R. Usha

Bio: R. Usha is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Reynolds number & Instability. The author has an hindex of 17, co-authored 85 publications receiving 1061 citations. Previous affiliations of R. Usha include University of Hyderabad & Anna University.

Stability characteristics of suspension flow through wavy-walled channels

Abstract: A numerical study of the linear temporal stability characteristics of particulate suspension flow through a converging-diverging symmetric wavy-walled channel is considered. The basic flow is a superposition of plane channel flow of particulate suspension and periodic flow components arising due to the small amplitude sinusoidal waviness of the channel walls. The disturbance equations are derived within the framework of Floquet theory and solved using the spectral collocation method. The effects of small amplitude sinusoidal waviness of the channel walls and those of the presence of particles on the initial growth of the disturbances are examined. Two-dimensional stability calculations for particulate suspensions indicate the presence of fast growing unstable modes that arise due to the waviness of the walls. Neutral stability calculations are performed in the disturbances wavenumber-Reynolds number (αs−Re) plane, for the wavy channel with representative values of wavenumber (λ) and the wall amplitude to semi-channel height ratio (∈w) for different values of volume fraction density of the particles (C). It is observed that the critical Reynolds number for transition decreases with increase of ∈w and C. However, the flow can be modulated by suitable wall excitation which in turn can stabilize the flow.

A Thin Conducting Liquid Film on a Spinning Disk in the Presence of a Magnetic Field: Dynamics and Stability

Abstract: 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

A Similar Flow Between Two Rotating Disks in the Presence of a Magnetic Field

Abstract: A similarity solution is obtained for a flow between two rotating parallel disks which, at time t * are spaced a distance H (1 − αt *)1/2 apart and a magnetic field proportional to B0 (1 − αt *)−1/2 is applied perpendicular to the disks. Approximate analytic solutions are given and a numerical solution to the resulting nonlinear ordinary differential equations is presented. The effects of magnetic forces on the velocity profiles, the normal forces and the torques which the fluid exerts on the disks are studied. It is observed that by increasing the magnetic force a considerable increase in the load can be achieved. Also, the torques are more sensitive to changes in the squeeze Reynolds number than to changes in the rotation Reynolds number.

Dynamics and stability of thin liquid films

Abstract: The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows down a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics, and biophysics; these include nanofluidics and microfluidics, coating flows, intensive processing, lava flows, dynamics of continental ice sheets, tear-film rupture, and surfactant replacement therapy. These flows have attracted considerable attention in the literature, which have resulted in many significant developments in experimental, analytical, and numerical research in this area. These include advances in understanding dewetting, thermocapillary- and surfactant-driven films, falling films and films flowing over structured, compliant, and rapidly rotating substrates, and evaporating films as well as those manipulated via use of electric fields to produce nanoscale patterns. These developments are reviewed in this paper and open problems and exciting research avenues in this thriving area of fluid mechanics are also highlighted.

Viscous flow due to a shrinking sheet

Abstract: The viscous flow induced by a shrinking sheet is studied. Existence and (non)uniqueness are proved. Exact solutions, both numerical and in closed form, are found.

Principles Of Enhanced Heat Transfer

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