We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we use the (3+1) formalism to formulate the post-Newtonian approximation for the perfect fluid. As an application we show the method for constructing the equilibrium configuration of nonaxisymmetric uniformly rotating fluid. We also discuss the grav...

INTRODUCTION This paper represents the numerical simulation of blood flow in the circle of Willis (CoW). Circle of Willis is responsible for the oxygenated blood distribution into the cerebral mass. To investigate the blood behavior, two Newtonian and non-Newtonian viscosity models were considered and the results were compared under steady state conditions. METHODS Methodologically, the arter...

The flow of blood in narrow arteries with bell-shaped mild stenosis is investigated that treats blood as non-Newtonian fluid by using the K-L model. When skin friction and resistance of blood flow are normalized with respect to non-Newtonian blood in normal artery, the results present the effect of stenosis length. When skin friction and resistance of blood flow are normalized with respect to N...

Post-Newtonian expansions of the Brill-Lindquist and Misner-Lindquist solutions of the timesymmetric two-black-hole initial value problem are derived. The static Hamiltonians related to the expanded solutions, after identifying the bare masses in both solutions, are found to differ from each other at the third post-Newtonian approximation. By shifting the position variables of the black holes t...

in this paper, changes of casson non-newtonian fluid velocity profile, for different distribution of porosity, have been investigated. for distribution of porosity, fixed, radial and exponential variations has been considered. for all three states, brinkman model has been used as momentum equation. since the casson fluid is a good model for blood, this analysis can be used in studying about cho...

Abstract The effects of a chemical reaction and radiative heat flux in nonlinear mixed thermo-solutal convection flow viscoelastic nanoliquid from stretchable surface are investigated theoretically. Newtonian heating is also considered. upper-convected Maxwell (UCM) model deployed to represent the non-Newtonian characteristics. includes influence thermal radiation that simulated via an algebrai...

In this paper, 3D particle focusing in a straight channel with asymmetrical expansion-contraction cavity arrays (ECCA channel) is achieved by exploiting the dean-flow-coupled elasto-inertial effects. First, the mechanism of particle focusing in both Newtonian and non-Newtonian fluids was introduced. Then particle focusing was demonstrated experimentally in this channel with Newtonian and non-Ne...

The stationary flow of blood in a two-dimensional model of the bifurcation of the human carotid artery is simulated numerically using a finite element method. The Reynolds number is taken as equal to 300, corresponding to the value during the end-diastolic phase of the heart cycle. As constitutive equations, the Newtonian model and the non-Newtonian power-law and Casson models are used. The cho...

We study the non–linear dynamics of self–gravitating irrotational dust in a general relativistic framework, using synchronous and comoving (i.e. Lagrangian) coordinates. All the equations are written in terms of a single tensor variable, the metric tensor of the spatial sections orthogonal to the fluid flow. This treatment allows an unambiguous expansion in inverse (even) powers of the speed of...

The explosive viscous liquid becomes inject to warhead by discharge system. The injection device is consisted of a piston to move down and leads the viscous fluid through the cylindrical pipe towards the end of the duct. Then the viscous fluid leads into a convergent path that will be injected to the warhead or other injection equipment. In this project, the path of viscous fluid flow is divide...