Optimal multicommodity flow through the complete graph with random edge capacities

We consider a multicommodity flow problem on a complete graph whose edges have random, independent, and identically distributed capacities. We show that, as the number of nodes tends to infinity, the maximumutility, given by the average of a concave function of each commodity How, has an almost-sure limit. Furthermore, the asymptotically optimal flow uses only direct and two-hop paths, and can be obtained in a distributed manner.

Unsteady mixed convection on the stagnation-point flow adjacent to a vertical plate with a magnetic field

An analysis is performed to study the unsteady combined forced and free convection flow (mixed convection flow) of a viscous incompressible electrically conducting fluid in the vicinity of an axisymmetric stagnation point adjacent to a heated vertical surface. The unsteadiness in the flow and temperature fields is due to the free stream velocity, which varies arbitrarily with time. Both constant wall temperature and constant heat flux conditions are considered in this analysis. By using suitable transformations, the Navier-Stokes and energy equations with four independent variables (x, y, z, t) are reduced to a system of partial differential equations with two independent variables (eta, tau). These transformations also uncouple the momentum and energy equations resulting in a primary axisymmetric flow, in an energy equation dependent on the primary flow and in a buoyancy-induced secondary flow dependent on both primary flow and energy. The resulting system of partial differential equations has been solved numerically by using both implicit finite-difference scheme and differential-difference method. An interesting result is that for a decelerating free stream velocity, flow reversal occurs in the primary flow after certain instant of time and the magnetic field delays or prevents the flow reversal. The surface heat transfer and the surface shear stress in the primary flow increase with the magnetic field, but the surface shear stress in the buoyancy-induced secondary flow decreases. Further the heat transfer increases with the Prandtl number, but the surface shear stress in the secondary flow decreases.

Heat transfer in plane Couette flow of a rarefied gas using Bhatnagar-Gross-Krook model

Using the linearized BGK model and the method of moments of half-range distribution functions the temperature jumps at two plates are determined, and it is found that the results are in fair agreement with those of Gross and Ziering, and Ziering.

Flow driven electronic transport in carbon nan otubes

The flow of a liquid on single-walled carbon nanotube bundles induces an electrical signal (voltage/current) in the sample along the direction of the flow. The electrical response is found to be logarithmic in the flow speed over a wide range. The magnitude of the flow induced electrical signal generated depends sensitively on the ionic conductivity and the polar nature of the liquid, and electrical biasing of the nanotubes can control its direction. Our measurements suggest that the dominant mechanism responsible for this highly sub-linear response should involve a direct forcing of the free charge carriers in the nanotubes by the fluctuating Coulombic field of the liquid flowing past it.

Studies in bubble formation—I bubble formation under constant flow conditions

A model based on two step mechanism of bubble formation is proposed. The resulting equations are used to explain the discrepancies existing in the literature. Data have been collected over a wide range of variables to test the model.

Secondary flow induced by the rotation of two concentric spheres about their common diameter in micropolar fluids

In this paper, we have studied the secondary flow induced in a micropolar fluid by the rotation of two concentric spheres about a fixed diameter. The secondary flow exhibits behaviour commonly observed in visco-elastic fluids. In particular we have obtained the expressions for microrotation vector. Numerical results have been obtained for a number of values of relative rotations of the two spheres for a chosen set of values of fluid parameters. The results are presented graphically and compared with the previous investigations.

Secondary flow of Rivlin-Ericksen fluids between two concentric spheres oscillating about a fixed diameter

The paper deals with the study of the nature of secondary flow of aRivlin-Ericksen fluid, contained between two concentric spheres, which perform oscillations about a fixed diameter. The steady part of the secondary flow is discussed in detail in the following three cases (i) the outer sphere at rest, the inner oscillating, (ii) the two spheres oscillating with the same angular velocity in the same sense and (iii) the spheres oscillating with the same angular velocity in opposite sense. In a previous paper, a similar problem was discussed for theOldroyd fluids. We find that the secondary flow is strongly dependent on the common frequency of oscillation of the two spheres and on the rotational nature of the motion for the present investigation also. Certain contrasting features of interest between the secondary flow field of the two fluids are also noted.

Heat transfer to newtonian fluids in coiled pipes in laminar flow

Data on pressure drop and heat transfer to aqueous solutions of glycerol flowing in different types of coiled pipes are presented for laminar flow in the range of NRe from 80 to 6000. An empirical correlation is set up which can account the present data as well as the data available in literature within ±10 per cent deviation. Conventional momentum and heat transfer analogy equation is used to analyse the present data.

Steady flow of a maxwell fluid in a porous cylindrical annulus with circular cross-section

When a fluid with memory is injected into any flow region some assumptions regarding the initial state of stress have to be made in order to determine the state of stress at any subsequent instant. For a Maxwell fluid, it is assumed that the fluid near the surface of injection is suddenly stressed and responds by starting flow in accordance with the mechanical model chosen. The flow of a Maxwell fluid with a single relaxation time has been determined under the above assumption in the following two cases: (i) annulus between two porous concentric circular cylinders, and (ii) space between two porous and infinitely extending parallel plates. The nature of flow in the present case is similar to that of the Reiner-Rivlin fluids obtained by Narasimhan2).

From environmental concerns towards sustainable food provisioning. : Material flow and food consumption scenario studies on sustainability of agri-food systems

Agriculture is an economic activity that heavily relies on the availability of natural resources. Through its role in food production agriculture is a major factor affecting public welfare and health, and its indirect contribution to gross domestic product and employment is significant. Agriculture also contributes to numerous ecosystem services through management of rural areas. However, the environmental impact of agriculture is considerable and reaches far beyond the agroecosystems. The questions related to farming for food production are, thus, manifold and of great public concern. Improving environmental performance of agriculture and sustainability of food production, sustainabilizing food production, calls for application of wide range of expertise knowledge. This study falls within the field of agro-ecology, with interphases to food systems and sustainability research and exploits the methods typical of industrial ecology. The research in these fields extends from multidisciplinary to interdisciplinary and transdisciplinary, a holistic approach being the key tenet. The methods of industrial ecology have been applied extensively to explore the interaction between human economic activity and resource use. Specifically, the material flow approach (MFA) has established its position through application of systematic environmental and economic accounting statistics. However, very few studies have applied MFA specifically to agriculture. The MFA approach was used in this thesis in such a context in Finland. The focus of this study is the ecological sustainability of primary production. The aim was to explore the possibilities of assessing ecological sustainability of agriculture by using two different approaches. In the first approach the MFA-methods from industrial ecology were applied to agriculture, whereas the other is based on the food consumption scenarios. The two approaches were used in order to capture some of the impacts of dietary changes and of changes in production mode on the environment. The methods were applied at levels ranging from national to sector and local levels. Through the supply-demand approach, the viewpoint changed between that of food production to that of food consumption. The main data sources were official statistics complemented with published research results and expertise appraisals. MFA approach was used to define the system boundaries, to quantify the material flows and to construct eco-efficiency indicators for agriculture. The results were further elaborated for an input-output model that was used to analyse the food flux in Finland and to determine its relationship to the economy-wide physical and monetary flows. The methods based on food consumption scenarios were applied at regional and local level for assessing feasibility and environmental impacts of relocalising food production. The approach was also used for quantification and source allocation of greenhouse gas (GHG) emissions of primary production. GHG assessment provided, thus, a means of crosschecking the results obtained by using the two different approaches. MFA data as such or expressed as eco-efficiency indicators, are useful in describing the overall development. However, the data are not sufficiently detailed for identifying the hot spots of environmental sustainability. Eco-efficiency indicators should not be bluntly used in environmental assessment: the carrying capacity of the nature, the potential exhaustion of non-renewable natural resources and the possible rebound effect need also to be accounted for when striving towards improved eco-efficiency. The input-output model is suitable for nationwide economy analyses and it shows the distribution of monetary and material flows among the various sectors. Environmental impact can be captured only at a very general level in terms of total material requirement, gaseous emissions, energy consumption and agricultural land use. Improving environmental performance of food production requires more detailed and more local information. The approach based on food consumption scenarios can be applied at regional or local scales. Based on various diet options the method accounts for the feasibility of re-localising food production and environmental impacts of such re-localisation in terms of nutrient balances, gaseous emissions, agricultural energy consumption, agricultural land use and diversity of crop cultivation. The approach is applicable anywhere, but the calculation parameters need to be adjusted so as to comply with the specific circumstances. The food consumption scenario approach, thus, pays attention to the variability of production circumstances, and may provide some environmental information that is locally relevant. The approaches based on the input-output model and on food consumption scenarios represent small steps towards more holistic systemic thinking. However, neither one alone nor the two together provide sufficient information for sustainabilizing food production. Environmental performance of food production should be assessed together with the other criteria of sustainable food provisioning. This requires evaluation and integration of research results from many different disciplines in the context of a specified geographic area. Foodshed area that comprises both the rural hinterlands of food production and the population centres of food consumption is suggested to represent a suitable areal extent for such research. Finding a balance between the various aspects of sustainability is a matter of optimal trade-off. The balance cannot be universally determined, but the assessment methods and the actual measures depend on what the bottlenecks of sustainability are in the area concerned. These have to be agreed upon among the actors of the area

Flow of an electrically conducting non-newtonian fluid between two rotating coaxial cones in the presence of external magnetic field due to an axial current

Bhatnagar and Rathna (Quar. Journ. Mech. Appl. Maths., 1963,16, 329) investigated the flows of Newtonian, Reiner-Rivlin and Rivlin-Ericksen fluids between two rotating coaxial cones. In case of the last two types of fluids, they predicted the breaking of secondary flow field in any meridian plane. We find that such breaking is avoided by the application of a sufficiently strong azimuthal magnetic field arising from a line current along the axis of the cones.