Unsteady flow over a stretching surface with a magnetic field in a rotating fluid

The effect of the magnetic field on the unsteady flow over a stretching surface in a rotating fluid has been studied. The unsteadiness in the flow field is due to the time-dependent variation of the velocity of the stretching surface and the angular velocity of the rotating fluid. The Navier-Stokes equations and the energy equation governing the flow and the heat transfer admit a self-similar solution if the velocity of the stretching surface and the angular velocity of the rotating fluid vary inversely as a linear function of time. The resulting system of ordinary differential equations is solved numerically using a shooting method. The rotation parameter causes flow reversal in the component of the velocity parallel to the strerching surface and the magnetic field tends to prevent or delay the flow reversal. The surface shear stresses dong the stretching surface and in the rotating direction increase with the rotation parameter, but the surface heat transfer decreases. On the other hand, the magnetic field increases the surface shear stress along the stretching surface, but reduces the surface shear stress in the rotating direction and the surface heat transfer. The effect of the unsteady parameter is more pronounced on the velocity profiles in the rotating direction and temperature profiles.

Unsteady free convection flow in the stagnation-point region of a rotating sphere

The unsteady free convection boundary-layer flow in the forward stagnation-point region of a sphere, which is rotating with time-dependent angular velocity in an ambient fluid, has been studied. Both constant wall temperature and constant hear flux conditions have been considered. The non-linear coupled parabolic partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The skin friction and the heat transfer are enhanced by the buoyancy force. The effect of the buoyancy force is found to be more pronounced for smaller Prandtl numbers than for larger Prandtl numbers. For a given buoyancy force, the heat transfer increases with an increase in Prandtl number, but the skin friction decreases.

Unsteady free convection flow in the stagnation-point region of a three-dimensional body

The unsteady free convection flow in the stagnation-point region of a heated three-dimensional body placed in an ambient fluid is studied under boundary layer approximations. We have considered the case where there is an initial steady state that is perturbed by a step-change in the wall temperature. The non-linear coupled partial differential equations governing the free convection flow are solved numerically using a finite difference scheme. The presented results show the temporal development of the momentum and thermal boundary layer characteristics.

A Ca2+-dependent early functional heterogeneity in amoebae of Dictyostelium discoideum, revealed by flow cytometry

When freshly starved amoebae of Dictyostelium discoideum are loaded with the Ca2+-specific dye indo-1/AM and analyzed in a fluorescence-activated cell sorter, they exhibit a quasi-bimodal distribution of fluorescence. This permits a separation of the population into two classes: H, or ''high Ca2+-indo-1 fluorescence,'' and L, or ''low Ca2+-indo-1 fluorescence.'' Simultaneous monitoring of Ca2+-indo-1 and Ca2+-chlortetracycline fluorescence shows that by and large the same cells tend to have high (or low) levels of both cytoplasmic and sequestered Ca2+. Next we label H cells with tetramethylrhodamine isothiocyanate (TRITC) and mix them in a 1:4 ratio with L cells, In the slugs that result, TRITC fluorescence is confined mainly to the anterior prestalk region. This implies that amoebae with relatively high Ca2+ at the vegetative stage tend to develop into prestalk cells and those with low Ca2+ into prespores. Polysphondylium violaceum, a cellular slime mold that does not possess prestalk and prespore cells, also does not display a Ca2+-dependent heterogeneity at the vegetative stage or in slugs. Finally, confirming earlier findings with the fluorophore fura-2 (Azhar ef al., Curr. Sci. 68, 337-342 (1995)), a prestalk-prespore difference in cellular Ca2+ is present in the cells of the slug in vivo. These findings are discussed in light of the possible roles of Ca2+ for cell differentiation in D. discoideum.

Mixed Convection Boundary Layer Flow Past a Horizontal Circular Cylinder Embedded in a Bidisperse Porous Medium

Adopting a two-temperature and two-velocity model, appropriate to a bidisperse porous medium (BDPM) proposed by Nield and Kuznetsov (2008), the classical steady, mixed convection boundary layer flow about a horizontal, isothermal circular cylinder embedded in a porous medium has been theoretically studied in this article. It is shown that the boundary layer analysis leads to expressions for the flow and heat transfer characteristics in terms of an inter-phase momentum parameter, a thermal diffusivity ratio, a thermal conductivity ratio, a permeability ratio, a modified thermal capacity ratio, and a buoyancy or mixed convection parameter. The transformed partial differential equations governing the flow and heat transfer in the f-phase (the macro-pores) and the p-phase (the remainder of the structure) are solved numerically using a very efficient implicit finite-difference technique known as Keller-box method. A good agreement is observed between the present results and those known from the open literature in the special case of a traditional Darcy formulation (monodisperse system).

Fast decay of the velocity autocorrelation function in dense shear flow of inelastic hard spheres

We find in complementary experiments and event-driven simulations of sheared inelastic hard spheres that the velocity autocorrelation function psi(t) decays much faster than t(-3/2) obtained for a fluid of elastic spheres at equilibrium. Particle displacements are measured in experiments inside a gravity-driven flow sheared by a rough wall. The average packing fraction obtained in the experiments is 0.59, and the packing fraction in the simulations is varied between 0.5 and 0.59. The motion is observed to be diffusive over long times except in experiments where there is layering of particles parallel to boundaries, and diffusion is inhibited between layers. Regardless, a rapid decay of psi(t) is observed, indicating that this is a feature of the sheared dissipative fluid, and is independent of the details of the relative particle arrangements. An important implication of our study is that the non-analytic contribution to the shear stress may not be present in a sheared inelastic fluid, leading to a wider range of applicability of kinetic theory approaches to dense granular matter.

Flow and heat transfer in a stagnation-point flow over a stretching sheet with a magnetic field

The flow and heat transfer problem in the boundary layer induced by a continuous moving surface is important in many manufacturing processes in industry such as the boundary layer along material handling conveyers, the aerodynamic extrusion of plastic sheet, the cooling of an infinite metalic plate in a cooling bath (which may also be electrolyte). Glass blowing, continuous casting and spinning of fibres also involve the flow due to a stretching surface. Sakiadis [1] was the first to study the flow induced by a semi-infinite moving wall in an ambient fluid. On the other hand, Crane [2] first studied the flow over a linearly stretching sheet in an ambient fluid. Subsequently, Crane [3] also investigated the corresponding heat transfer problem. Since then several authors [4-8] have studied various aspects of this problem such as the effects of mass transfer, variable wall temperature, constant heat flux, magnetic field etc. Recently, Andersson [9] has obtained an exact solution of the Navier-Stokes equations for the MHD flow over a linearly stretching sheet in an ambient fluid. Also Chiam [10] has studied the heat transfer with variable thermal conductivity on a stretching sheet when the velocities of the sheet and the free stream are equal.

Flow behavior of long chain plasticizing liquids: Segment size calculations in carboxylate esters

This is the first comprehensive report on the calculation of segment size, which signifies the asic unit of flow in long chain plasticizing liquids, by a novel multi-pronged approach. Unlike,low molecular weight liquids and high polymer melts these complex long chain liquids encompasses the least understood domain of the liquid state. In the present work the flow behaviour of carboxylate ester (300-900 Da) has been explained through segmental motion taking into account the independence of molecular weight region. The segment size have been calculated by various methods based on satistical thermodynamics, molecular dynamics and group additivity nd their merits analysed.

Flow behavior of LDPE and its blends with LLDPE I and II: A comparative study

Studies on melt rheological properties of blends of low density polyethylene (LDPE) with selected grades of linear low density polyethylene (LLDPE), which differ widely in their melt flow indices, are reported, The data obtained in a capillary rheometer are presented to describe the effects of blend composition and shear rate on flow behavior index, melt viscosity, and melt elasticity. In general, blending of LLDPE I that has a low melt flow index (2 g/10 min) with LDPE results in a decrease of its melt viscosity, processing temperature, and the tendency of extrudate distortion, depending on blending ratio. A blending ratio around 20-30% LLDPE I seems optimum from the point of view of desirable improvement in processability behavior. On the other hand, blending of LLDPE II that has a high melt flow index (10 g/10 min) with LDPE offers a distinct advantage in increasing the pseudoplasticity of LDPE/LLDPE II blends.

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter = 9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 10(8). Under these conditions the convection is turbulent, and the time-averaged velocity at any point is `zero'. The Reynolds number based on the Taylor microscale, Re-lambda, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6-7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as (RaSc1/2)-Sc-1/2, and the Reynolds number would scale as (RaSc-1/2)-Sc-1/2. The velocity and the flux measurements appear to be consistent with the Ra-1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are Much higher compared to what would be obtained in Rayleigh-Benard (R-B) convection for similar density differences.

Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface

The unsteady magnetohydrodynamic viscous flow and heat transfer of Newtonian fluids induced by an impulsively stretched plane surface in two lateral directions are studied by using an analytic technique, namely, the homotopy method. The analytic series solution presented here is highly accurate and uniformly valid for all time in the entire region. The effects of the stretching ratio and the magnetic field on the surface shear stresses and heat transfer are studied. The surface shear stresses in x- and y-directions and the surface heat transfer are enchanced by increasing stretching ratio for a fixed value of the magnetic parameter. For a fixed stretching ratio, the surface shear stresses increase with the magnetic parameter, but the heat transfer decreases. The Nusselt number takes longer time to reach the steady state than the skin friction coefficients. There is a smooth transition from the initial unsteady state to the steady state.

Biomethanation of herbaceous biomass residues using 3-zone plug flow like digesters - A case study from India

Biomethanation of herbaceous biomass feedstock has the potential to provide clean energy source for cooking and other activities in areas where such biomass availability predominates. A biomethanation concept that involves fermentation of biomass residues in three steps, occurring in three zones of the fermentor is described. This approach while attempting take advantage of multistage reactors simplifies the reactor operation and obviates the need for a high degree of process control or complex reactor design. Typical herbaceous biomass decompose with a rapid VFA flux initially (with a tendency to float) followed by a slower decomposition showing balanced process of VFA generation and its utilization by methanogens that colonize biomass slowly. The tendency to float at the initial stages is suppressed by allowing previous days feed to hold it below digester liquid which permits VFA to disperse into the digester liquid without causing process inhibition. This approach has been used to build and operate simple biomass digesters to provide cooking gas in rural areas with weed and agro-residues. With appropriate modifications, the same concept has been used for digesting municipal solid wastes in small towns where large fermentors are not viable. With further modifications this concept has been used for solid-liquid feed fermentors. Methanogen colonized leaf biomass has been used as biofilm support to treat coffee processing wastewater as well as crop litter alternately in a year. During summer it functions as a biomass based biogas plants operating in the three-zone mode while in winter, feeding biomass is suspended and high strength coffee processing wastewater is let into the fermentor achieving over 90% BOD reduction. The early field experience of these fermentors is presented.

Unsteady Natural Convection Flow in a Square Cavity Filled with a Porous Medium Due to Impulsive Change in Wall Temperature

Unsteady natural convection flow in a two- dimensional square cavity filled with a porous material has been studied. The flow is initially steady where the left- hand vertical wall has temperature T-h and the right- hand vertical wall is maintained at temperature T-c ( T-h > T-c) and the horizontal walls are insulated. At time t > 0, the left- hand vertical wall temperature is suddenly raised to (T-h) over bar ((T-h) over bar > T-h) which introduces unsteadiness in the flow field. The partial differential equations governing the unsteady natural convection flow have been solved numerically using a finite control volume method. The computation has been carried out until the final steady state is reached. It is found that the average Nusselt number attains a minimum during the transient period and that the time required to reach the final steady state is longer for low Rayleigh number and shorter for high Rayleigh number.

Flow pattern analysis in a highly stenotic patient-specific carotid bifurcation model using a turbulence model

The aim of this study is to investigate the blood flow pattern in carotid bifurcation with a high degree of luminal stenosis, combining in vivo magnetic resonance imaging (MRI) and computational fluid dynamics (CFD). A newly developed two-equation transitional model was employed to evaluate wall shear stress (WSS) distribution and pressure drop across the stenosis, which are closely related to plaque vulnerability. A patient with an 80% left carotid stenosis was imaged using high resolution MRI, from which a patient-specific geometry was reconstructed and flow boundary conditions were acquired for CFD simulation. A transitional model was implemented to investigate the flow velocity and WSS distribution in the patient-specific model. The peak time-averaged WSS value of approximately 73Pa was predicted by the transitional flow model, and the regions of high WSS occurred at the throat of the stenosis. High oscillatory shear index values up to 0.50 were present in a helical flow pattern from the outer wall of the internal carotid artery immediately after the throat. This study shows the potential suitability of a transitional turbulent flow model in capturing the flow phenomena in severely stenosed carotid arteries using patient-specific MRI data and provides the basis for further investigation of the links between haemodynamic variables and plaque vulnerability. It may be useful in the future for risk assessment of patients with carotid disease.

On the nature of power flow equations in security analysis

The power system network is assumed to be in steady-state even during low frequency transients. However, depending on generator dynamics, and toad and control characteristics, the system model and the nature of power flow equations can vary The nature of power flow equations describing the system during a contingency is investigated in detail. It is shown that under some mild assumptions on load-voltage characteristics, the power flow equations can be decoupled in an exact manner. When the generator dynamics are considered, the solutions for the load voltages are exact if load nodes are not directly connected to each other