, roll separating force, power input, and the pressure distribution. We observed that as the material parameter increases, the detachment point increases which results in increased sheet thickness.

Numerical study of non-isothermal analysis of exiting sheet thickness in the calendering of micropolar-Casson fluid

2021 ◽  
pp. 875608792110250
Author(s):  
Zaheer Abbas ◽  
Sabeeh Khaliq
Keyword(s):  
Temperature Distribution ◽  
Pressure Gradient ◽  
Power Function ◽  
Numerical Study ◽  
Sheet Thickness ◽  
Casson Fluid ◽  
Integration Technique ◽  
Finite Difference Approximations ◽  
Isothermal Analysis ◽  
Coupling Number

This theoretical analysis reports on the non-isothermal calendering process of micropolar-Casson fluid and studies the viscoplastic and microrotation effects by utilizing the lubrication approximation (LAT). Exact dimensionless velocity and pressure gradient solutions are achieved. Then a numerical integration technique determined other mechanical quantities. Implementing the finite difference approximations resolved the energy expression. Graphs show how material parameters influence the pressure, pressure gradient, leave-off distance, temperature distribution, force, and power function. Temperature distribution increases with increased coupling number N and decreased Casson parameter [Formula: see text]. Force and power function increase with increased coupling number and decreased Casson parameter. Both Casson and coupling number control the pressure distribution and exiting sheet thickness.

Blade coating analysis of viscous nanofluid having Cu–water nanoparticles using flexible blade coater

2020 ◽  
Vol 36 (4) ◽  
pp. 348-367 ◽  
Author(s):  
Marya Kanwal ◽  
Xinhua Wang ◽  
Hasan Shahzad ◽  
Yingchun Chen ◽  
Hui Chai
Keyword(s):  
Pressure Gradient ◽  
Shooting Method ◽  
Volume Fraction ◽  
Volumetric Flow Rate ◽  
Lubrication Approximation ◽  
Nanoparticle Volume Fraction ◽  
Porous Substrate ◽  
Flow Equations ◽  
The Impact ◽  
Blade Coating

This article presents the blade coating analysis of viscous nanofluid passing over a porous substrate using a flexible blade coater. Water-based copper nanoparticles are considered to discuss the blade coating process. The lubrication approximation theory is applied to develop the flow equations. The analytical solution is obtained for velocity, volumetric flow rate, and pressure gradient, while shooting method is applied to obtain the pressure, thickness, and load. Different models for dynamic viscosity have been applied to observe the impact of related parameters on pressure, pressure gradient, and velocity. These results are presented graphically. Interesting engineering quantities such as load, deflection, and thickness are computed numerically and are shown in the tabulated form. It is found that nanoparticle volume fraction increases the pressure gradient, pressure and has minor effects on velocity. For model 1, an increase in the volume fraction reduces the coating thickness, load, and deflection, while model 2 has opposite effects on the mentioned quantities. Also, model 2 has a greater impact on pressure and pressure gradient when compared to model 1.

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]

Calendering analysis of non-isothermal viscous nanofluid containing Cu-water nanoparticles using two co-rotating rolls

2020 ◽  
pp. 875608792095161
Author(s):  
Zaheer Abbas ◽  
Sabeeh Khaliq
Keyword(s):  
Temperature Distribution ◽  
Pressure Gradient ◽  
Dynamic Viscosity ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Power Input ◽  
Physical Parameters ◽  
Nanoparticle Volume Fraction ◽  
Flow Equations ◽  
The Impact

This study is a non-isothermal analysis of the calendering process using a water based nanofluid with Cu-nanoparticles. The basic flow equations are simplified under the lubrication approximation theory (LAT) and non-dimensionalized. Theoretical velocity and pressure gradient solutions are achieved, and temperature distribution is numerically computed by finite difference method. The impact of nanoparticle volume fraction on pressure distribution, fluid velocity, temperature distribution, power input, and separating force are presented through graphs and discussed. Nanoparticle volume fraction enhances the magnitude of pressure, pressure gradient, and temperature distribution. Power input and roll-separating force also rise for higher nanoparticle volume fraction. Model II of dynamic viscosity of nanofluid has a greater impact on physical parameters as compared to the model I of dynamic viscosity.

Roll-over-web coating analysis of micropolar-Casson fluid: a theoretical investigation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zaheer Abbas ◽  
Sabeeh Khaliq
Keyword(s):  
Pressure Gradient ◽  
Numerical Technique ◽  
Sheet Thickness ◽  
Pressure Profile ◽  
Power Input ◽  
Casson Fluid ◽  
Closed Form Solutions ◽  
Opposite Behavior ◽  
Roll Separating Force ◽  
Coupling Number

Abstract The theoretical model of micropolar-Casson fluid is studied in roll-coating over a moving substrate based on the lubrication theory. Closed-form solutions for the velocity, pressure gradient, and microrotation are attained, while a numerical technique employed to compute interesting engineering variables such as pressure, roll-separating force, separating point, and power input. The influence of involved parameters on the physical and engineering quantities are displayed via graphs and table. The coupling number (N) and viscoplastic parameter (β) provide the controlling mechanism for the exit sheet thickness, separating force, and power input. Also, the pressure gradient and pressure profile in the nip region enhances for large values of coupling number (N) whereas the viscoplastic parameter (β) gives the opposite behavior.

A Complete Solution for Thermal-Elastohydrodynamic Lubrication of Line Contacts Using Circular Non-Newtonian Fluid Model

1992 ◽  
Vol 114 (3) ◽  
pp. 540-551 ◽  
Author(s):  
Hsing-Sen S. Hsiao ◽  
Bernard J. Hamrock
Keyword(s):  
Boundary Conditions ◽  
Newtonian Fluid ◽  
Energy Equation ◽  
Control Volume ◽  
Fluid Model ◽  
Complete Solution ◽  
Circular Model ◽  
Line Contacts ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A complete solution is obtained for elastohydrodynamically lubricated conjunctions in line contacts considering the effects of temperature and the non-Newtonian characteristics of lubricants with limiting shear strength. The complete fast approach is used to solve the thermal Reynolds equation by using the complete circular non-Newtonian fluid model and considering both velocity and stress boundary conditions. The reason and the occasion to incorporate stress boundary conditions for the circular model are discussed. A conservative form of the energy equation is developed by using the finite control volume approach. Analytical solutions for solid surface temperatures that consider two-dimensional heat flow within the solids are used. A straightforward finite difference method, successive over-relaxation by lines, is employed to solve the energy equation. Results of thermal effects on film shape, pressure profile, streamlines, and friction coefficient are presented.

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