Narrow Results

The pulsatile flow characteristics of a power law fluid in a channel filled with a homogeneous porous medium are investigated by employing the Darcy–Brinkman–Forchheimer model. Finite element method in conjunction with β-family of time discretization schemes for parabolic equation have been used to numerically solve the model for analyzing the flow. Influence of various parameters, such as power law index (n), Darcy number (Da*), Forchheimer coefficient (Γ), pulsatile amplitude parameter (A), and Womerseley parameter (α), on the flow properties have been analyzed. Increasing Γ or decreasing Da* leads to decrease in velocities and shear stress for all values of n.

Unsteady pulsatile flow of blood through a porous-saturated, tapered and overlapping stenotic artery in the presence of magnetic field is examined theoretically and computationally. The power law constitutive model is employed to simulate hameo-rheological characteristics. The governing equation is derived assuming the flow to be unsteady, laminar, uni-directional and one-dimensional (1D). A robust, finite difference method is employed for the solution of the governing equation, subject to appropriate boundary conditions. Based on this solution, an extensive quantitative analysis is performed to analyze the effects of blood rheology, body acceleration, magnetohydrodynamic parameter, permeability parameter and arterial geometrical parameters of stenosis on various quantities of interest such as axial velocity, flow rate, resistance impedance and wall shear stress. The computations demonstrate that velocity, flow rate and shear stress increase while resistance to flow decreases with greater permeability parameter. Additionally, the effects of magnetic field are observed to be converse to those of permeability i.e., flow is decelerated and resistance is increased, demonstrating the powerful utility of exploiting magnetic fields in hemodynamic flow control (e.g., intra-corporeal surgical procedures). Furthermore, the size of trapped bolus of fluid is also found to be reduced for large values of the permeability parameter indicating that progressively more porous media circumvent bolus growth.

In this paper, effects of stationary contraction on mixing and transport of a non-Newtonian fluid in the small intestine are analyzed theoretically. A semi-analytical method is developed to solve the governing equations of fluids flow in the intestine using lubrication theory. Results indicate that the stationary contraction helps in conferring two functions – (1) shearing of the contents, and (2) bidirectional transport over a short distance. The flow resulting from contraction is symmetric and occurs in both the directions; however, they do not lead to a net flow rate in one direction. The amount of shearing developed during such flows is reflective of their mixing ability. The effort of such peristalsis is largely determined by the flow behavior index; where energy requirements of developing similar shearing forces are higher for dilatants and lower for pseudoplastics. Flow is sensitive to frequency of contraction, luminal occlusion and wavelength of the contraction.

A direct difference method has been developed for Non-Newtonian power law fluids to solve the simultaneous non-linear partial differential equations of melt spinning, and to determine the critical draw ratio for draw resonance. The results show that for shear thin fluids, the logarithm of the critical draw ratio has a well defined linear relationship with the power index for isothermal and uniform tension melt spinning. When the power index approaches zero, the critical draw ratio points at unity, indicating no melt spinning can be processed stably for such fluids. For shear thick fluids, the critical draw ratio increases in a more rapid way with increasing the power index.