Nonsimilar incompressible laminar boundary-layer flows in micropolar fluids

The solution of the steady laminar incompressible nonsimilar boundary-layer problem for micropolar fluids over two-dimensional and axisymmetric bodies has been presented. The partial differential equations governing the flow have been transformed into new co-ordinates having finite range. The resulting equations have been solved numerically using implicit finite-difference scheme. The computations have been carried out for a cylinder and a sphere. The results indicate that the separation in micropolar fluids occurs at earlier streamwise locations as compared to Newtonian fluids. The skin friction and velocity profiles depend on the shape of the body and are almost insensitive to microrotation or coupling parameter, provided the coupling parameter is small. On the other hand, the microrotation profiles and microrotation gradient depend on the microrotation parameter and they are insensitive to the coupling parameter.

The effect of suction on boundary layer for rotating flows with or without magnetic field

The effect of suction on the steady laminar incompressible boundarylayer flow for a stationary infinite disc with or without magnetic field, when the fluid at a large distance from the surface of the disc undergoes a solid body rotation, has been studied. The governing coupled nonlinear equations have been solved numerically using the shooting method with least square convergence criterion. It has been found that suction tends to reduce the velocity overshoot and damp the oscillation.

Compressible magnetohydrodynamic boundary layer swirling nozzle and diffuser flows with a magnetic field

The flow, heat and mass transfer problem for boundary layer swirling flow of a laminar steady compressible electrically conducting gas with variable properties through a conical nozzle and a diffuser with an applied magnetic field has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme after they have been transformed into dimensionless form using the modified Lees transformation. The results indicate that the skin friction and heat transfer strongly depend on the magnetic field, mass transfer and variation of the density-viscosity product across the boundary layer. However, the effect of the variation of the density-viscosity product is more pronounced in the case of a nozzle than in the case of a diffuser. It has been found that large swirl is required to produce strong effect on the skin friction and heat transfer. Separationless flow along the entire length of the diffuser can be obtained by applying appropriate amount of suction. The results are found to be in good agreement with those of the local nonsimilarity method, but they differ quite significantly from those of the local similarity method.

Substance flow analysis in Finland : Four case studies on N and P flows

Nitrogen (N) and phosphorus (P) are essential elements for all living organisms. However, in excess, they contribute to several environmental problems such as aquatic and terrestrial eutrophication. Globally, human action has multiplied the volume of N and P cycling since the onset of industrialization. The multiplication is a result of intensified agriculture, increased energy consumption and population growth. Industrial ecology (IE) is a discipline, in which human interaction with the ecosystems is investigated using a systems analytical approach. The main idea behind IE is that industrial systems resemble ecosystems, and, like them, industrial systems can then be described using material, energy and information flows and stocks. Industrial systems are dependent on the resources provided by the biosphere, and these two cannot be separated from each other. When studying substance flows, the aims of the research from the viewpoint of IE can be, for instance, to elucidate the ways how the cycles of a certain substance could be more closed and how the flows of a certain substance could be decreased per unit of production (= dematerialization). In Finland, N and P are studied widely in different ecosystems and environmental emissions. A holistic picture comparing different societal systems is, however, lacking. In this thesis, flows of N and P were examined in Finland using substance flow analysis (SFA) in the following four subsystems: I) forest industry and use of wood fuels, II) food production and consumption, III) energy, and IV) municipal waste. A detailed analysis at the end of the 1990s was performed. Furthermore, historical development of the N and P flows was investigated in the energy system (III) and the municipal waste system (IV). The main research sources were official statistics, literature, monitoring data, and expert knowledge. The aim was to identify and quantify the main flows of N and P in Finland in the four subsystems studied. Furthermore, the aim was to elucidate whether the nutrient systems are cyclic or linear, and to identify how these systems could be more efficient in the use and cycling of N and P. A final aim was to discuss how this type of an analysis can be used to support decision-making on environmental problems and solutions. Of the four subsystems, the food production and consumption system and the energy system created the largest N flows in Finland. For the creation of P flows, the food production and consumption system (Paper II) was clearly the largest, followed by the forest industry and use of wood fuels and the energy system. The contribution of Finland to N and P flows on a global scale is low, but when compared on a per capita basis, we are one of the largest producers of these flows, with relatively high energy and meat consumption being the main reasons. Analysis revealed the openness of all four systems. The openness is due to the high degree of internationality of the Finnish markets, the large-scale use of synthetic fertilizers and energy resources and the low recycling rate of many waste fractions. Reduction in the use of fuels and synthetic fertilizers, reorganization of the structure of energy production, reduced human intake of nutrients and technological development are crucial in diminishing the N and P flows. To enhance nutrient recycling and replace inorganic fertilizers, recycling of such wastes as wood ash and sludge could be promoted. SFA is not usually sufficiently detailed to allow specific recommendations for decision-making to be made, but it does yield useful information about the relative magnitude of the flows and may reveal unexpected losses. Sustainable development is a widely accepted target for all human action. SFA is one method that can help to analyse how effective different efforts are in leading to a more sustainable society. SFA's strength is that it allows a holistic picture of different natural and societal systems to be drawn. Furthermore, when the environmental impact of a certain flow is known, the method can be used to prioritize environmental policy efforts.

Two temperature viscous accretion flows around rotating black holes: Description of under-fed systems to ultra-luminous X-ray sources

We discuss two temperature accretion disk flows around rotating black holes. As we know that to explain observed hard X-rays the choice of Keplerian angular momentum profile is not unique, we consider the sub-Keplerian regime of the disk. Without any strict knowledge of the magnetic field structure, we assume the cooling mechanism is dominated by bremsstrahlung process. We show that in a range of Shakura-Sunyaev viscosity parameter 0.2 greater than or similar to alpha greater than or similar to 0.0005, flow behavior varies widely, particularly by means of the size of disk, efficiency of cooling and corresponding temperatures of ions and electrons. We also show that the disk around a rotating black hole is hotter compared to that around a Schwarzschild black hole, rendering a larger difference between ion and electron temperatures in the former case. With all the theoretical solutions in hand, finally we reproduce the observed luminosities (L) of two extreme cases-the under-fed AGNs and quasars (e.g. Sgr A') with L greater than or similar to 10(33) erg/s to ultra-luminous X-ray sources with L similar to 10(41) erg/s, at different combinations of mass accretion rate, ratio of specific heats, Shakura-Sunyaev viscosity parameter and Kerr parameter, and conclude that Sgr A' may be an intermediate spinning black hole.

The possible role of meridional flows in suppressing magnetic buoyancy

The equation of motion for a toroidal flux ring in a stellar convective envelope is derived, and the equilibrium of such a ring is considered. Necessary conditions for the stability of toroidal flux rings are derived, and results of stability calculations for a particular model of the meridional flow are presented. The motions of the flux rings when the rings are far from their equilibrium position or when equilibrium does not exist are considered. The results confirm the linear stability analysis, and show that in the absence of stable equilibrium, the rings move toward the solar surface along a trajectory which is parallel to the rotation axis. It is expected that viscosity will tend to reduce the rotational velocity difference between the flux ring and its surroundings, thus reducing the Coriolis force and altering the equilibrium. The storage time of toroidal flux rings is estimated, and some implications for the sun are discussed.

Rheology of dense sheared granular flows

Rapid granular flows are defined as flows in which the time scales for the particle interactions are small compared to the inverse of the strain rate, so that the particle interactions can be treated as instantaneous collisions. We first show, using Discrete Element simulations, that even very dense flows of sand or glass beads with volume fraction between 0.5 and 0.6 are rapid granular flows. Since collisions are instantaneous, a kinetic theory approach for the constitutive relations is most appropriate, and we present kinetic theory results for different microscopic models for particle interaction. The significant difference between granular flows and normal fluids is that energy is not conserved in a granular flow. The differences in the hydrodynamic modes caused by the non-conserved nature of energy are discussed. Going beyond the Boltzmann equation, the effect of correlations is studied using the ring kinetic approximation, and it is shown that the divergences in the viscometric coefficients, which are present for elastic fluids, are not present for granular flows because energy is not conserved. The hydrodynamic model is applied to the flow down an inclined plane. Since energy is not a conserved variable, the hydrodynamic fields in the bulk of a granular flow are obtained from the mass and momentum conservation equations alone. Energy becomes a relevant variable only in thin 'boundary layers' at the boundaries of the flow where there is a balance between the rates of conduction and dissipation. We show that such a hydrodynamic model can predict the salient features of a chute flow, including the flow initiation when the angle of inclination is increased above the 'friction angle', the striking lack of observable variation of the volume fraction with height, the observation of a steady flow only for certain restitution coefficients, and the density variations in the boundary layers.

Optimal auctions for multi-unit procurement with volume discount bids

Our attention, is focused on designing an optimal procurement mechanism which a buyer can use for procuring multiple units of a homogeneous item based on bids submitted by autonomous, rational, and intelligent suppliers. We design elegant optimal procurement mechanisms for two different situations. In the first situation, each supplier specifies the maximum quantity that can be supplied together with a per unit price. For this situation, we design an optimal mechanism S-OPT (Optimal with Simple bids). In the more generalized case, each supplier specifies discounts based on the volume of supply. In this case, we design an optimal mechanism VD-OPT (Optimal with Volume Discount, bids). The VD-OPT mechanism uses the S-OPT mechanism as a building block. The proposed mechanisms minimize the cost to the buyer, satisfying at the same time, (a) Bayesian, incentive compatibility and (b) interim individual rationality.

Secondary flows induced by the rotation of a sphere or coaxial cones in micropolar fluids

The micropolar fluids like Newtonian and Non-Newtonian fluids cannot sustain a simple shearing motion, wherein only one component of velocity is present. They exhibit both primary and secondary motions when the boundaries are subject to slow rotations. The primary motion, as in Non-Newtonian fluids, characterized by the equation due to Rivlin-Ericksen, Oldroyd, Walters etc., resembles that of Newtonian fluid for slow steady rotation. We further notice that the micro-rotation becomes identically equal to the vorticity present in the fluid and the condition b) of "Wall vorticity" can alone be satisfied at the boundaries. As regards, the secondary motion, we notice that it can be determined by the above procedure for a special class of fluids, namely that for which j0(n2-n3)=4 n3/l2. Moreover for this class of fluids, the micro-rotation is identical with the vorticity of the fluid everywhere. Also the stream function for the secondary flow is identical with that for the Newtonian fluid with a suitable definition of the Reynolds number. In contrast with the Non-Newtonian fluids, characterized by the equation due to Rivlin-Ericksen, Oldroyd, Walters etc., this class of micropolar fluids does not show separation. This is in conformity with the statement of Condiff and Dahler (3) that in any steady flow, internal spin matches the vorticity everywhere provided that (i) spin boundary conditions are satisfied, (ii) body torques and non-conservative body forces are absent, and (iii) inertial and spin-inertial terms are either negligible or vanish identically.

A general treatment of two dimensional plane flows, for a micropolar fluid

In this paper we have studied the flow of a micropolar fluid, whose constitutive equations were given by Eringen, in two dimensional plane flow. In two notes, we have discussed the validity of the boundary condition v=a ω and its effect on the entire flow field. We have restricted our study to the case when Stokes' approximation is valid, i. e. slow motion for it is difficult to uncouple the equations in the most general case.

A class of one-dimensional steady-state flows in radiation-gas-dynamics

The study of steady-state flows in radiation-gas-dynamics, when radiation pressure is negligible in comparison with gas pressure, can be reduced to the study of a single first-order ordinary differential equation in particle velocity and radiation pressure. The class of steady flows, determined by the fact that the velocities in two uniform states are real, i.e. the Rankine-Hugoniot points are real, has been discussed in detail in a previous paper by one of us, when the Mach number M of the flow in one of the uniform states (at x=+∞) is greater than one and the flow direction is in the negative direction of the x-axis. In this paper we have discussed the case when M is less than or equal to one and the flow direction is still in the negative direction of the x-axis. We have drawn the various phase planes and the integral curves in each phase plane give various steady flows. We have also discussed the appearance of discontinuities in these flows.

A new method of producing local enhancement of buoyancy in liquid flows

We describe here a novel method of generating large volumetric heating in a liquid. The method uses the principle of ohmic heating of the liquid, rendered electrically conducting by suitable additives if necessary. Electrolysis is prevented by the use of high frequency alternating voltage and chemically treated electrodes. The technique is demonstrated by producing substantial heating in an initially neutral jet of water. Simple flow visualisation studies, made by adding dye to the jet, show marked changes in the growth and development of the jet with heat addition.