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.

Analysis of gradually and spatially varied flow in sand-bed channels

Seepage through a sand bed affects the channel hydrodynamics, which in turn alters channel stability. Thus, the effect of seepage on its hydrodynamic parameters needs to be ascertained. The present work analyses spatially varied flow of a sand-bed channel subjected to seepage in the downward direction through a sand bed. Numerically calculated flow profiles affected by seepage have been verified using experimental observations. The present work also analyses the friction slope, velocity and bed shear stress variations along the channel for both seepage and no-seepage conditions. It was found that the downward seepage-induced channel flow has larger friction slope and bed shear stress than that of no-seepage.

Instability of the self-similar flow into a cavity

In this paper we have investigated the instability of the self-similar flow behind the boundary of a collapsing cavity. The similarity solutions for the flow into a cavity in a fluid obeying a gas law p = Kργ, K = constant and 7 ≥ γ > 1 has been solved by Hunter, who finds that for the same value of γ there are two self-similar flows, one with accelerating cavity boundary and other with constant velocity cavity boundary. We find here that the first of these two flows is unstable. We arrive at this result only by studying the propagation of disturbances in the neighbourhood of the singular point.

Flow of a maxwell liquid fluid between two rotating coaxial cones having the same vertex

We consider the secondary flows arising in the motion of a Maxwell fluid between two rotating coaxial cones having the same vertex. We find that in any meridian plane passing through the common axis of the cones, the flow field is divided into two regions. Such a division of flow field was first reported by Bhatnagar and Rathna.

Steady laminar flow with suction or injection and heat transfer through porous pipe

Following the method due to Bhatnagar (P. L.) [Jour. Ind. Inst. Sic., 1968, 1, 50, 1], we have discussed in this paper the problem of suction and injection and that of heat transfer for a viscous, incompressible fluid through a porous pipe of uniform circular cross-section, the wall of the pipe being maintained at constant temperature. The method utilises some important properties of differential equations and some transformations that enable the solution of the two-point boundary value and eigenvalue problems without using trial and error method. In fact, each integration provides us with a solution for a suction parameter and a Reynolds number without imposing the conditions of smallness on them. Investigations on non-Newtonian fluids and on other bounding geometries will be published elsewhere.

Heat transfer in rarefied couette flow on the basis of discrete ordinate method

The method of discrete ordinates, in conjunction with the modified "half-range" quadrature, is applied to the study of heat transfer in rarefied gas flows. Analytic expressions for the reduced distribution function, the macroscopic temperature profile and the heat flux are obtained in the general n-th approximation. The results for temperature profile and heat flux are in sufficiently good accord both with the results of the previous investigators and with the experimental data.

Correlation between terrestrial heat flow and thermal conductivity

The significant correlation coefficient between the terrestial heat flow and thermal conductivity computed from the continental heat flow data by Horai and Nur [1]2) may be explained as a natural consequence of terrestrial heat flow through a random medium. The theory predicts a value of 0.40 for the correlation coefficient. A simple statistical test shows that the majority of the computed coefficients belong to the statistical population whose mean is equal to the theoretical correlation coefficient. There are, however, a few observations of unsually high correlation coefficient which cannot be explained by the above hypothesis.

Flow of a power law fluid in an annulus with porous walls

The steady flow of a power law fluid in annuli with porous walls is investigated. The solution for the axial velocity component is obtained as a power series in terms of the cross flow Reynolds number, the first term of the series giving the solution for the case of the solid wall annulus. The cross flow is restricted to be such that the rate of injection of fluid at one wall of the annulus is equal to the rate of suction at the other wall and also we have considered only very small values of the cross flow velocity. The velocity profiles are drawn for different values of n and for different gaps and the results are discussed in detail. The behaviour of the average flux, in different eases is also discussed.

Compressible axially symmetric laminar boundary layer flow in the stagnation region of a blunt body in the presence of magnetic field

In this paper, the steady laminar viscous hypersonic flow of an electrically conducting fluid in the region of the stagnation point of an insulating blunt body in the presence of a radial magnetic field is studied by similarity solution approach, taking into account the variation of the product of density and viscosity across the boundary layer. The two coupled non-linear ordinary differential equations are solved simultaneously using Runge-Kutta-Gill method. It has been found that the effect of the variation of the product of density and viscosity on skin friction coefficient and Nusselt number is appreciable. The skin friction coefficient increases but Nusselt number decreases as the magnetic field or the total enthalpy at the wall increases