Numerical analysis of the forward roll coating of a Rabinowitsch fluid

2019 ◽  
Vol 36 (2) ◽  
pp. 191-208 ◽  
Author(s):  
Zahid M ◽  
M Zafar ◽  
MA Rana ◽  
MTA Rana ◽  
MS Lodhi
Keyword(s):  
Pressure Distribution ◽  
Flow Rate ◽  
Coating Thickness ◽  
Equations Of Motion ◽  
Power Input ◽  
Roll Coating ◽  
Point Separation ◽  
Velocity Flow ◽  
Engineering Parameters ◽  
Separation Force

This paper analyses an isothermal roll coating for a Rabinowitsch fluid. Equations of motion are simplified using lubrication approximation theory. Analytical solutions of velocity, flow rate and pressure-gradient are calculated. Outcomes of coating thickness, pressure distribution, split position, stresses, forces, the power input to the roller and the temperature rise between the coating rollers and substrate are obtained. The effects of some involved parameters are displayed through graphs and tables. It is noted that the Rabinowitsch parameter is a controlling quantity for coating thickness, flow rate, separation point, separation force, pressure distribution, and power input. Moreover, an exponential and monotonic change in the above-mentioned engineering parameters is a function of the Rabinowitsch fluid parameter.

Mathematical analysis of a non-Newtonian polymer in the forward roll coating process

2020 ◽  
Vol 40 (8) ◽  
pp. 703-712 ◽  
Author(s):  
Muhammad Zahid ◽  
Muhammad Zafar ◽  
Muhammad A. Rana ◽  
Muhammad S. Lodhi ◽  
Abdul S. Awan ◽  
...  
Keyword(s):  
Pressure Distribution ◽  
Flow Rate ◽  
Coating Thickness ◽  
Power Input ◽  
Control Flow ◽  
Roll Coating ◽  
Material Parameters ◽  
Engineering Parameters ◽  
Profile Flow ◽  
Forward Roll Coating

AbstractThis article describes the development of a mathematical model of forward roll coating of a thin film of a non-Newtonian material when it passes through a small gap between the two counter-rotating rolls. The conservation equations of mass, momentum, and energy in the light of LAT (lubrication approximation theory) are non-dimensionalized and solutions for the velocity profile, flow rate, pressure distribution, pressure, forces, stresses, power input to the roller, and temperature distribution are calculated analytically. It is found that by changing (increasing/decreasing) the value of material parameters, one can really control the engineering parameters like, stress and the most important the coating thickness and is a quick reference for the engineer working in coating industries. Some results are shown graphically. From the present study, it has been established that the material parameter is a device to control flow rate, coating thickness, separation points, and pressure distribution.

scholarly journals Mathematical Analysis of Pseudoplastic Polymers during Reverse Roll-Coating

Polymers ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2285
Author(s):  
Fateh Ali ◽  
Yanren Hou ◽  
Muhammad Zahid ◽  
Muhammad Afzal Rana
Keyword(s):  
Pressure Distribution ◽  
Flow Rate ◽  
Perturbation Technique ◽  
Power Input ◽  
Weissenberg Number ◽  
Point Of View ◽  
Governing Equations ◽  
Velocity Flow ◽  
Separation Force ◽  
Physical Quantities

This article presents a mathematical model and theoretical analysis of coating of a thin film of non-Newtonian polymers as they travel through a small space between two reverse-rotating rolls. The dimensionless forms of the governing equations are simplified with the help of the lubrication approximation theory (LAT). By using the perturbation technique, the analytical solutions for velocity, flow rate and pressure gradient were obtained. From an engineering point of view, some significant results such as thickness of the coated web, pressure distribution, separation points, separation force and power input were computed numerically. The effect of velocities ratio k and Weissenberg number We on these physical quantities is presented graphically; others are shown in tabular form. It is noted that the involved material parameters provide a mechanism to control the flow rate, pressure distribution, the thickness of coating, separation force and power input. Moreover, the separation point is shifted toward the nip region by increasing velocities ratio k.

Roll coating analysis of a second-grade material

2017 ◽  
Vol 34 (3) ◽  
pp. 232-255 ◽  
Author(s):  
M Zahid ◽  
MA Rana ◽  
AM Siddiqui
Keyword(s):  
Coating Thickness ◽  
Fluid Model ◽  
Power Input ◽  
Control Flow ◽  
Second Grade ◽  
Adiabatic Temperature Rise ◽  
Roll Coating ◽  
Grade Fluid ◽  
Grade Material ◽  
Separation Force

In this study, the lubrication approximation theory is used to provide numerical results in roll coating over a moving flat porous web. The rate of injection at the roll surface is assumed equal to the rate of suction on the web. The second-grade fluid is used, which reduces with appropriate modifications to the Newtonian fluid model. Results are obtained in such quantities as coating thickness, split location, pressure distribution, stresses, forces, the power input to the roll, and adiabatic temperature rise between the coating roll and the coated web. Some of these results are shown graphically. It is found that material parameters β and Reynolds number are the parameters to control flow rate, coating thickness separation points, separation force, power input, and pressure.

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.

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

2021 ◽  
pp. 875608792110296
Author(s):  
Fateh Ali ◽  
Yanren Hou ◽  
Muhammad Zahid ◽  
MA Rana ◽  
Muhammad Usman
Keyword(s):  
Heat Transfer ◽  
Flow Rate ◽  
Coating Thickness ◽  
Gradient Flow ◽  
Power Input ◽  
Jeffrey Fluid ◽  
Governing Equations ◽  
Controlling Parameter ◽  
Separation Force ◽  
Velocity Pressure

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.

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.

Mathematical model of pressure distribution in a main pipeline during pumping with the use of drug reducing agents, taking into account their degradation

2021 ◽  
pp. 396-406
Author(s):  
Мурсалим Мухутдинович Гареев ◽  
Марат Иозифович Валиев ◽  
Филипп А. Карпов
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Pressure Distribution ◽  
Flow Rate ◽  
Pressure Head ◽  
Petroleum Products ◽  
Reducing Agents ◽  
Main Pipeline ◽  
Main Mode ◽  
Pipeline Pressure

Путевая деградация противотурбулентных присадок (ПТП) может стать причиной изменения основных параметров режима магистрального трубопровода - давления и расхода - относительно установившихся значений и осложнить контроль их отклонений от нормативных показателей. При этом до настоящего момента отсутствовала методика расчета режимов перекачки при использовании ПТП с учетом деградации. Авторами была поставлена цель по разработке методики для математического описания распределения давления в трубопроводе с учетом путевой деградации присадки, а также при различных концентрациях ПТП. Для достижения указанной цели предлагается дополнить уравнение баланса напоров с учетом эмпирической зависимости эффективности присадки от длины трубопровода. При расчетах давления в промежуточных точках трассы предлагается использовать данные опытно-промышленных испытаний по изменению эффективности ПТП. Для иллюстрации применения методики рассматриваются примеры перекачки нефти и нефтепродуктов с добавлением присадок в различных концентрациях. На основании экспериментальных данных получена адекватная математическая модель снижения эффективности ПТП по длине магистрального трубопровода для различных концентраций вводимой присадки. Path degradation of drug reducing agents (DRA) can cause changes in the main mode parameters of the main pipeline; pressure and flow rate, relative to the stable values, and complicate the adjustment of their deviations from the standard indicators. At the same time, up until now there has been no methodology for calculating pumping modes when using DRA that takes degradation into account. The authors set a goal to develop a methodology to mathematically describe the pressure distribution in the pipeline, taking into account the path degradation of the agent, as well as the parameters at different DRA concentrations. To achieve this goal, it is proposed to supplement the equation of the pressure head balance with the empirical dependency of agent efficiency on the length of the pipeline. When calculating the pressure at intermediate points of the route, it is proposed to use the pilot run data on the change in the DRA efficiency. To illustrate the application of the methodology, examples of pumping oil and petroleum products with added agents in various concentrations are discussed. On the basis of the experimental data, an adequate mathematical model of the DRA efficiency reduction along the length of the main pipeline for different concentrations of introduced agent was obtained.

scholarly journals Analysis of dynamics variation against thixotropic parameter’s preferential range

2018 ◽  
Vol 45 (2) ◽  
pp. 231-251
Author(s):  
Nazish Shahid
Keyword(s):  
Shear Stress ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Axial Velocity ◽  
Fluid Model ◽  
Current Model ◽  
Velocity Shear ◽  
Structural Parameter ◽  
Velocity Flow ◽  
Analysis Of Dynamics

Variation in the dynamics of a steady-state blood flow through a stenosed tapered artery has been investigated corresponding to changes in thixotropic parameter ? over the range [0,1]. To probe the role of parameter ? and differentiate the current model from other known non-Newtonian models, expressions of axial velocity, shear stress, wall shear stress and flow rate have been calculated depending upon this parameter and pressure gradient. Also, pressure gradient has been deduced uniquely with the help of the continuity equation. Our choice of calculating pressure gradient has led to obtaining shear stress such that its dependence on the structural parameter of our model, unlike most available results, motivates for further investigation. The simultaneous effects of varying yield stress and parameter ? on axial velocity, flow resistance and flow rate have been studied such that the differences between the Herschel?Bulkley fluid model and our current model can be pointed out. To validate the suitability of our model and some results in history, we have also obtained limiting results for particular values of ?.

scholarly journals Investigating the In-Flow Characteristics of Multi-Operation Conditions of Cross-Flow Fan in Air Conditioning Systems

Processes ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 959
Author(s):  
Weijie Zhang ◽  
Jianping Yuan ◽  
Qiaorui Si ◽  
Yanxia Fu
Keyword(s):  
Pressure Distribution ◽  
Flow Rate ◽  
Total Pressure ◽  
Air Conditioning ◽  
Pressure Pulsation ◽  
Flow Characteristics ◽  
Cross Flow ◽  
Operating Conditions ◽  
Aerodynamic Noise ◽  
Cross Flow Fan

Cross-flow fans are widely used in numerous applications such as low-pressure ventilation, household appliances, laser instruments, and air-conditioning equipment. Cross-flow fans have superior characteristics, including simple structure, small size, stable airflow, high dynamic pressure coefficient, and low noise. In the present study, numerical simulation and experimental research were carried out to study the unique secondary flow and eccentric vortex flow characteristics of the internal flow field in multi-operating conditions. To this end the vorticity and the circumferential pressure distribution in the air duct are obtained based on the performed experiments and the correlation between spectral characteristics of multiple operating conditions and the inflow state is established. The obtained results show that when the area of the airflow passage decreases while the area of the eccentric vortex area gradually increases, then the airflow of the cross-flow fan decreases, the outlet expands, and the flow pattern uniformity reduces. It was found that wakes form in the vicinity of the blade and the tail of the volute tongue, which generate pressure pulsation, and aerodynamic noise. The pressure distribution along the inner circumference shows that the total minimum pressure appears in the eccentric vortex near the volute tongue and the volute returns near the zone. Moreover, it was found that the total pressure near the eccentric vortex is significantly smaller than that of the main flow zone. As the flow rate decreases, the pressure pulsation amplitude of the eccentric vortex region significantly increases, while the static and total pressure pulsation amplitudes are gradually increased. Close to the eccentric vortex on the inner side of the blade in the volute tongue area, total pressure is low, total pressure on the outside of the blade is not affected, and pressure difference between the inner and outer sides is large. When the flow rate of the cross-flow fan is 0.4 Qd, there is no obvious peak at the harmonic frequency of the blade passage frequency. This shows that the aerodynamic noise is caused by the main unstable flow.

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