The effect of boundary slip on the transient pulsatile flow of a modified second-grade fluid

We investigate the effect of boundary slip on the transient pulsatile fluid flow through a vessel with body acceleration. The Fahraeus-Lindqvist effect, expressing the fluid behavior near the wall by the Newtonian fluid while in the core by a non-Newtonian fluid, is also taken into account. To describe the non-Newtonian behavior, we use the modified second-grade fluid model in which the viscosity and the normal stresses are represented in terms of the shear rate. The complete set of equations are then established and formulated in a dimensionless form. For a special case of the material parameter, we derive an analytical solution for the problem, while for the general case, we solve the problem numerically. Our subsequent analytical and numerical results show that the slip parameter has a very significant influence on the velocity profile and also on the convergence rate of the numerical solutions

Positive solutions of eigenvalue problems for a class of fractional differential equations with derivatives

By establishing a maximal principle and constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of a class of fractional differential equations is discussed. Some sufficient conditions for the existence of positive solutions are established

Transient Flows of Newtonian Fluid through a Rectangular Microchannel with Slip Boundary

We study the transient flow of a Newtonian fluid in rectangular microchannels taking into account boundary slip. An exact solution is derived by using the separation of variables in space and Fourier series expansion in time. It is found that, for different forms of driving pressure field, the effect of boundary slip on the flow behavior is qualitatively different. If the pressure gradient is constant, the flow rate is almost linearly proportional to the slip parameter ℓ when ℓ is large; if the pressure gradient is in a waveform, as the slip parameter ℓ increases, the amplitude of the flow rate increases until approaching a constant value when ℓ becomes sufficiently large

Solvability and asymptotic properties for an elliptic geophysical fluid flows model in a planar exterior domain

In this paper, we study the solvability and asymptotic properties of a recently derived gyre model of nonlinear elliptic Schrödinger equation arising from the geophysical fluid flows. The existence theorems and the asymptotic properties for radial positive solutions are established due to space theory and analytical techniques, some special cases and specific examples are also given to describe the applicability of model in gyres of geophysical fluid flows

Study of a Newtonian Fluid through Circular Channels with Slip Boundary Taking into Account Electrokinetic Effect

We study the slip flow of fluids driven by the combined effect of electrical force and pressure gradient. The underlying boundary value problem is solved through the use of Fourier series expansion in time and Bessel function in space. The exact solutions and numerical investigations show that the slip length and electrical field parameters have significant effects on the velocity profile. By varying these system parameters, one can achieve smooth velocity profiles or wave form profiles with different wave amplitude and frequency. This opens the way for optimizing the flow by choosing the slip length, the electrical field, and electrolyte solutions

An exponentially fitted enthalpy control volume algorithm for coupled fluid flow and heat transfer

This paper develops an efficient numerical method for solving the coupled fluid flow and heat transfer with solidification problem. The governing equations are the continuity equation, the Navier-Stokes equations and the convection-diffusion equation with a source term due to phase change. Fluid flow in the mushy region is modeled on the basis of Darcy's law for porous media and the solidification process is simulated using a single domain approach via the use of an enthalpy scheme for the convection-diffusion equation. The formulation of the numerical method is cast into the framework of the Petrov-Galerkin finite element method with a step test function across the control volume and locally constant approximation to the fluxes of heat and fluid. The formulation leads to the derivation of exponential interpolating functions for the control volume. The use of the exponentially fitted control volume improves the accuracy of results especially for problems with sharp interior or boundary layers such as the solution around the solidification front. The method is then illustrated through a numerical example

Effect of branchings on blood flow in the system of human coronary arteries

In this work, we investigate the behavior of the pulsatile blood flow in the system of human coronary arteries. Blood is modeled as an incompressible non-Newtonian fluid. The transient phenomena of blood flow through the coronary system are simulated by solving the three dimensional unsteady state Navier-Stokes equations and continuity equation. Distributions of velocity, pressure and wall shear stresses are determined in the system under pulsatile conditions on the boundaries. Effect of branching vessel on the flow problem is investigated. The numerical results show that blood pressure in the system with branching vessels of coronary arteries is lower than the one in the system with no branch. The magnitude of wall shear stresses rises at the bifurcation

Mathematical study of blood flow in the real model of the right coronary artery: Bypass graft system

In this paper, we study the blood flow in the real model of the right coronary artery -bypass graft system under the real pulsatile condition. The human blood is assumed as an incompressible Non-Newtonian fluid and its flow is modeled by the unsteady state Navier-Stokes equations and the continuity equation. The effect of the existence and intensity of a stenosis in the right coronary artery on the blood flow behaviour is investigated. Numerical simulations are also undertaken to analyse the influence of the bifurcation angle of the bypass graft on blood pressure, velocity distribution and wall shear rate