Showing papers on "Herschel–Bulkley fluid published in 1972"
TL;DR: In this paper, a new boundary condition, motivated by an analogy with phenomenological theories of turbulence, is proposed for plane or axisymmetric stagnation point flow of a micropolar fluid over a flat plate.
183 citations
TL;DR: In this paper, the authors present a theoretical study of the vibration and stability of a uniformly curved tube containing flowing fluid, where the assumption of the inextensibility of the tube is applied to derive the equation of motion.
Abstract: This paper presents a theoretical study of the vibration and stability of a uniformly curved tube containing flowing fluid. The assumption of the inextensibility of the tube is applied to derive the equation of motion. A solution for the natural frequency is obtained and numerical results are presented. The effects of flow velocity, fluid pressure, and the Coriolis force on the natural frequency are discussed. It is shown that when the flow velocity and fluid pressure exceed a certain value, the tube becomes subject to buckling‐type instability. Critical loads in terms of the flow velocity and fluid pressure are presented for fixed‐fixed, hinged‐hinged, and fixed‐hinged end conditions.
83 citations
TL;DR: The analysis of grease-lubricated rolling element bearings is presented in this article, where a theory for predicting roller film thickness based on the assumed flow model is derived, and the results show that grease will develop a larger film thickness than the base oil at first but the film thickness falls during rolling until it reaches a steady thickness usually lower than that of its base oil.
Abstract: The analysis of grease-lubricated rolling element bearings is presented. Experimentally determined flow curves for grease are found to be well correlated by the Herschel-Bulkley model flow equation. A theory for predicting roller film thickness based on the assumed flow model is derived. Experimental results show that grease will develop a larger film thickness than the grease base oil at first, but the film thickness falls during rolling until it reaches a steady thickness usually lower than that of its base oil. This effect is shown to depend on the degree of shear degradation of the grease, its resulting flow curve, and the temperature rise due to shear in the inlet. The grease yield stress is found to have a negligible effect on EHL performance. Presented at the 27th ASLE Annual Meeting in Houston, Texas, May 1–4, 1972
79 citations
TL;DR: In this article, a two-phase poroelastic material is taken as a model of a living bone in the sense that the osseous tissue is treated as a linear isotropic perfectly elastic solid, and the fluid substances filling the pores as a Newtonian viscous fluid.
Abstract: Two-phase poroelastic material is taken as a model of a living bone in the sense that the osseous tissue is treated as a linear isotropic perfectly elastic solid, and the fluid substances filling the pores as a Newtonian viscous fluid. Using Biot equations, derived in his consolidation theory, and assuming a plane state of strain governing equations involving fluid excess pressure and the stress function are derived. Laplace transform technique enables one to find explicit solutions for stresses. It is found that under a constant external load the bone element starts to creep, so that the viscoelastic properties of the adopted bone model seem to be in agreement with the experimental findings ofSedlin.
16 citations
TL;DR: In this article, a linearized stability analysis has been applied to a fluid flowing in a gravity field between horizontal planes in Couette flow under conditions such that the temperature of the bottom plane exceeds that of the top.
Abstract: A linearized stability analysis has been applied to a fluid flowing in a gravity field between horizontal planes in Couette flow under conditions such that the temperature of the bottom plane exceeds that of the top. It is shown that, under conditions likely to be encountered with polymer solutions, oscillatory instabilities will not be controlling. Criteria are offered for ascertaining when an analysis based upon a second-order fluid model may be expected to yield physically meaningful results. It is also shown that, for the fluid model considered, critical conditions for stability are not changed when disturbances which vary in the flow direction are substituted for those which are a function of the coordinate transverse to the flow.
8 citations
4 citations
TL;DR: In this article, the authors apply the variational principle of minimum entropy production with constant fluxes to the description of the stationary flow of a non-Newtonian viscous incompressible fluid between two parallel plates in relative motion.
Abstract: It has previously been shown by one of the authors that the variational principle of minimum entropy production with constant fluxes, established by Glansdorff and Prigogine, may be used in presence of convection by defining appropriately the generalized fluxes and forces. In this paper, this principle is applied to the description of the stationary flow of a non-Newtonian viscous incompressible fluid between two parallel plates in relative motion. The fluid is characterized by a viscosity decreasing exponentially with the temperature and by a thermal conductivity independent of the temperature.
3 citations
01 Jul 1972
TL;DR: In this paper, the behavior of a heat-conducting Rivlin-Ericksen fluid characterized by a set of constitutive equations involving the coupled dependence of stress and heat flux on temperature gradient and the first two Rivlin Ericksen tensors is considered.
Abstract: The Koh‐Eringen formulation of nonlinear thermoviscoelasticity is used to study the behavior of a heat‐conducting Rivlin‐Ericksen fluid characterized by a set of constitutive equations involving the coupled dependence of stress and heat flux on temperature gradient and the first two Rivlin‐Ericksen tensors. Slow steady‐state flow of the fluid under a small temperature gradient is considered. With the use of a perturbation technique, the basic equations and boundary conditions are derived for each increasing order of approximation. The first order equations are precisely those of a Newtonian fluid. Succeeding higher order corrections involve linear equations also although the results of preceding lower order approximations are used. The given boundary conditions are satisfied in the first order analysis. Homogeneous boundary conditions are then applicable for higher order corrections. Two specific problems are considered: (1) pressure flow of the fluid between two parallel plates in relative motion and at different constant temperatures; and (2) Couette‐helical flow in the annular region between two coaxial circular cylinders in relative translational velocity parallel to the axis and at two different constant temperatures. Numerical results are plotted for several Eckert numbers and other thermomechanical parameters.
2 citations
TL;DR: In this paper, the Navier-Stokes equations were solved for one class of unsteady axisymmetric two-dimensional rotational flows for the case of a line source or sink of constant intensity in the fluid.
Abstract: We obtain the solution of the Navier-Stokes equations for one class of unsteady axisymmetric two-dimensional rotational flows for the case of a line source or sink of constant intensity in the fluid.
TL;DR: In this paper, the existing theory of immiscible fluid flow is extended to the seepage with nonzero initial shear stress of viscoplastic media, and an analog of the Buckley-Leverett frontal-displacement theory is constructed.
Abstract: The existing theory of immiscible fluid flow is extended to the seepage with nonzero initial shear stress of viscoplastic media. An analog of the Buckley-Leverett frontal-displacement theory is constructed.
TL;DR: In this article, the authors considered an incompressible fluid flowing through a straight, circular tube whose walls are uniformly porous, and the loss of fluid through the wall is proportional to the mean static pressure in the tube.
Abstract: This paper considers an incompressible fluid flowing through a straight, circular tube whose walls are uniformly porous. The flow is steady and one dimensional. The loss of fluid through the wall is proportional to the mean static pressure in the tube. Several formulations of the wall shear stress are considered; these formulations were motivated by the results from Hamel's radial flow problem, boundary layer flows/and boundary layer suction profiles. For each of these formulations exact solutions for the mean axial velocity and the mean static pressure of the fluid are obtained. Sample results are plotted on graphs. For the constant wall shear stress problem, the theoretical solutions compare favorably with some experimental results.
TL;DR: In this paper, a fluid model with internal rotation (micropolar fluid) was proposed, which accounts for the proper rotation of the fluid molecules or particles suspended in the fluid, which makes possible a more detailed description of the behavior of fluids with complex internal structure.
Abstract: A fluid model with internal rotation (micropolar fluid) was proposed in [1–5], in which the general equations were derived and solutions of certain steady-state problems were presented (the equations presented in [5] and the steady-state solutions of these equations [5–7] differ somewhat from the corresponding results of [1–4, 8]). The essential feature of this model is the account for the proper rotation of the fluid molecules or particles suspended in the fluid, which makes possible a more detailed description of the behavior of fluids with complex internal structure—for example, suspensions and biological fluids [5, 8].