350 research outputs found
Fluids of differential type: Critical review and thermodynamic analysis
No full textDunn, J.E.; Rajagopal, K.R.. (1992). Fluids of differential type: Critical review and thermodynamic analysis. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4423
Shear flows of a new class of power-law fluids
No full textWe consider the flow of a class of incompressible fluids which are constitutively
defined by the symmetric part of the velocity gradient being a function, which can be nonmonotone,
of the deviator of the stress tensor. These models are generalizations of the
stress power-law models introduced and studied by J. Málek, V. Pr°uša, K.R. Rajagopal :
Generalizations of the Navier-Stokes fluid from a new perspective. Int. J. Eng. Sci. 48
(2010), 1907–1924. We discuss a potential application of the new models and then consider
some simple boundary-value problems, namely steady planar Couette and Poiseuille flows
with no-slip and slip boundary conditions. We show that these problems can have more
than one solution and that the multiplicity of the solutions depends on the values of the
model parameters as well as the choice of boundary conditions.K.R. Rajagopal thanks the National Science Foundationhttp://link.springer.com/journal/10492hb201
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A theoretical and numerical study of the flow of granular materials. Quarterly report, April 1, 1992--June 30, 1992
No full textLinearized stability equations for flow of granular materials down an inclined plane are derived for a continuum model [cf. Goodman and Cowin (1971), Rajagopal and Massoudi (1990)]. The basic flow exhibits multiplicity of solutions, one in which the volume fraction increases monotonically from the inclined plane to the free surface, and the other in which the volume fraction increases monotonically. Solutions to the basic equations were presented in the previous report. Next, we have to solve the stability equations, numerically
On modeling the response of the synovial fluid: Unsteady flow of a shear-thinning, chemically-reacting fluid mixture
No full textAbstractWe study the flow of a shear-thinning, chemically-reacting fluid that could be used to model the flow of the synovial fluid. The actual geometry where the flow of the synovial fluid takes place is very complicated, and therefore the governing equations are not amenable to simple mathematical analysis. In order to understand the response of the model, we choose to study the flow in a simple geometry. While the flow domain is not a geometry relevant to the flow of the synovial fluid in the human body it yet provides a flow which can be used to assess the efficacy of different models that have been proposed to describe synovial fluids. We study the flow in the annular region between two cylinders, one of which is undergoing unsteady oscillations about their common axis, in order to understand the quintessential behavioral characteristics of the synovial fluid. We use the three models given in Hron et al. [J. Hron, J. Málek, P. Pustějovská, K.R. Rajagopal, On the modeling of the synovial fluid, Adv. in Tribol. 2010 (2010) 12 pages, doi:10.1155/2010/104957. Article ID 104957] to study the problem, by appealing to a semi-inverse method. The assumed structure for the velocity field automatically satisfies the constraint of incompressibility, and the balance of linear momentum is solved together with a convection-diffusion equation. The results are compared to those associated with the Newtonian model. We also study the case in which an external pressure gradient is applied along the axis of the cylindrical annulus
Secondary flows due to axial shearing of a third grade fluid between two eccentrically placed cylinders
No full textIn general, purely axial flows of non-Newtonian fluids are not possible in straight pipes of noncircular cross section. The secondary flow pattern for the flow of various non-Newtonian fluids in pipes of non-circular cross section has been studied by many authors. The method which is used is invariably a perturbation technique using either the driving force for the problem or one of the material constants as the parameter for the expansion. The former implies that the solution is a perturbation of the state of rest, while the latter implies that the null solution corresponds to the Newtonian solution. However, in many problems of practical relevance, flows of a particular non-Newtonian fluid, with specific values for the non-Newtonian parameters (not necessarily small), take place under a finite driving force, making such approaches of dubious value. For instance, as a consequence of perturbing in the driving force, the secondary flows appear only at the fourth order. In this paper we use a perturbation technique in which the perturbation parameter is a geometric measure of the departure from the geometry in which rectilinear flow is possible. Such an approach allows one to study perturbation of flows which are not the null state, and this, in turn, leads to secondary flows at first order
Bodies described by non-monotonic strain-stress constitutive equations containing a crack subject to anti-plane shear stress
No full textIn this paper the state of stress and strain close to sharp cracks in bodies subjected to an anti-plane state of stress is studied within the context of a non-monotonic strain-stress relation within the context of a generalization of the Cauchy theory of elasticity, providing an exact analytical solution to the problem. A discussion is provided to highlight the main features of stress and strain distributions, and the implications of the new theory for fracture assessments. In particular, it is proved that the intensity of the complete stress field can be expressed as a function of the Stress Intensity Factor K III , as in the case of conventional linearized elasticity theory, thus promoting a K based-approach to the fracture of elastic solids obeying a constitutive relation wherein the linearized strain is expressed as a non-linear function of the Cauchy stres
Linear stability of Hagen–Poiseuille flow in a chemically reacting fluid
No full textIn this short paper we study the linearized stability of the flow of a chemically reacting fluid in a cylindrical pipe, under the assumption that the length of the pipe is far greater than its diameter. The fluid models that are considered have relevance to the flow of both polymeric liquids that are capable of undergoing chemical reactions and biological fluids such as the synovial fluid whose viscosity changes due to the concentration of the hyaluronan. The viscosity of the class of fluids that we consider can increase or decrease due to the concentration of the chemical that is being carried by the fluid and it can also shear thin or shear thicken. We non-dimensionalize the equations governing the motion of the fluid and then carry out an approximation wherein we retain terms that are of order unity in the Reynolds number and Péclet number. We further simplify the problem by seeking a special semi-inverse solution, in the same spirit as that which is used in the study of classical Hagen–Poiseuille flow, and look for solutions for the velocity field and the concentration that vary only with the radial coordinate. Under the above mentioned approximation, one can obtain an exact solution for the basic flow which then allows us to analytically consider the stability of the base flow to sufficiently small disturbances. On the basis of earlier studies of such fluids in the modeling of biological fluids, especially the synovial fluid, we consider two types of variation of the viscosity with the concentration. We find that flows in the cylindrical pipe, within the context of our approximation, are stable to sufficiently small disturbances, for both variations of the viscosity that are considered
Couette flow with frictional heating in a fluid with temperature and pressure dependent viscosity
No full textThis study investigates the effects of variable viscosity and frictional heating on the laminar flow in a horizontal channel having a wall at rest and a moving wall subjected to a prescribed shear stress. The wall at rest is thermally insulated, while the moving wall is kept at a uniform temperature. This investigation concerns fluids whose viscosity depends exponentially on the pressure and temperature. An appropriate approximation is introduced to analyze the interplay between the dependence of viscosity on the pressure and temperature and the viscous dissipation. It is shown that the nonlinear term in the equation for the balance of energy representing the frictional heating may lead to the existence of dual solutions of the boundary value problem for fixed values of the material parameters that characterize the fluid. The results obtained are compared with those predicted by the generalization of the Oberbeck–Boussinesq approximation for a fluid with pressure and temperature dependent viscosity. It is found that the results for the approximation carried out in this paper and those that stem from the Oberbeck–Boussinesq approximation are markedly different
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