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.

Influence of crack tip constraint on void growth in ductile FCC single crystals

Effect of constraint (stress triaxiality) on void growth near a notch tip in a FCC single crystal is investigated. Finite element simulations within the modified boundary layer framework are conducted using crystal plasticity constitutive equations and neglecting elastic anisotropy. Displacement boundary conditions based on model, elastic, two term K-T field are applied on the outer boundary of a large circular domain. A pre-nucleated void is considered ahead of a stationary notch tip. The interaction between the notch tip and the void is studied under different constraints (T-stress levels) and crystal orientations. It is found that negative T-stress retards the mechanisms of ductile fracture. However, the extent of retardation depends on the crystal orientation. Further, it is found that there exists a particular orientation which delays the ductile fracture processes and hence can potentially improve ductility. This optimal orientation depends on the constraint level. (C) 2010 Published by Elsevier B.V.

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.

Unsteady free convection flow under the influence of a magnetic field

The unsteady free convection boundary layer at the stagnation point of a two-dimensional body and an axisymmetric body with prescribed surface heat flux or temperature has been studied. The magnetic field is applied parallel to the surface and the effect of induced magnetic field has been considered. It is found that for certain powerlaw distribution of surface heat flux or temperature and magnetic field with time, the governing boundary layer equations admit a self-similar solution locally. The resulting nonlinear ordinary differential equations have been solved using a finite element method and a shooting method with Newton's corrections for missing initial conditions. The results show that the skin friction and heat transfer coefficients, and x-component of the induced magnetic field on the surface increase with the applied magnetic field. In general, the skin friction, heat transfer and x-component of the induced magnetic field for axisymmetric case are more than those of the two-dimensional case. Also they change more when the surface heat flux or temperature decreases with time than when it increases with time. The skin friction, heat transfer and x-component of the induced magnetic field are significantly affected by the magnetic Prandtl number and they increase as the magnetic Prandtl number decreases. The skin friction and x-component of the magnetic field increase with the dissipation parameter, but heat transfer decreases.

Varistors based on n-BaTiO3 ceramics

Stable and highly reproducible voltage-limiting characteristics have been observed at room temperature for polycrystalline ceramics prepared from donor-doped BaTiO3 solid solutions containing isovalent lattice substitute ions that lower the Curie point Tc. When the ambient temperature Ta is decreased such that Ta < Tc, the same ceramics show current-limiting behaviour. The leakage current, the breakdown voltage and the non-linear coefficient (α = 30−50) could be varied with grain-boundary layer (GBL) modifiers and postsintering annealing. The magnitude of the abnormally high dielectric constant (epsilon (Porson)r greater than, approximately 105) indicates the prevalence of GBL capacitance in these ceramics. Analyses of the current-voltage relations show that GBL conduction at Ta < Tc corresponds to tunnelling across asymmetric barriers formed under steady state Joule heating. At Ta > Tc, trap-related conduction gives way to tunnelling across symmetric barriers as the field strength increases.

Influence of Bi 3+ ions in enhancing the magnitude of positive temperature coefficients of resistance in n-BaTiO3 ceramics

Bi3+ ions substituting at Ba-sites in a limited concentration range with another donor dopant occupying the Ti-sites in polycrystalline BaTiO3 enhanced the positive temperature coefficient of resistance (PTCR) by over seven orders of magnitude. These ceramics did not require normal post sinter annealing or a change to an oxygen atmosphere during annealing. These ceramics had low porosities coupled with better stabilities to large applied electric fields and chemically reducing atmospheres. Bi3+ ions limited the grain growth to less than 8 mum in size, they enhanced the concentration of acceptor-type trap centres at the grain-boundary-layer regions and maintained complete tetragonality at low grain sizes in BaTiO3 ceramics.

Nonlinear effects on rotating disk flow in a cylindrical casing

The flow due to a finite disk rotating in an incompressible viscous fluid has been studied. A modified Newton-gradient finite difference scheme is used to obtain the solution of full Navier-Stokes equations numerically for different disk and cylinder sizes for a wide range of Reynolds numbers. The introduction of the aspect ratio and the disk-shroud gap, significantly alters the flow characteristics in the region under consideration, The frictional torque calculated from the flow data reveals that the contribution due to nonlinear terms is not negligible even at a low Reynolds number. For large Reynolds numbers, the flow structure reveals a strong boundary layer character.

Experimental studies of a distorted turbulent spot in a three-dimensional flow

We report here on the results of a series of experiments carried out on a turbulent spot in a distorted duct to study the effects of a divergence with straight streamlines preceded by a short stretch of transverse streamline curvature, both in the absence of any pressure gradient. It is found that the distortion produces substantial asymmetry in the spot: the angles at which the spot cuts across the local streamlines are altered dramatically (in contradiction of a hypothesis commonly made in transition zone modelling), and the Tollmien-Schlichting waves that accompany the wing tips of the spot are much stronger on the outside of the bend than on the inside. However there is no strong effect on the internal structure of the spot and the eddies therein, or on such propagation characteristics as overall spread rate and the celerities of the leading and trailing edges. Both lateral streamline curvature and non-homogeneity of the laminar boundary layer into which the spot propagates are shown to be strong factors responsible for the observed asymmetry. It is concluded that these factors produce chiefly a geometric distortion of the coherent structure in the spot, but do not otherwise affect its dynamics in any significant way.

Tropical deep convection, convective available potential energy and sea surface temperature

The convective available potential energy (CAFE) based on monthly mean sounding has been shown to be relevant to deep convection in the tropics. The variation of CAFE with SST has been found to be similar to the variation of the frequency of deep convection at one station each in the tropical Atlantic and W. Pacific oceans. This suggests a strong link between the frequency of tropical convection and CAFE. It has been shown that CAFE so derived can be interpreted as the work potential of the atmosphere above the boundary layer with ascent in the convective region and subsidence in the surrounding cloud-free region.

Studies on Cavitation Inception Process in Separated Flows

Studies related to cavitation inception process in separated flows are reported. Experimental observations of bubble appearance in grooves with laminar or turbulent boundary layer over them have clearly shown that gaseous diffusion process is significantly enhanced in turbulent flow. This process can lead to local nuclei size modification in environment similar to that of flow over a groove, like laminar separation "bubbles." Cavitation inception modeling including this aspect is carried out for predicting inception conditions associated with "bubble-ring" cavitation commonly observed on hemispherically nosed axisymmetric body. Qualitative dependence of predicted inception numbers with velocity is found to agree very well with experimental observations of Carroll (1981).

Free convection in power-law fluids near a three-dimensional stagnation point

Numerical results are presented for the free-convection boundary-layer equations of the Ostwald de-Waele non-Newtonian power-law type fluids near a three-dimensional (3-D) stagnation point of attachment on an isothermal surface. The existence of dual solutions that are three-dimensional in nature have been verified by means of a numerical procedure. An asymptotic solution for very large Prandtl numbers has also been derived. Solutions are presented for a range of values of the geometric curvature parameter c, the power-law index n, and the Prandtl number Pr.

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a vertical heated plate

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a heated vertical plate is studied for high Rayleigh numbers. Similarity solutions are obtained within the frame work of boundary layer theory for a power law variation in surface temperature,T Wpropx lambda and surface injectionv Wpropx(lambda–1/2). The analysis incorporates the expression connecting porosity and permeability and also the expression connecting porosity and effective thermal diffusivity. The influence of thermal dispersion on the flow and heat transfer characteristics are also analysed in detail. The results of the present analysis document the fact that variable porosity enhances heat transfer rate and the magnitude of velocity near the wall. The governing equations are solved using an implicit finite difference scheme for both the Darcy flow model and Forchheimer flow model, the latter analysis being confined to an isothermal surface and an impermeable vertical plate. The influence of the intertial terms in the Forchheimer model is to decrease the heat transfer and flow rates and the influence of thermal dispersion is to increase the heat transfer rate.

Unsteady laminar compressible swirling flow with massive blowing

THE study of swirling boundary layers is of considerable importance in many rotodynamic machines such as rockets, jet engines, swirl generators, swirl atomizers, arc heaters, etc. For example, the introduction of swirl in a flow acceleration device such as a nozzle in a rocket engine promises efficient mass flow control. In nuclear rockets, swirl is used to retain the uranium atoms in the rocket chamber. With these applications in mind, Back1 and Muthanna and Nath2 have obtained the similarity solutions for a low-speed three-dimensional steady laminar compressible boundary layer with swirl inside an axisymmetric surface of variable cross section. The aim of the present analysis is to study the effect of massive blowing rates on the unsteady laminar swirling compressible boundary-layer flow of an axisymmetric body of arbitrary cross section when the freestream velocity and blowing rate vary with time. The type of swirl considered here is that of a free vortex superimposed on the longitudinal flow of a compressible fluid with variable properties. The analysis is applicable to external flow over a body as well as internal flow along a surface. For the case of external flow, strong blowing can have significant use in cooling the surface of hypervelocity vehicles, particularly when ablation occurs under large aerodynamic or radiative heating, but there may not be such an important application of strong blowing in the case of internal flow. The governing partial differential equations have been solved numerically using an implicit finite difference scheme with a quasilinearization technique.3 High temperature gas effects, such as radiation, dissociation, and ionization, etc., are not investigated. The nomenclature is usually that of Ref. 4 and is listed in the full paper.

Turbulent heat flux variation over the Monsoon-Trough region during MONTBLEX-90

Tower data collected during the Monsoon-Trough Boundary Layer Experiment (MONTBLEX-90) have been analysed to understand the observed structure of the surface layer over an arid region (Jodhpur) and a moist region (Kharagpur) during active and weak phases of the 1990 southwest monsoon. Turbulent heat and momentum fluxes are estimated by the eddy correlation method using sonic data. The turbulent momentum flux at both Jodhpur and Kharagpur was larger when the winds were stronger, reaching a maximum of the order of 0.5 N m(-2) on 5 and 6 August when a low pressure system was located over the region. The heat flux at Jodhpur is high during weak monsoon days, the maximum being 450 W m(-2), whereas during active days the flux never exceeds 200 W m(-2). At Kharagpur, the flux does not vary significantly between active and weak monsoon days, the maximum in either phase being 160 W m(-2) At Jodhpur, there is significant contrast in the near-surface air temperature, being higher during weak monsoon days as compared to active days. Cloud cover did not vary significantly in both the regions. The turbulent heat flux variation at both the sites appears to be correlated mainly with soil mixture, and less sensitive to cloud cover.

Nonsimilar solutions for mixed convection in non-Newtonian fluids along horizontal surfaces in porous media

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in power-law type non-Newtonian fluids along horizontal surfaces with variable heat flux distribution. The mixed convection regime is divided into two regions, namely, the forced convection dominated regime and the free convection dominated regime. The two solutions are matched. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.