The effect of air shear on the development of a thin conducting fluid film on a rough rotating disk has been analysed. A uniform magnetic field acts parallel to the axis of the rough rotating disk. The numerical solution of the governing equations of motion using the initial and boundary conditions have been obtained by a finite difference method. The effect of air shear on the temporal evolution of the free surface of the fluid and on the retention of the liquid lubricant has been analysed. © WILEY-VCH Verlag Berlin GmbH.

Usha R

Department of Mathematics

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The Role of Induced Air Shear on the Development of a Conducting Fluid Film over a Rough Spinning Disk in the Presence of a Transverse Magnetic Field

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

A theoretical analysis of the effects of a magnetic field on the dynamics of a thin nonuniform conducting film of an incompressible viscous fluid on a rotating disk has been considered. A nonlinear evolution equation describing the shape of the film interface has been derived as a function of space and time and has been solved numerically. The temporal evolution of the free surface of the fluid and the rate of retention of the liquid film on the spinning disk have been obtained for different values of Hartmann number M, evaporative mass flux parameter E, and Reynolds number Re. The results show that the relative volume of the fluid retained on the spinning disk is enhanced by the presence of the magnetic field. The stability characteristics of the evolution equation have been examined using linear theory. For both zero and nonzero values of the nondimensional parameter describing the magnetic field, the results show that (a) the infinitesimal disturbances decay for small wave numbers and are transiently stable for larger wave numbers when there is either no mass transfer or there is evaporation from the film surface, and although the magnitude of the disturbance amplitude is larger when the magnetic field is present, it decays to zero earlier than for the case when the magnetic field is absent, and (b) when absorption is present at the film surface, the film exhibits three different domains of stability: disturbances of small wave numbers decay, disturbances of intermediate wave numbers grow transiently, and those of large wave numbers grow exponentially. The range of stable wave numbers increases with increase in Hartmann number. © 2009 by ASME.

Journal of Applied Mechanics, Transactions ASME

A thin conducting liquid film on a spinning disk in the presence of a magnetic field: Dynamics and stability

A numerical solution is obtained for the development of a conducting fluid film on the surface of a spinning disc, in the presence of a magnetic field applied perpendicular to the disc. A finite-difference method is employed to obtain the solution of Navier-Stokes equations modified to include magnetic forces due to MHD interactions. The combined effects of film inertia, acceleration of the disc and magnetic forces are analysed. The numerical results reveal that the rate of thinning of the fluid film is strongly influenced by the inertial and magnetic forces when the Reynolds number is large and that the existing asymptotic theory by Ray and Dandapat [24] is inadequate for predicting transient film thickness. When the disc has a finite acceleration at the start-up, the magnetic and inertia effects are important even at low Reynolds numbers and the thinning rate is reduced. It is observed that for both low and high Reynolds number flows, the film thickness increases with Hartmann number M for a fixed time and the rate of depletion is less for large M than for small M.

Acta Mechanica

Spinning of a liquid film from a rotating disc in the presence of a magnetic field - A numerical solution

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Mammalian Mitochondrial ncRNA Database

Die Lineale Ausdehnungslehre ein neuer Zweig der Mathematik

Psychological Science

Books Received October 2000-February 2001

Journal of Physics D: Applied Physics

Spin coating in the presence of a transverse magnetic field and non-uniform rotation: a numerical study

The role of induced air shear on the development of a conducting fluid film over a rough spinning disk in the presence of a transverse magnetic field

Journal	ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
ISSN	00442267
Open Access	No