A theoretical analysis of roll-over-web coating assessment of viscous nanofluid containing Cu-water nanoparticles

2019 ◽  
Vol 36 (1) ◽  
pp. 55-75 ◽  
Author(s):  
Sabeeh Khaliq ◽  
Zaheer Abbas
Keyword(s):  
Pressure Gradient ◽  
Volume Fraction ◽  
Power Input ◽  
Lubrication Approximation ◽  
Nanoparticle Volume Fraction ◽  
Cu Nanoparticles ◽  
Roll Coating ◽  
Inverse Effect ◽  
Physical Quantities ◽  
The Web

The roll-coating analysis of viscous nanofluid using lubrication approximation theory over a flat porous sheet is investigated. We considered water-based copper ( Cu) nanoparticles to discuss the roll-coating analysis. The rate of fluid entering at the roll surface is assumed equal to the rate of fluid leaving on the web surface. The resulting differential equation developed under lubrication approximation and closed-form expressions is obtained for velocity and pressure gradient. The effects of entering velocity, Reynolds number, geometric parameter, and nanoparticle volume fraction with different models on physical quantities such as pressure, pressure gradient, velocity, force, power input are calculated. Some of these effects are presented graphically. It is noted that increasing nanoparticle volume fraction increases the pressure gradient, pressure distribution and has negligible effect on the velocity profile. Model II has a greater effect on pressure and pressure gradient than model I and has an inverse effect on force and power factor.

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.

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.

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.

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.

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.

Numerical analysis of blade coating of a third-order fluid

2018 ◽  
Vol 35 (2) ◽  
pp. 157-180 ◽  
Author(s):  
Saira Bhatti ◽  
Muhammad Zahid ◽  
Muhammad Afzal Rana ◽  
Abdul Majeed Siddiqui ◽  
Hafiz Abdul Wahab
Keyword(s):  
Pressure Gradient ◽  
Coating Thickness ◽  
Equations Of Motion ◽  
Power Input ◽  
Narrow Channel ◽  
Governing Equations ◽  
Third Order ◽  
Velocity Pressure ◽  
Blade Coating ◽  
The Web

In this study, the blade coating process of a third-order fluid has been investigated. Flow between the narrow channel formed by the rigid blade and the web is generated due to the web motion and the constant pressure gradient. The governing equations of motion are simplified using lubrication approximation theory. We obtained analytical solutions for velocity field, pressure distribution, pressure gradient and coating thickness using perturbation method. How the model’s dimensionless parameters affect velocity, pressure gradient, pressure and coating thickness are presented graphically and in tabulated form. We found that the third-order parameter provides a mechanism to control velocity, pressure, power input and the final coating thickness.

Theoretical analysis of roll-over-web coating of a micropolar fluid under lubrication approximation theory

2018 ◽  
Vol 34 (4) ◽  
pp. 418-438 ◽  
Author(s):  
Hafiz M Atif ◽  
Nasir Ali ◽  
Muhammad A Javed ◽  
Fazal Abbas
Keyword(s):  
Pressure Gradient ◽  
Micropolar Fluid ◽  
Power Input ◽  
Separation Point ◽  
Leibniz Rule ◽  
Lubrication Approximation ◽  
Newton’S Iterative Method ◽  
Runge Kutta Method ◽  
Load Carrying ◽  
Velocity Pressure

The theoretical model of roll coating onto a moving sheet is developed based on micropolar fluid constitutive equations and lubrication approximation. Closed form expressions for velocity, microrotation and pressure gradient are obtained. Runge-Kutta method is used to calculate the engineering quantities of interest such as, pressure, roll-separating (load-carrying) force and power input. The separation point is numerically calculated using Newton’s iterative method together with generalized Leibniz rule. The effects of involved parameters on the pressure gradient, velocity, pressure and other mechanical quantities are displayed through various graphs. Extreme pressure is observed in the nip region for larger coupling numbers and microrotation parameters. This leads to increased load-carrying force and power input for micropolar fluid when compared to a Newtonian fluid. Moreover, the separation point decreases from its Newtonian value with increasing [Formula: see text]

Ciliary Flow of Casson Nanofluid with the Influence of MHD having Carbon Nanotubes

2020 ◽  
Vol 16 ◽  
Author(s):  
Adel Alblawi ◽  
Saba Keyani ◽  
S. Nadeem ◽  
Alibek Issakhov ◽  
Ibrahim M. Alarifi
Keyword(s):  
Carbon Nanotubes ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Pressure Rise ◽  
Shear Stresses ◽  
Left Wall ◽  
Coupled Equations ◽  
The Right

Objective: In this paper, we consider a model that describes the ciliary beating in the form of metachronal waves along with the effects of Magnetohydrodynamic fluid over a curved channel with slip effects. This work aims at evaluating the effect of Magnetohydrodynamic (MHD) on the steady two dimensional (2-D) mixed convection flow induced in carbon nanotubes. The work is done for both the single wall nanotube and multiple wall nanotube. The right wall and the left wall possess a metachronal wave that is travelling along the outer boundary of the channel. Methods: The wavelength is considered as very large for cilia induced MHD flow. The governing linear coupled equations are simplified by considering the approximations of long wavelength and small Reynolds number. Exact solutions are obtained for temperature and velocity profile. The analytical expressions for the pressure gradient and wall shear stresses are obtained. Term for pressure rise is obtained by applying Numerical integration method. Results: Numerical results of velocity profile are mentioned in a table form, for various values of solid volume fraction, curvature, Hartmann number [M] and Casson fluid parameter [ζ]. Final section of this paper is devoted to discussing the graphical results of temperature, pressure gradient, pressure rise, shear stresses and stream functions. Conclusion: Velocity profile near the right wall of the channel decreases when we add nanoparticles into our base fluid, whereas an opposite behaviour is depicted near the left wall due to ciliated tips whereas the temperature is an increasing function of B and ߛ and decreasing function of ߶.

scholarly journals Marangoni convection in layers of water-based nanofluids under the effect of rotation

2021 ◽  
Vol 19 (1) ◽  
pp. 1029-1046
Author(s):  
Abeer H. Bakhsh ◽  
Abdullah A. Abdullah
Keyword(s):  
Marangoni Convection ◽  
Volume Fraction ◽  
Steady State Solution ◽  
Horizontal Layer ◽  
Brownian Diffusion ◽  
Nanoparticle Volume Fraction ◽  
Rigid Surface ◽  
Fixed Temperature ◽  
Modified Model ◽  
Conservation Condition

Abstract A linear stability analysis is performed for the onset of Marangoni convection in a horizontal layer of a nanofluid heated from below and affected by rotation. The top boundary of the layer is assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition while the bottom boundary is assumed to be a rigid surface with fixed temperature. The motion of the nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. A modification model is used in which the effects of Brownian diffusion and thermophoresis are taken into consideration by new expressions in the nanoparticle mass flux. Also, material properties of the nanofluid are modelled by non-constant constitutive expressions depending on nanoparticle volume fraction. The steady-state solution is shown to be well approximated by an exponential distribution of the nanoparticle volume fraction. The Chebyshev-Tau method is used to obtain the critical thermal and nanoparticle Marangoni numbers. Different stability boundaries are obtained using the modified model and the rotation.

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