Herschel–Bulkley fluid

About: Herschel–Bulkley fluid is a research topic. Over the lifetime, 1946 publications have been published within this topic receiving 49318 citations.

Stability of plane Poiseuille flow of a fluid with pressure-dependent viscosity

Abstract: We study the linear stability of a plane Poiseuille flow of an incompressible fluid whose viscosity depends linearly on the pressure. It is shown that the local critical Reynolds number is a sensitive function of the applied pressure gradient and that it decreases along the channel. While in the limit of small pressure gradients conventional results for a pressure-independent Newtonian fluid are recovered, a significant stabilisation of the flow and an elongation of the critical disturbance wavelength are observed when the longitudinal pressure gradient is increased. These features drastically distinguish the stability characteristics of a piezo-viscous flow from its pressure-independent Newtonian counterpart.

An Inclined Plume

Abstract: The equations of motion can be arranged for the flow of a heavy fluid down an inclined plane, with a slightly lighter fluid at rest above the heavy fluid. The layer of heavy fluid has low initial momentum and the layer itself is then compared with the total depth of the flow. The equation is integrated and comparison of orders of magnitude of the quantities involved allow the equation to be simplified. As a first approximation the flow is assumed to be self-preserving, and this assumption permits the equations to be solved. The characteristic velocity, Um, at any section is shown to be constant; the characteristic density at any section is proportional to 1/x; the coefficient of wall friction, Cf, is constant and the Richardson number, Ri, is constant. Published experimental work is used to verify these results.

Observations of Blood Flow in an Inclined Improved Generalized Multiple Stenosed Artery Influenced by a Magnetic Field

Abstract: In the current mathematical model magnetic field, the inclination of the artery has been developed to understand the effect on blood flow. This model also reveals the effect of core velocity, wall shear stress and volumetric flow rate on the wall of the artery under the stenotic conditions. Blood has been taken as a Herschel-Bulkley fluid in which several stenoses are taken at equal distances in an inclined artery. Using appropriate boundary conditions, analytical expressions have been fulfilled for all these flow characteristics. The results are shown numerically and graphically, as well as comparative studies have been presented in addition to the current results. This information can be valuable in developing the latest diagnosis for the treatment of atherosclerotic artery, the progress of equipment and the development of medicines.

Some New Results in the Theory of Fractional Second Grade and Ordinary Oldroyd-B Fluids

Abstract: In this thesis some results regarding the flow behavior of second grade fluid with fractional derivatives and ordinary Oldroyd-B fluid under different circumstances have been studied.Firstly, some basic concepts regarding fluid motion and integral transforms have been discussed.Then the fluid motion of fractional second grade and ordinary Oldroyd-B fluids through a cylinder and annulus is studied. In chapter 2, the motion of fractional second grade fluid through an infinite circular cylinder has been studied.After time t = 0+ the fluid motion is produced by rotating the circular cylinder about its axis.Laplace and finite Hankel transforms are used to find exact solutions.The similar solutions for Newtonian and ordinary second grade fluids are obtained as limiting cases of general solutions by making → 1 and 1 → 0, respectively → 1 .Chapter 3 intends to establish exact solutions for the unsteady flow of a fractional second grade fluid between two infinite coaxial circular cylinders.The general expressions for velocity and shear stress are obtained by using Laplace and finite Hankel transforms.The motion of the fluid is produced by the inner cylinder which is rotating around its axis due to a time-dependent torque per unit length 2R1at2.The solutions that have been obtained satisfy all imposed initial and boundary conditions. For → 1, respectively → 1 and 1 → 0, the corresponding solutions for ordinary second grade and Newtonian fluids, performing the same motion, are obtained as limiting cases. In chapter 4 the unsteady helical flow of an Oldroyd-B fluid through an infinite circular cylinder is studied.The motion of the fluid is produced by cylinder that, after time t = 0+, is subject to both torsional and longitudinal time dependent shear stresses.The general solutions are presented in series form in terms of Bessel functions J0(•), J1(•) and J2(•), and satisfy all imposed initial and boundary conditions.The corresponding solutions for Newtonian, second grade and Maxwell fluids are obtained as limiting cases of general solutions.Finally, the obtained solutions are compared by graphical illustrations and the influence of material parameters on the fluid motion is also underlined. Chapter 5 concerns with the unsteady Taylor-Couette flow of an Oldroyd-B fluid in an annulus due to a time-dependent torque applied to the inner cylinder.Motion is studied by means of finite Hankel transforms.The exact solutions are presented in series form in terms of usual Bessel functions, satisfy both the governing equations, and all imposed initial and boundary conditions.Similar solutions for Newtonian, second grade and Maxwell fluids performing the same motion are obtained as limiting cases of general solution.Finally, some characteristics of the fluid motion, as well as the influence of pertinent parameters on the behavior of the fluid motion, analyzed by graphs.

Linear hydraulic fracture with tortuosity: Conservation laws and fluid extraction

Abstract: Fluid extraction from a pre-existing two-dimensional hydraulic fracture with tortuosity is investigated. The tortuous fracture is replaced by a symmetric open fracture without asperities (deformations) on opposite crack walls but with a modified Reynolds flow law and a modified crack law (the linear crack law). The Perkins–Kern–Nordgren approximation is made in which the normal stress at the fracture walls is proportional to the half-width of the symmetric model fracture. By using the multiplier method two conservation laws for the non-linear diffusion equation for the half-width are derived. Two analytical solutions generated by the Lie point symmetries associated with the conserved vectors are obtained. One is the known solution for a fracture with constant volume. The other is new and is the limiting solution for fluid extraction. A jet of fluid escapes from the fracture entry and the volume of the fracture decreases. There is a dividing cross-section between fluid flowing towards the fracture entry and fluid flowing towards the fracture tip which explains why the length of the fracture continues to grow as fluid is extracted. As tortuosity increases the position of the dividing cross-section moves closer to the entry. A numerical solution is presented for the other cases of fluid extraction. Comparison of the fluid flux for different operating conditions within the fluid extraction region shows that the limiting solution yields the maximum rate of fluid extraction from the fracture. As the fracture becomes more tortuous its length becomes less dependent on the operating conditions at the fracture entry. For fluid extraction working conditions close to the constant volume operating condition the width averaged fluid velocity increases approximately linearly along the whole length of the fracture. For these working conditions, an approximate analytical solution for the half-width for fluid extraction, which agrees well with the numerical solution, is derived by assuming that the width averaged fluid velocity increases exactly linearly along the fracture.