The unsteady thin conducting liquid film of non-uniform thickness on a rotating disk which is cooled axisymmetrically from below has been analysed numerically by solving the evolution equation of the free surface. Transient film profiles for different initial liquid film distributions have been obtained. The results reveal that the thinning process and film planarisation are markedly influenced by the heat dissipating or cooling parameter β, Prandtl number σ and Reynolds number Re. © 2002 Elsevier Science Ltd. All rights reserved.

Usha R

Department of Mathematics

Conductive films

Cooling

Heat losses

Reynolds number

Rotating disks

SPIN COATING

Thin films

CONDUCTING LIQUID FILMS

FLUID DYNAMICS

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IIT Madras

Analysis of cooling of a conducting fluid film of non-uniform thickness on a rotating disk

International Journal of Non-Linear Mechanics

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 theoretical analysis of the thermal effects on the dynamics of a thin nonuniform film of a nonvolatile incompressible viscous fluid on a heated rotating disk has been considered and the effects of temperature-dependent viscosity and surface tension have been analyzed. A nonlinear evolution equation describing the shape of the film interface has been derived as a function of space and time and its stability characteristics have been examined using linear theory. It has been observed that the infinitesimal disturbances decay for small wave numbers and are transiently stable for large wave numbers, for both zero and nonzero values of Biot number. © 2005 American Institute of Physics.

Fulltext

Physics of Fluids

Dynamics and stability of a thin liquid film on a heated rotating disk film with variable viscosity

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

The development of a flow of a viscous conducting fluid over a rough spinning disk in the presence of a transverse magnetic field has been analysed for different patterns of surface roughness of the disk and different initial distributions of the height of the liquid lubricant. The numerical solution of the governing equation of motion subject to initial and boundary conditions has been obtained by a finite-difference method. The temporal evolution of the free surface of the fluid and the rate of retention of the liquid lubricant on the spinning disk have been obtained for different values of the two parameters M, the Hartmann number and Nratio, the ratio of the surface tension effect to the centrifugation effect. In the absence of the magnetic field, the results have been observed to agree with those of [6]. It has been observed that the effect of surface roughness is to enhance the relative volume of the fluid retained on the spinning disk and this is further enhanced by the presence of the magnetic field.

Zeitschrift fur Angewandte Mathematik und Physik

Flow of thin liquid film over a rough rotating disk in the presence of a transverse magnetic field

The development of a heat conducting fluid film on a rotating disk has been analyzed numerically under the planar interface assumption and the film thickness, the flow characteristics, the temperature distribution and the rate of heat transfer are determined. The range of validity of the time scales and Reynolds number bounds have been presented for the existing asymptotic solution for film cooling on a rotating disk. The effects of the Reynolds number Re, cooling parameter β and the Prandtl number σ on the variation of film thickness, and temperature distribution have been examined.

Journal	International Journal of Non-Linear Mechanics
ISSN	00207462
Open Access	No