scholarly journals Mathematical modelling for flexible blade coater with magnetohydrodynamic and slip effects in blade coating process

2019 ◽  
Vol 36 (1) ◽  
pp. 38-54 ◽  
Author(s):  
X Wang ◽  
H Shahzad ◽  
Y Chen ◽  
M Kanwal ◽  
Z Ullah
Keyword(s):  
Magnetic Field ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Volumetric Flow Rate ◽  
Maximum Pressure ◽  
Coating Process ◽  
Shooting Technique ◽  
Slip Effects ◽  
Thickness Parameter ◽  
Blade Coating

A new mathematical model for a flexible blade coater is proposed and analysed for slip and magnetohydrodynamic (MHD) effects in blade coating process. The slip is considered at the blade surface and magnetic field is imposed normal to the flow. To obtain the velocity profile, pressure, pressure gradient, volumetric flow rate and maximum pressure both exact and numerical solutions are utilized. In order to obtain the numerical solution shooting technique is applied. The interesting physical quantities like load and deflection are calculated and presented in graphical and tabulated form. The influence of the Hartman number the slip parameter and normalized coating thickness parameter on the flow and deflection are discussed graphically. In the presence of magnetic field and slip the fluid velocity and hence blade deflection can be controlled.

scholarly journals Mathematical modeling of slip and magnetohydrodynamics effects in blade coating

2018 ◽  
Vol 35 (1) ◽  
pp. 9-21 ◽  
Author(s):  
M Sajid ◽  
H Shahzad ◽  
M Mughees ◽  
N Ali
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Shooting Method ◽  
Hartmann Number ◽  
Volumetric Flow Rate ◽  
Maximum Pressure ◽  
Slip Parameter ◽  
Slip Effects ◽  
Blade Coating ◽  
The Web

A mathematical analysis for magnetohydrodynamics and slip effects is presented for blade coating onto a moving sheet of viscous fluid. An applied magnetic field is imposed normal to the flow and slip is considered at the web surface. The shooting method is applied to obtain the numerical solution of governing differential equations. Both numerical and exact solutions are utilized to describe the velocity profile, volumetric flow rate, pressure gradient, pressure and maximum pressure. How slip parameter and the Hartmann number influences properties is discussed through the graphical results. It is calculated that the presence of slip and applied magnetic field controls the sheet velocity in the blade coating process.

scholarly journals Effect of variable viscosity on laminar convection flow of an electrically conducting fluid in uniform magnetic field

2002 ◽  
pp. 49-62 ◽  
Author(s):  
S. Chakraborty ◽  
A.K. Borkakati
Keyword(s):  
Magnetic Field ◽  
Flat Plate ◽  
Uniform Magnetic Field ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Conducting Fluid ◽  
Fluid Viscosity ◽  
Electrically Conducting ◽  
Viscosity Parameter ◽  
Electrically Conducting Fluid

The flow of a viscous incompressible electrically conducting fluid on a continuous moving flat plate in presence of uniform transverse magnetic field, is studied. The flat plate which is continuously moving in its own plane with a constant speed is considered to be isothermally heated. Assuming the fluid viscosity as an inverse linear function of temperature, the nature of fluid velocity and temperature in presence of uniform magnetic field are shown for changing viscosity parameter at different layers of the medium. Numerical solutions are obtained by using Runge-Kutta and Shooting method. The coefficient of skin friction and the rate of heat transfer are calculated at different viscosity parameter and Prandt l number. .

scholarly journals Effect of magnetic field on Newtonian fluid sandwiched between non-Newtonian fluids through porous cylindrical shells

2021 ◽  
Author(s):  
Deepak Kumar Maurya ◽  
Satya Deo
Keyword(s):  
Magnetic Field ◽  
Newtonian Fluid ◽  
Flow Rate ◽  
Hartmann Number ◽  
Viscosity Ratio ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Volumetric Flow Rate ◽  
Shear Stresses ◽  
Micropolar Fluids

Abstract The present work deals with the influence of magnetic field on Newtonian fluid sandwiched between two porous cylindrical pipes which are filled with micropolar fluids. Fluid motion is occurring along z*-axis and applied magnetic field is taken in the direction perpendicular to the direction of fluid motion. On applying appropriate boundary conditions, velocity profiles, microrotations, flow rate and shear stresses are obtained for the corresponding fluid regions. The graphs for volumetric flow rate and fluid velocity are plotted and discussed for different values of micropolar parameter, couple stress parameter, porosity, viscosity ratio parameter, Hartmann number, conductivity ratio parameters and Darcy numbers.MSC (2020): 76A05, 76S05, 76W05, 35Q35

Entropy Analysis of MHD Variable Thermal Conductivity Fluid Flow Past a Convectively Heated Stretching Cylinder

2018 ◽  
Vol 387 ◽  
pp. 244-259 ◽  
Author(s):  
Sanatan Das ◽  
Subhajit Chakraborty ◽  
Oluwole Daniel Makinde ◽  
Rabindra Nath Jana
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Entropy Generation ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Convective Heating ◽  
Bejan Number ◽  
Stretching Cylinder ◽  
Entropy Analysis ◽  
Entropy Generation Number

The present study is related to entropy analysis during magnetohydrodynamic (MHD) boundary layer flow of a viscous incompressible electrically conducting fluid past a stretching cylinder with convective heating in the presence of a transverse magnetic field. The governing boundary layer equations in cylindrical form are simplified by means of appropriate similarity transformations. Numerical solutions with high precision are obtained using Runge-Kutta fourth order scheme with eminent shooting technique. The effects of the pertinent parameters on the fluid velocity, temperature, entropy generation number, Bejan number as well as the shear stress at the surface of the cylinder are discussed graphically and quantitatively. It is examined that due to the presence of magnetic field, entropy generation can be controlled and reduced. Bejan number is plotted to present a comparative analysis of entropy generation due to heat transfer and fluid friction. It is found that Bejan number is an increasing function of Biot number.

Non-isothermal blade coating analysis of viscous fluid with temperature-dependent viscosity using lubrication approximation theory

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sabeeh Khaliq ◽  
Zaheer Abbas
Keyword(s):  
Temperature Distribution ◽  
Viscous Fluid ◽  
Coating Thickness ◽  
Maximum Pressure ◽  
Coating Process ◽  
Lubrication Approximation ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity ◽  
Blade Coating

Abstract Blade coating process is studied in a nonisothermal analysis of viscous fluid with temperature-dependent viscosity by employing both plane and exponential coaters. The governing expressions are nondimensionalized and simplified under the assumption of lubrication approximation theory. Then, perturbative technique is used to find the solution for velocity, pressure, temperature distribution, and coating thickness. The influence of dimensionless parameter ε, Graetz number Gz, and normalized coating thickness γ on the velocity, maximum pressure, temperature distribution, and pressure gradient is portrayed through graphs, whereas load and coating thickness variations reported in a tabular manner. It is found that maximum pressure, coating thickness, and blade load decreases for temperature variations in viscosity, which leads to improved efficiency of blade coating process and life of the moving substrate.

Numerical Study of Unsteady Jeffery Fluid Flow With Magnetic Field Effect and Variable Fluid Properties

2016 ◽  
Vol 8 (4) ◽  
Author(s):  
Fazle Mabood ◽  
Reda G. Abdel-Rahman ◽  
Giulio Lorenzini
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Variable Viscosity ◽  
Numerical Study ◽  
Magnetic Field Effect ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Shooting Technique ◽  
Fluid Properties

A mathematical model has been constructed for determining the effects of variable viscosity and thermal conductivity on unsteady Jeffery flow over a stretching sheet in the presence of magnetic field and heat generation. The governing partial differential equations are transformed into a set of nonlinear coupled ordinary differential equations and then solved numerically by using the Runge–Kutta–Fehlberg method with shooting technique. A critical analysis with earlier published papers is done and the results are found to be in accordance with each other. Numerical solutions are then obtained and investigated in detail for different physical parameters such as skin-friction coefficient and reduced Nusselt number as well as other parametric values such as the velocity and temperature.

Mathematical modeling of Johnson-Segalman fluid in blade coating process

2021 ◽  
pp. 875608792098355
Author(s):  
Marya Kanwal ◽  
Xinhua Wang ◽  
Hasan Shahzad ◽  
Muhammad Sajid ◽  
Cheng Yiqi
Keyword(s):  
Work Load ◽  
Weissenberg Number ◽  
Coating Process ◽  
Lubrication Approximation ◽  
Shooting Technique ◽  
Flow Equations ◽  
Reduced Equations ◽  
Velocity Pressure ◽  
Blade Coating ◽  
Parameter Influence

This article deals with the blade coating process for Johnson-Segalman (JS) fluid using plane coater. Flow equations are simplified with the Lubrication approximation theory (LAT). The equations are normalized using suitable scales. Reduced equations are solved numerically using the shooting technique. Also, for small Weissenberg numbers, a perturbation solution is obtained. How Weissenberg number and slip parameter influence the pressure gradient, velocity, pressure, load, and thickness are expressed graphically and via table. In the present work, load on the blade is crucial as it controls the thickness quality. One observes that an increased Weissenberg number decreases load, while the coating thickness increases when compared to the viscous case.

On steady compressible flows with compact vorticity; the compressible Hill's spherical vortex

1998 ◽  
Vol 374 ◽  
pp. 285-303 ◽  
Author(s):  
D. W. MOORE ◽  
D. I. PULLIN
Keyword(s):  
Finite Difference ◽  
Compressible Flows ◽  
Numerical Solutions ◽  
Flow Direction ◽  
Fluid Velocity ◽  
Major Axis ◽  
Sonic Point ◽  
Euler Flow ◽  
Compressible Euler ◽  
Spherical Vortex

We consider steady compressible Euler flow corresponding to the compressible analogue of the well-known incompressible Hill's spherical vortex (HSV). We first derive appropriate compressible Euler equations for steady homentropic flow and show how these may be used to define a continuation of the HSV to finite Mach number M∞=U∞/C∞, where U∞, C∞ are the fluid velocity and speed of sound at infinity respectively. This is referred to as the compressible Hill's spherical vortex (CHSV). It corresponds to axisymmetric compressible Euler flow in which, within a vortical bubble, the azimuthal vorticity divided by the product of the density and the distance to the axis remains constant along streamlines, with irrotational flow outside the bubble. The equations are first solved numerically using a fourth-order finite-difference method, and then using a Rayleigh–Janzen expansion in powers of M2∞ to order M4∞. When M∞>0, the vortical bubble is no longer spherical and its detailed shape must be determined by matching conditions consisting of continuity of the fluid velocity at the bubble boundary. For subsonic compressible flow the bubble boundary takes an approximately prolate spheroidal shape with major axis aligned along the flow direction. There is good agreement between the perturbation solution and Richardson extrapolation of the finite difference solutions for the bubble boundary shape up to M∞ equal to 0.5. The numerical solutions indicate that the flow first becomes locally sonic near or at the bubble centre when M∞≈0.598 and a singularity appears to form at the sonic point. We were unable to find shock-free steady CHSVs containing regions of locally supersonic flow and their existence for the present continuation of the HSV remains an open question.

Electrohydrodynamic rotation of drops at large electric Reynolds numbers

2016 ◽  
Vol 788 ◽  
Author(s):  
Ehud Yariv ◽  
Itzchak Frankel
Keyword(s):  
Electric Fields ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Reynolds Numbers ◽  
Mirror Image ◽  
Liquid Drops ◽  
Weakly Conducting ◽  
Strong Electric Fields ◽  
Quincke Rotation ◽  
Asymmetric Solution

When subject to sufficiently strong electric fields, particles and drops suspended in a weakly conducting liquid exhibit spontaneous rotary motion. This so-called Quincke rotation is a fascinating example of nonlinear symmetry-breaking phenomena. To illuminate the rotation of liquid drops we here analyse the asymptotic limit of large electric Reynolds numbers, $\mathit{Re}\gg 1$, within the framework of a two-dimensional Taylor–Melcher electrohydrodynamic model. A non-trivial dominant balance in this singular limit results in both the fluid velocity and surface-charge density scaling as $\mathit{Re}^{-1/2}$. The flow is governed by a self-contained nonlinear boundary-value problem that does not admit a continuous fore–aft symmetric solution, thus necessitating drop rotation. Furthermore, thermodynamic arguments reveal that a fore–aft asymmetric solution exists only when charge relaxation within the suspending liquid is faster than that in the drop. The flow problem possesses both mirror-image (with respect to the direction of the external field) and flow-reversal symmetries; it is transformed into a universal one, independent of the ratios of electric conductivities and dielectric permittivities in the respective drop phase and suspending liquid phase. The rescaled angular velocity is found to depend weakly upon the viscosity ratio. The corresponding numerical solutions of the exact equations indeed collapse at large $\mathit{Re}$ upon the asymptotically calculated universal solution.

A shallow-liquid theory in magnetohydrodynamics

1960 ◽  
Vol 7 (1) ◽  
pp. 81-107 ◽  
Author(s):  
L. E. Fraenkel
Keyword(s):  
Magnetic Field ◽  
Mechanical Energy ◽  
Fluid Velocity ◽  
Linear Equations ◽  
Qualitative Difference ◽  
Meridional Plane ◽  
Plane Flow ◽  
Non Linear ◽  
Moderate Magnetic Field ◽  
Approximate Equations

The non-linear and linear ‘shallow-water’ theories, which describe long gravity waves on the free surface of an inviscid liquid, are extended to the case of an electrically conducting liquid on a horizontal bottom, in the presence of a vertical magnetic field. The dish holding the liquid, and the medium outside it, are assumed to be non-conducting. The approximate equations are based on a small ratio of depth to wavelength, on the properties of mercury, and on a moderate magnetic field strength. These equations have a ‘magneto-hydraulic’ character, for in the shallow liquid layer the horizontal fluid velocity and current density are independent of the vertical co-ordinate.Some explicit solutions of the linear equations are obtained for plane flows and for axi-symmetric flows in which the velocity vector lies in a vertical, meridional plane. The amplitudes of waves in a dish, and the amplitudes behind wave fronts progressing into undisturbed liquid, are found to be exponentially damped, the mechanical energy associated with a disturbance being dissipated by Joule heating.The approximate non-linear equations for plane flow are studied by means of characteristic variables, and it appears that, because of the magnetic damping effect, there is less qualitative difference between solutions of the non-linear and linear approximate equations at large times than is the case when the magnetic field is absent. In particular, the characteristic curves depart only a finite distance from their ‘undisturbed positions’.

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