Nonaxisymmetric unsteady motion over a rotating disk in the presence of free convection and magnetic field

The nonaxisymmetric unsteady motion produced by a buoyancy-induced cross-flow of an electrically conducting fluid over an infinite rotating disk in a vertical plane and in the presence of an applied magnetic field normal to the disk has been studied. Both constant wall and constant heat flux conditions have been considered. It has been found that if the angular velocity of the disk and the applied magnetic field squared vary inversely as a linear function of time (i.e. as (1??t*)?1, the governing Navier-Stokes equation and the energy equation admit a locally self-similar solution. The resulting set of ordinary differential equations has been solved using a shooting method with a generalized Newton's correction procedure for guessed boundary conditions. It is observed that in a certain region near the disk the buoyancy induced cross-flow dominates the primary von Karman flow. The shear stresses induced by the cross-flow are found to be more than these of the primary flow and they increase with magnetic parameter or the parameter ? characterizing the unsteadiness. The velocity profiles in the x- and y-directions for the primary flow at any two values of the unsteady parameter ? cross each other towards the edge of the boundary layer. The heat transfer increases with the Prandtl number but reduces with the magnetic parameter.

Transient Flow of a Compressible Viscous Fluid Near an Infinite Disk

We have consider ed the transient motion of art electrically conducting viscous compressible fluid which is in contact with an insulated infinite disk. The initial motion is considered to be due to the uniform rotation of the disk in an otherwise stationary fluid or due to the uniform rigid rotation of the fluid over a stationary disk. Different cases of transient motion due to finite impulse imparted either to the disk or to the distant fluid have been investigated. Effects of the imposed axial magnetic field and the disk temperature on the transient flow are included. The nonlinear partial differential equations governing the motion are solved numerically using an implicit finite-difference scheme along with the Newton's linearisation technique.

Conjugate MHD flow past a flat plate

A boundary layer solution for the conjugate forced convection flow of an electrically conducting fluid over a semi-infinite flat plate in the presence of a transverse magnetic field is presented. The governing nonsimilar partial differential equations are solved numerically using the Keller box method. Values of the temperature profiles of the plate are obtained for various values of the parameters entering the problem and are given in a table and shown on graphs.

Basis set dependence of the molecular electrostatic potential topography. A case study of substituted benzenes

The basis set dependence of the topographical structure of the molecular electrostatic potential (MESP), as well as the effect of substituents on the MESP distribution, has been investigated with substituted benzenes as test cases. The molecules are studied at HF-SCF 3�21G and 6�31G** levels, with a further MESP topographical investigation at the 3�21G, double-zeta, 6�31G*, 6�31G**, double-zeta polarized and triple-zeta polarized levels. The MESP critical points for a 3�21G optimized/6�31G** basis are similar to the corresponding 6�31G** optimized/6�31G** ones. More generally, the qualitative features of the MESP topography computed at the polarized level are independent of the level at which optimization is carried out. For a proper representation of oxygen lone pairs, however, optimization using a polarized basis set is required. The nature of the substituent drastically changes the MESP distribution over the phenyl ring. The values and positions of MESP minima indicate the most active site for electrophilic attack. This point is strengthened by a study of disubstituted benzenes.

Quantitation of spermatogenesis by DNA flow cytometry: Comparative study among six species of mammals

Suspensions of testicular germ cells from six species of mammals were prepared and stained for the DNA content with a fluorochrome (ethidium bromide) adopting a common technique and subjected to DNA flow cytometry. While uniform staining of the germ cells of the mouse, hamster, rat and monkey could be obtained by treating with 0.5% pepsin for 60 min followed by staining with ethidium bromide for 30 min, that of the guinea pig and rabbit required for optimal staining pepsinization for 90 min and treatment with ethidium bromide for 60 min. The procedure adopted here provided a uniform recovery of over 80% of germ cells with each one of the species tested and the cell population distributed itself according to the DNA content (expressed as C values) into 5 major classes-spermatogonia (2C), cells in S-phase, primary spermatocytes (4C), round spermatids (1C), and elongating/elongated spermatids (HC). Comparison of the DNA distribution pattern of the germ cell populations between species revealed little variation in the relative quantities of cells with 2C (8-11%), S-phase (6-9%), and 4C (6-9%) amount of DNA. Though the spermatid cell populations exhibited variations (1C:31-46%, HCI:7-20% and and HC2:11-25%) they represented the bulk of germ cells (70-80%). The overall conversion of 2C to 1C (1C:2C ratio) and meiotic transformation of 4C cells to IC (1C:4C ratio) kinetics were relatively constant between the species studied. The present study clearly demonstrates that DNA flow cytometry can be adopted with ease and assurance to quantify germ cell transformation and as such spermatogenesis by analysing a large number of samples with consistency both within and across the species barrier. Any variation from the norms in germ cell proportions observed following treatment, for e.g. hormonal stimulation or deprivation can then be ascribed due to a specific effect of the hormone/drug on single/multiple steps in germ cell transformation

Work fluctuations in an elastic dumbbell model of polymers in planar elongational flow

We use a path-integral approach to calculate the distribution P(w, t) of the fluctuations in the work W at time t of a polymer molecule (modeled as an elastic dumbbell in a viscous solvent) that is acted on by an elongational flow field having a flow rate (gamma) over dot. We find that P(w, t) is non-Gaussian and that, at long times, the ratio P(w, t)/ P (-w, t) is equal to expw/(k(B)T)], independent of (gamma) over dot. On the basis of this finding, we suggest that polymers in elongational flows satisfy a fluctuation theorem.

Nonsimilar mixed convection flow of a non-Newtonian fluid past a vertical wedge

The flow and heat transfer characteristics of a second-order fluid over a vertical wedge with buoyancy forces have been analysed. The coupled nonlinear partial differential equations governing the nonsimilar mixed convection flow have been solved numerically using Keller box method. The effects of the buoyancy parameter, viscoelastic parameter, mass transfer parameter, pressure gradient parameter, Prandtl number and viscous dissipation parameter on the skin friction and heat transfer have been examined in detail. Particular cases of the present results match exactly with those available in the literature.

Dielectric barrier discharge plasma interaction with the airflow over an airfoil

The effect of various parameters on the velocity of the induced jet produced by a dielectric barrier discharge (DBD) plasma was studied experimentally. The glow discharge was created at atmospheric conditions by using a high voltage RF power supply. Flow visualization and photographic studies of the plasma were performed. The parametric investigation of the characteristics of the plasma show that the width of the plasma in the uniform glow discharge regime was an indication of the velocity induced under stagnant conditions. It was observed that the spanwise overlap of the two electrodes, dielectric thickness, voltage and frequency of the applied voltage are the major parameters that govern the velocity and the extent of plasma in the streamwise direction.

Stability of fluid flow past a membrane

The stability of fluid flow past a membrane of infinitesimal thickness is analysed in the limit of zero Reynolds number using linear and weakly nonlinear analyses. The system consists of two Newtonian fluids of thickness R* and H R*, separated by an infinitesimally thick membrane, which is flat in the unperturbed state. The dynamics of the membrane is described by its normal displacement from the flat state, as well as a surface displacement field which provides the displacement of material points from their steady-state positions due to the tangential stress exerted by the fluid flow. The surface stress in the membrane (force per unit length) contains an elastic component proportional to the strain along the surface of the membrane, and a viscous component proportional to the strain rate. The linear analysis reveals that the fluctuations become unstable in the long-wave (alpha --> 0) limit when the non-dimensional strain rate in the fluid exceeds a critical value Lambda(t), and this critical value increases proportional to alpha(2) in this limit. Here, alpha is the dimensionless wavenumber of the perturbations scaled by the inverse of the fluid thickness R*(-1), and the dimensionless strain rate is given by Lambda(t) = ((gamma) over dot* R*eta*/Gamma*), where eta* is the fluid viscosity, Gamma* is the tension of the membrane and (gamma) over dot* is the strain rate in the fluid. The weakly nonlinear stability analysis shows that perturbations are supercritically stable in the alpha --> 0 limit.

Unsteady mhd flow and heat transfer on a rotating disk in an ambient fluid

An unsteady flow and heat transfer of a viscous incompressible electrically conducting fluid over a rotating infinite disk in an otherwise ambient fluid are studied. The unsteadiness in the flow field is caused by the angular velocity of the disk which varies with time. The magnetic field is applied normal to the disk surface. The new self-similar solution of the Navier-Stokes and energy equations is obtained numerically. The solution obtained here is not only the solution of the Navier-Stokes equations, but also of the boundary layer equations. Also, for a simple scaling factor, it represents the solution of the flow and heat transfer in the forward stagnation-point region of a rotating sphere or over a rotating cone. The asymptotic behaviour of the solution for a large magnetic field or for a large independent variable is also examined. The surface shear stresses in the radial and tangential directions and the surface heat transfer increase as the acceleration parameter increases. Also the surface shear stress in the radial direction and the surface heat transfer decrease with increasing magnetic field, but the surface shear stress in the tangential direction increases. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

An experimental study of reverse transition in two-dimensional channel flow

An experimental investigation on reverse transition from turbulent to laminar flow in a two-dimensional channel was carried out. The reverse transition occurred when Reynolds number of an initially turbulent flow was reduced below a certain value by widening the duct in the lateral direction. The experiments were conducted at Reynolds numbers of 625, 865, 980 and 1250 based on half the height of the channel and the average of the mean velocity. At all these Reynolds numbers the initially turbulent mean velocity profiles tend to become parabolic. The longitudinal and vertical velocity fluctuations ($\overline{u^{\prime 2}}$ and $\overline{v^{\prime 2}}$) averaged over the height of the channel decrease exponentially with distance downstream, but $\overline{u^{\prime}v^{\prime}} $ tends to become zero at a reasonably well-defined point. During reverse transition $\overline{u^{\prime}}\overline{v^{\prime}}/\sqrt{\overline{u^{\prime 2}}}\sqrt{\overline{v^{\prime 2}}}$ also decreases as the flow moves downstream and Lissajous figures taken with u’ and v’ signals confirm this trend. There is approximate similarly between $\overline{u^{\prime 2}} $ profiles if the value of $\overline{u^{\prime 2}_{\max}} $ and the distance from the wall at which it occurs are taken as the reference scales. The spectrum of $\overline{u^{\prime 2}} $ is almost similar at all stations and the non-dimensional spectrum is exponential in wave-number. All the turbulent quantities, when plotted in appropriate co-ordinates, indicate that there is a definite critical Reynolds number of 1400±50 for reverse transition.

On cavity flow at high Reynolds numbers

The flow in a square cavity is studied by solving the full Navier–Stokes and energy equations numerically, employing finite-difference techniques. Solutions are obtained over a wide range of Reynolds numbers from 0 to 50000. The solutions show that only at very high Reynolds numbers (Re [gt-or-equal, slanted] 30000) does the flow in the cavity completely correspond to that assumed by Batchelor's model for separated flows. The flow and thermal fields at such high Reynolds numbers clearly exhibit a boundary-layer character. For the first time, it is demonstrated that the downstream secondary eddy grows and decays in a manner similar to the upstream one. The upstream and downstream secondary eddies remain completely viscous throughout the range of Reynolds numbers of their existence. It is suggested that the behaviour of the secondary eddies may be characteristic of internal separated flows.

Aerodynamic pressure variation over SMA wire integrated morphing aerofoil

An analysis of the pressure variation over an aerofoil with integrated Shape Memory Alloy (SMA) wire is reported. A computational model based on finite elements and potential flow computation is proposed to obtain the deflections of the upper and the lower skins of the aerofoil subjected to aerodynamic pressure and hysteretic deformation of the SMA wire. The computational model couples a one-dimensional phenomenological constitutive model of SMA wire with the laminar incompressible aerodynamic pressure induced deformation of the aerofoil skins. The SMA wires are actuated by thermoelectric control system with auxiliary compensator feeding the piezoelectric stack actuators to adjust the hysteretic dynamics of the SMA wire. At each step of this coupled deformation process, the deflected/morphed shape of the aerofoil is d while recalculating to get the pressure distribution. Panel method based on incompressible and inviscid flow is employed for this purpose. The aerodynamic lift is then obtained from the pressure distributions. Numerical results on the variation of coefficient of pressure are reported.

Linear stability, transient growth and the role of viscosity stratification in compressible Couette flow

Linear stability and the nonmodal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the uniform shear flow with constant viscosity, and (b) the nonuniform shear flow with stratified viscosity. Both mean flows are linearly unstable for a range of supersonic Mach numbers (M). For a given M, the critical Reynolds number (Re) is significantly smaller for the uniform shear flow than its nonuniform shear counterpart; for a given Re, the dominant instability (over all streamwise wave numbers, α) of each mean flow belongs to different modes for a range of supersonic M. An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean flow to perturbations. It is shown that the energy transfer from mean flow occurs close to the moving top wall for “mode I” instability, whereas it occurs in the bulk of the flow domain for “mode II.” For the nonmodal transient growth analysis, it is shown that the maximum temporal amplification of perturbation energy, Gmax, and the corresponding time scale are significantly larger for the uniform shear case compared to those for its nonuniform counterpart. For α=0, the linear stability operator can be partitioned into L∼L̅ +Re2 Lp, and the Re-dependent operator Lp is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: G(t∕Re)∼Re2. In contrast, the dominance of Lp is responsible for the invalidity of this scaling law in nonuniform shear flow. An inviscid reduced model, based on Ellingsen-Palm-type solution, has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and nonmodal instability, it is shown that the viscosity stratification of the underlying mean flow would lead to a delayed transition in compressible Couette flow.

Present status of Gottigere Tank : Indicator of Decision maker’s apathy

Gottigere lake with a water spread area of about 14.98 ha is located in the Bellandur Lake catchment of the South Pennar River basin. In recent years, this lake catchment has been subjected to environmental stress mainly due to the rampant unplanned developmental activities in the catchment. The functional ability of the ecosystem is impaired due to structural changes in the ecosystem. This is evident from poor water quality, breeding of disease vectors, contamination of groundwater in the catchment, frequent flooding in the catchment due to topography alteration, decline in groundwater table, erosion in lake bed, etc. The development plans of the region (current as well as the proposed) ignore the integrated planning approaches considering all components of the ecosystem. Serious threats to the sustainability of the region due to lack of holistic approaches in aquatic resources management are land use changes (removal of vegetation cover, etc.), point and non-point sources of pollution impairing water quality, dumping of solid waste (building waste, etc.). Conservation of lake ecosystem is possible only when the physical and chemical integrity of its catchment is maintained. Alteration in the catchment either due to land use changes (leading to paved surface area from vegetation cover), alteration in topography, construction of roads in the immediate vicinity are detrimental to water yield in the catchment and hence, the sustenance of the lake. Open spaces in the form of lakes and parks aid as kidney and lung in an urban ecosystem, which maintain the health of the people residing in the locality. Identification of core buffer zones and conservation of buffer zones (500 to 1000 m from shore) is to be taken up on priority for conservation and sustainable management of Bangalore lakes. Bangalore is located over a ridge delineating four watersheds, viz. Hebbal, Koramangala, Challaghatta and Vrishabhavathi. Lakes and tanks are an integral part of natural drainage and help in retaining water during rainfall, which otherwise get drained off as flash floods. Each lake harvests rainwater from its catchment and surplus flows downstream spilling into the next lake in the chain. The topography of Bangalore has uniquely supported the creation of a large number of lakes. These lakes form chains, being a series of impoundments across streams. This emphasises the interconnectivity among Bangalore lakes, which has to be retained to prevent Bangalore from flooding or from water scarcity. The main source of replenishment of groundwater is the rainfall. The slope of the terrain allows most of the rainwater to flow as run-off. With the steep gradients available in the major valleys of Bangalore, the rainwater will flow out of the city within four to five hours. Only a small fraction of the rainwater infiltrates into the soil. The infiltration of water into the subsoil has declined with more and more buildings and paved road being constructed in the city. Thus the natural drainage of Bangalore is governed by flows from the central ridge to all lower contours and is connected with various tanks and ponds. There are no major rivers flowing in Bangalore and there is an urgent need to sustain these vital ecosystems through proper conservation and management measures. The proposed peripheral ring road connecting Hosur Road (NH 7) and Mysore Road (SH 17) at Gottigere lake falls within the buffer zone of the lake. This would alter the catchment integrity and hence water yield affecting flora, fauna and local people, and ultimately lead to the disappearance of Gottigere lake. Developmental activities in lake catchments, which has altered lake’s ecological integrity is in violation of the Indian Fisheries Act – 1857, the Indian Forest Act – 1927, Wildlife (Protection) Act – 1972, Water (Prevention and Control of Pollution) Act – 1974, Water (Prevention and Control of Pollution) Act – 1977, Forest (Conservation Act) – 1980, Environmental (Protection) Act – 1986, Wildlife (Protection) Amendment Act – 1991 and National Conservation Strategy and Policy Statement on Environment and Development – 1992. Considering 65% decline of waterbodies in Bangalore (during last three decades), decision makers should immediately take preventive measures to ensure that lake ecosystems are not affected. This report discusses the impacts due to the proposed infrastructure developmental activities in the vicinity of Gottigere tank.