Showing papers by "Kumbakonam R. Rajagopal published in 1993"

Steady flows of non‐Newtonian fluids past a porous plate with suction or injection

Abstract: The problem of the steady flow of three classes of non-linear fluids of the differential type past a porous plate with uniform suction or injection is studied. The flow which is studied is the counterpart of the classical ‘asymptotic suction’ problem, within the context of the non-Newtonian fluid models. The non-linear differential equations resulting from the balance of momentum and mass, coupled with suitable boundary conditions, are solved numerically either by a finite difference method or by a collocation method with a B-spline function basis. The manner in which the various material parameters affect the structure of the boundary layer is delineated. The issue of paucity of boundary conditions for general non-linear fluids of the differential type, and a method for augmenting the boundary conditions for a certain class of flow problems, is illustrated. A comparison is made of the numerical solutions with the solutions from a regular perturbation approach, as well as a singular perturbation.

Lubrication With Binary Mixtures: Liquid-Liquid Emulsion

Abstract: There are numerous instances of technical importance in which multicomponent lubricants are utilized either by design or by necessity. In many of these cases one of the components is a liquid while the other component is a gas, as in squeeze film dampers during high frequency operation, or both components are liquids, as in the oil-water emulsion used in metal forming processes. In this paper our objective is to develop a self-consistent theory of hydrodynamic lubrication with bicomponent, liquid-liquid lubricants. The basic scientific method utilized is the continuum theory of mixtures. In this, first instance we test the model on journal bearings lubricated with water-in-oil and oil-in-water emulsions.

Lubrication With Binary Mixtures: Bubbly Oil

Abstract: Mixtures do not exhibit Newtonian behavior even when their individual components themselves are Newtonian, and thus classical lubrication theory is not applicable to bearings lubricated with mixtures. Our objective is to extend hydrodynamic lubrication theory to lubrication with mixtures of a Newtonian liquid and an ideal gas. To this end, we make use of the theory of interacting continua and derive two coupled non-linear equations in component densities. The extended theory is tested on finite journal bearings: our results of pressure distribution show good qualitative agreement with the experimental data of Braun et al

A boundary value problem in groundwater motion analysis — comparison of predictions based on darcy’s law and the continuum theory of mixtures

Abstract: The classical problem of the radial flow to a well in a confined horizontal aquifer is solved using two theories: (1) when the flow is based on Darcy’s law, and (2) when the flow is based on equations of the Continuum Theory of Mixtures. The latter reduce to Darcy’s law when the inertia of the fluid can be neglected, and when the viscosity of the fluid does not enter into the expression for the partial stress for the fluid. A comparison of the two solutions shows that there are conditions when Mixture Theory could predict results that provide a significant departure from those predicted by Darcy’s Law. In this paper we delineate the extent of validity of Darcy’s law, within the context of a more general theoretical framework. The results of our work indicate that Darcy’s law is indeed quite good for low flow rates for a fluid like water. However this is not the case for dense fluids, say oils or effluents, due to the inclusion of inertial effects in the equations of motions.

Lubrication With Binary Mixtures: Liquid-Liquid Emulsion in an EHL Conjunction

Abstract: Oil-in-water and water-in-oil emulsions are often employed as lubricants In many applications of emulsion lubricants both the deformation of the bounding solid surfaces and the pressure dependence of the viscosity of the lubricant contribute essentially to performance, thus defining lubrication in the elastohydrodynamic (EHD) mode In this paper we investigate lubrication with liquid-liquid binary mixtures of two Newtonian fluids in an EHD conjunction, and discuss the effect of varying the parameters of the problem on pressure, film thickness and volume fraction distribution

Lubrication With Emulsion in Cold Rolling

Abstract: Petroleum oil-in-water emulsion, where water is the continuous phase, is often employed under circumstances where the high heat capacity of water is beneficial while the poor lubricating properties of an oil-in-water emulsion can be tolerated Usage includes cold-rolling but also some hot rolling applications However, emulsions do not exhibit Newtonian behavior even when their individual components themselves are Newtonian, thus classical lubrication theory is not valid for these applications In this paper we employ the extended Reynolds equations of Al-Sharif et al, derived for binary mixture lubricants, to study strip-rolling lubricated with oil-in-water emulsion We are able to predict several experimentally observed phenomena such as oil-pooling, enhancement of oil-pooling with increased strip yield stress and with increased roller speed

Flow of an Oldroyd-B fluid between intersecting planes

Abstract: We have studied the non-radial flow of an Oldroyd-B fluid between intersecting planes. The effects of the Reynolds number Re and the elastic number σ are carefully delineated. Our results agree with the results of Strauss (Acta Mechanica, 21 (1975) 141) when σ = 0. In addition to studying the problem when σ ≠ 0, we carried out studies for values of Reynolds number which are two orders of magnitude larger than in previous studies. We find that there is an interesting structural change in the streamline patterns with changes in the Reynolds and Weissenberg numbers which was not observed in the earlier studies, and this has been documented for the first time.

Unsteady diffusion of fluids through a non-linearly elastic cylindrical annulus

Abstract: The unsteady radial diffusion motions of an incompressible fluid through an isotropic and transversely isotropic non-linearly elastic cylindrical annulus are studied by using the recent theory developed by Tao et al. [Mathematical Models and Methods in Applied Sciences 1 (1991)]. As the fluid diffuses through the solid, ahead of it there is a pure solid while behind the diffusing front there is a mixture of a fluid and a solid. Governing equations for both the constituents, within the content of the theory of mixture, are used in the mixture region. On the diffusing front, the evolution equations are used based on the previous work of Tao et al. [Mathematical Models and Methods in Applied Sciences 1 (1991)]. The problems are solved numerically using a finite difference method.

Flow of a non-Newtonian fluid between intersecting planes of which one is moving

Abstract: We study the flow of an Oldroyd-B fluid between two intersecting plates, one of which is fixed and the other moving along its plane. This problem was first considered by Strauss (1975) for the Maxwell fluid using a similarity transformation. We find that even in the case of a Maxwell fluid, which can be obtained by setting a specific parameter, say σ, in the Oldroyd-B model to zero, our results disagree with those of Strauss (1975). We find that circulating cells are present, adjacent to the stationary plate while Strauss (1975) finds them adjacent to the moving plate. We also delineate the effect of the coefficient σ, which is a measure of the elasticity of the flow, on the flow pattern. We find that an increase in the elastic parameter reduces the cellular structure.

Proportional shearing of a non-linear viscoelastic layer

Abstract: We study the non-linear shearing of a layer of a non-linear viscoelastic material where a boundary is sheared such that the displacement or the shear stress is proportional to the coordinate along that direction. Two boundary value problems are solved numerically, one with deformation prescribed at the boundary and the other with the traction prescribed. The numerical procedure is such that at each time step, the problem is equivalent to a system of two coupled non-linear partial integro-differential equations for time and the displacement functions. These equations are then integrated numerically.

Flow of granular materials down an inclined plane

Abstract: The mechanics of flowing granular materials such as coal, sand, fossil-fuel energy recovery, metal ores, etc., and their flow characteristics have received considerable attention in recent years because it has relevance to several technological problems. In a number of instances these materials are also heated prior to processing, or cooled after processing. The governing equations for the flow of granular materials taking into account the heat transfer mechanism are derived using the continuum model proposed by Rajagopal and Massoudi (1990). For a fully developed flow of granular materials down an inclined plane, these equations reduce to a system of coupled ordinary differential equations. The resulting boundary value problem is solved numerically and the results are presented. For a special case, it is possible to obtain an analytic solution; this is given in the Appendix A of this report.