The case of steady-state thermal conductiv ' ity of bulk fluid has been d ealt with. Here, it is intended to generalize the result above to unsteady thermal conduction[r]

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The study undertaken in this article is to develop a reliable and comprehensive numerical modelling of **particle** **transport** in pulmonary **flow** based on the use of CFD-ACE code of commercial calculation. This code includes a **fluid** solver that solves the Navier-Stokes in a finite volume formulation. The CFD-GEOM software was used to create the 3D surfaces of the generic model geometry Weibel and thereby generate the tetrahedral mesh unstructured finite volume. The air **flow** is assumed laminar stationary (or unsteady only in bronchial models) and incompressible, the particles of diameter 5 micrometers are spherical and non-interacting. So we have successfully modelled the flows and the **transport** of particles in simple configurations (Model Weibel) and realistic configuration (rat lung) and what we can say is that the simulation , although expensive in terms of computer memory and time (specially for **particle** deposition), does not present insurmountable difficulties. As against obtaining a realistic geometry and the associated mesh generation remains a delicate stage.

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Chapter 6 Conclusions
This work describes small scale laboratory debris **flow** experiments. These experi- ments were carried out using both dry glass beads and glass beads in mixtures of water or glycerol, which were released from behind a lock gate to **flow** down an inclined flume. The main objective was to gain a better understanding of how **fluid**- **particle** interaction determines dynamic morphological features under the influence of **particle** size, roughness element diameter, interstitial **fluid** viscosity and solid volume fraction. The design base of the physical model was after Froude and Reyn- olds **particle** number scaling similarity criteria to achieve dynamic similarity with full-scale debris flows, to ensure that gravity forces are correctly scaled and turbu- lent **fluid**-**particle** interaction. A statistical method based on the standard deviation from the local average velocities obtained from the **Particle** Image Velocimetry tech- nique allowed systematically to define of the characteristic front position and of **flow** height. Low and high deviation from the local mean define the two co-existent re- gimes of non-fluctuating and intermittent collisional regions, define by the low and high deviation from the local mean, showed the influence of **flow** composition and roughness element diameter.

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Porous filters have been used for removing particles with success for many years [4]. Their wide application in air pollution control and in different technologies is due to their reliability in the separation of particles and relatively low operating cost. One of the most important issues in filtration is to know how media’s physical **properties** varied during operating conditions. Filter’s collectors (microscopic scale) are properly designed if, during a reasonably long filtering operation, filter’s collection efficiency is high and media’s **flow** resistance is below assumed value [5-6]. Description of **flow** field

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Abstract. Direct numerical simulation, facilitated by a spectral element method, is used to predict a multi-phase **fluid** **flow** through a channel at a shear Reynolds number of 300.
Following validation of single- and multi-phase **flow** results against other DNS predictions available in the literature, a channel **flow** is simulated utilising a Lagrangian **particle** tracker to model 300,000 particles with a diameter of 100 m, having a density ratio equivalent to that of water to glass, and a **particle** volume fraction of approximately 0.01%. This **flow** is calculated using multiple levels of coupling between the particles and the **flow**; one-way, two-way and four-way. The mean streamwise velocity of the **fluid** and the particles, along with the shear and normal stresses, are compared for the different coupling methods, with the differences between them analysed and, although small, they are found to be consistent across the channel. A second set of runs is performed using in excess of 2 million particles in order to facilitate a tenfold increase in the **particle** volume fraction, to 0.1%, with the particles expected in this case to have a greater impact upon the **properties** of the **fluid**. The statistics of the **fluid** and particles in these simulations are then compared with those from the simulation with a lower concentration of particles in order to determine the magnitude of the effect the particles have on the **fluid** in this **flow**. The effects of the different couplings on the **flow** are much greater in this case due to the increased number of particles affecting the **flow**. Also, the presence of the particles is seen to increase the turbulence levels of the **fluid**, especially in the streamwise direction. The accuracy of the simulations clearly increases with the level of coupling. However, the speed of the simulations decreases. One way of achieving decreased run times, for both volume fraction cases, is to use a faster stochastic version of the **particle** tracking code for four-way coupling.

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Consider a Newtonian liquid (of viscosity
Consider a Newtonian liquid (of viscosity μ μ and density and density ρ ρ ) in laminar **flow** down an ) in laminar **flow** down an inclined flat plate of length
inclined flat plate of length L L and width and width W W . The liquid flows as a falling film with . The liquid flows as a falling film with

uid to move rapidly. Permeability is aected by the nature of porous material and owing
uid, and factors like temperature, oil content, moisture content, gas content etc. A porous food matrix consists of interconnected pores through, which uid can move (Datta, 2007).
During frying of a porous food matrix, like potato, moisture, oil and heat **transport** occur with temperature and pressure changing spatially and temporally. Initially, the pressure increases rapidly after immersing the potato samples into the hot oil for frying. As potato discs contain higher moisture content in the beginning, the pressure rise is high initially due to rapid evaporation and build up of pressure (Sandhu, Bansal, & Takhar, 2013b). Later, the vapors escape the matrix and cause negative pressure inside the potato structure due to matrix's suction potential and capillary eects. The negative pressure causes increase of oil uptake during frying. After frying, when the cooling starts, the pressure decreases further.

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The study of **flow** in open channels in a physical and mathematical approach started by Leonardo Da Vinci in 1500, the Italian experimentalist and engineer who showed eddies in his art sketches. This great interest of water motion was then carried out by another scientist Galileo Galilei through experiments. Galileo‘s student, Benedetto Castelli, who explained the continuity law in more details in his book in 1628, was credited as being the founder of river hydraulics afterward. Later on in the seventeenth century, Sir Isaac Newton introduced the law of viscosity where the proportionality of shear stress and the velocity gradient was stated in his proposal. Newton‘s work was continued by Prandtl where the shear stress relationship was used to create assumptions for turbulent flows. However in the eighteenth century, Daniel Bernoulli and Leonard Euler derived mathematical description of **fluid** mechanics, the excellence of equations were not to its maximum until Navier-Stokes equations (N-S) were derived by Claude-Louis Navier in 1822 and George Stokes in 1845 (Graf 1984; Anderson Jr 2005; Wright and Crosato 2011).

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In the strive for more accurate models, we can for instance take into consideration fissures or fractures which may have been formed in a porous rock. A rock under stress has a possibility of cracking up, and fractures of far greater diameter and much straighter than the intricate pore network might arise. Intuitively, depending on the amount of fracturing, this can be a considerable factor when describing how a **fluid** flows through the rock, both when it comes to the **fluid** velocity and the preferential paths of the **fluid**. We will look closer at how we can include the effects of fractures when modelling a porous medium. We will examine both the movement of the **fluid** and the heat transfer processes that occur. Some fracture model comparisons have been made earlier, see for instance [55] where they take a closer look at three different models for **flow** and solute **transport**.

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up-section trends o f O-enrichment in vein calcite indicate dominantly upwards fluid transport in both systems. Across-strike around the D A B Fault, the most strongly "'O-deplet[r]

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a Institute of Aerodynamics, RWTH Aachen University, Aachen, Germany; b JARA Center for Simulation and Data Science, RWTH Aachen University, Aachen, Germany
ABSTRACT
The efficient removal of material debris by flushing is critical for the performance and the surface quality of the electrical discharge machining (EDM) manufacturing process. The **particle** concentra- tion alters the thermal, mechanical, and electrical **properties** of the **particle**–dielectricum suspension and affects the manufacturing process and the surface quality by inducing high thermal loads. For the first time, we perform a direct **particle**–**fluid** simulation of the flushing cycle in a generic EDM cavity using a hierarchical Cartesian sharp-interface cut-cell method. The **flow** around each debris **particle** is completely resolved and the heat transfer between the particles and the **fluid** is taken into account. The rate of material removal and the cooling performance of the flushing mechanism are studied for three-volume loadings. The results show that the **flow** around the particles has a pro- nounced impact on the heat transfer between the dielectricum and the workpiece. A **particle** loading of 14% increases the mean heat transfer by approximately 16%. The **particle** loading also has a pro- nounced impact on the rate at which particles are flushed out of the cavity. Increasing the initial volume loading from 6% to 14% decreases the amount of particles that get flushed out of the cavity by 14%.

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The objective of this thesis is to develop for tumor-targeting in the hepatic artery system a 1-D model to predict pressure and **flow** rate, wall distensibility, and drug-**particle** trajectories. Several models for computing pressure fields and **flow** rates exist in the literature. A general model developed by Olufsen et al. (2000), consisting of a non-linear hyperbolic system of equations, was selected for FORTRAN 95 coding in the MATLAB environment. An algebraic pressure-area relationship was used for the **fluid**-structure interaction. A three-element Windkessel model was employed as the outlet boundary condition, while the **flow** conditions were specified at the inlet. Validations were accomplished for the cases of a single flexible bifurcation, a flexible tube with physiological inflow, a representative model of the aorta and 3-D simulations of the hepatic arterial system.

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Fig.7 Boundary treatments in SPH and DEM 6. Implementation and computational flowchart
The overall algorithm process is depicted in Fig.8. First of all, **particle** elements and boundaries are generated under initial conditions. Once the simulation begins, each **particle** element searches its surrounding **particle** elements through the linked-list scheme and interaction forces are computed. For structure **particle** elements, they are subjected to hydrodynamic forces from **fluid** **particle** elements, direct contact forces from solid **particle** elements and inherent bond forces from themselves. The bond forces determine the breakage of the bond if the excess of tensile strength is reached. The **fluid** **particle** elements are not only subjected to hydrodynamic forces but also under the reaction forces (e.g. drag forces and buoyancy forces) from solid **particle** elements using the technique of Shepard filter. In addition, to drag forces and buoyancy forces from **fluid** **particle** elements, direct contact forces also exist among solid **particle** elements. In terms of boundary treatment, boundary **particle** elements are specific for SPH **particle** elements through SPH algorithm. On the other hand, boundary lines work for DEM **particle** elements according to the linear contact model when DEM **particle** elements approaching to boundaries. After the calculations of interaction forces acting on each **particle** elements, its position, velocity and density are updated at each time step until the end of calculation.

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The physically based preconditioner is applied to each of these linear solvers with good improvements in efficiency in each case. The term physically based preconditioner used here refers to the fact that the preconditioners used in this study are based on the physical nature or physics of the problem being studied. In the case of **particle** **transport**, the linear system structure has a block structure due to the various angles that a **particle** may scatter when encountering a given point in a material. The preconditioner for the linear systems from the finite element methods for the first order **transport** equation is derived from the equation itself. More specifically, the preconditioner used is the system matrix that would be obtained if there were no scattering present. For each of the specific problems studied, the physically based preconditioner is compared with several algebraic preconditioners including some of those mentioned earlier like the Jacobi method and successive over-relaxation.

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Post Graduate Department of Physics, L.S. College, B.R.A. Bihar University, Muzaffarpur-842001.
Abstract : Using Molecular dynamics to compute the **transport** **properties** of Lennard-Jones **fluid** mixtures using Green-Kubo formula. This formula is applied to estimate the **transport** **properties** (TP's) such as shear viscosity and thermal inductivity of Ar-Kr. The theory provides good result in low density regime where this experimental data and simulation is found very good.

These classifications are essentially based upon the **properties** exhibited by the crude oil, including physical **properties**, composition, gas-oil ratio, appearance, and pressure-temperature phase diagrams:
1. Ordinary Black Oil. A typical pressure-temperature phase diagram for ordinary black oil is shown in Figure 1-2. It should be noted that quality lines, which are approximately equally spaced, characterize

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However, the **particle** methods have still some problems.
Calculation stability is one of the significant problems in the **particle** methods. Casting process involves a variety of phe- nomena which occur simultaneously from the pouring to the solidification. Because it is difficult to expect what kind of phenomena will occur at where and at which timing, higher calculation stability is required for the integrated simulation using **particle** methods. It is known that the oscillation of ve- locity and pressure occurs in the **flow** simulation, and the os- cillation decreases the calculation stability especially for a slow **flow** 5) . Hirata et al. have proposed a stable and rapid calculation method for the slow **flow** by ignoring inertia force and adjusting the gravitational force after the **fluid** **flow** can be assumed to be almost stopped 5) . However, the procedure requires precise estimation of the **flow** stop time. The original **flow** calculation by the **particle** method 3) is unstable for the slow **fluid** **flow**. Therefore the **flow** calculation without any improvement will decrease the calculation stability when the **flow** becomes slow during the casting processes. Recently, Hirata et al. reported the multiple relaxation method which improves calculation stability and speed 6) in the case of slow

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Relationships between **flow** and chimney formation In this study, chimneys formed at regions with high excurrent **flow** speeds, as predicted by the hypothesis that high **flow** speed induces conduit formation in this system. The relationship between **flow** and conduit formation has been addressed in several internal **fluid**-**transport** systems, in which **fluid** moves through pipe-like conduits to **transport** material within the organism. Increased **flow** is correlated with conduit formation or increased conduit size in the vertebrate circulatory system (Brown and Hudlicka, 2003; Langille, 1995; Prior et al., 2004), the gastrovascular canals of hydroid colonies (Buss, 2001; Dudgeon and Buss, 1996) and the veins of plasmodial slime molds (Nakagaki et al., 2000). This study suggests that similar relationships between **flow** and conduit formation also exist in external **fluid**-**transport** systems. Unlike systems studied previously, this system is involved in suspension feeding rather than internal **transport**, and its conduits (the chimneys) are simple openings rather than pipes.

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In the present study, we present the Lagrangian coherent structures (LCS) seen in the results of numerical simulations of hydromedusae swimming as well as several examples of **particle** motion in the resulting **flow**. The hydromedusae examined are Aequorea victoria Murbach and Shearer 1902, a paddling or rowing type of hydromedusa, and Sarsia tubulosa M. Sars 1835, a jetting type of hydromedusa. We believe this to be the first numerical study of this type. The actual motion of the hydromedusa, reproduced from digitized videos of the swimming hydromedusae, is used to compute the surrounding velocity field. A brief description of the numerical method for computing the velocity field is included in Materials and methods. The use of computational **fluid** dynamics (CFD) data instead of an empirical velocity field from digital **particle** image velocimetry (DPIV), or similar, results in higher resolution of the LCS as well as greater accuracy in subsequent calculations. Additionally, there are significant difficulties in obtaining high-quality results from DPIV for swimming hydromedusae. DPIV results are only available for the time during which the hydromedusa is properly oriented within the field of view, perhaps only a few swimming cycles depending on many factors. Additionally, the resolution obtained from DPIV depends on the concentration of particles in a given region. In general, the distribution of particles may be highly non-uniform. The particles will be drawn toward certain **flow** structures, just as dye is drawn into vortices in dye visualization experiments, but other areas of the **flow** may be left with few particles. None of these difficulties are present in our method. It is only necessary to capture a good swimming cycle. The periodic swimming motion may then be determined up to the resolution of the camera used and iterated for as many swimming cycles as desired.

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© 2012 Elsevier Ltd. All rights reserved. 1. Introduction
The study of two-dimensional boundary layer **flow** and heat transfer induced by continuous stretching and heated surfaces has acquired momentum due to its various applications in engineering/industrial disciplines. These applications include extrusion processes, wire and fiber coating, polymer processing, food-stuff processing, design of heat exchangers, and chemical processing equipment. The concept of continuous stretching will bring in a unidirectional orientation to the extrudate; consequently the quality of the final product considerably depends on the **flow** and heat transfer mechanism. To that end, the analysis of momentum and thermal transports within the **fluid** on a continuously stretching surface is important for gaining some fundamental understanding of such processes. Sakiadis [ 1 ] was the first amongst others to initiate such a problem by considering the boundary layer **fluid** **flow** over a continuous solid surface moving with constant velocity. The thermal behavior of the problem was studied by Erickson et al. [ 2 ], and experimentally verified by Tsou et al. [ 3 ]. Crane [ 4 ] extended the work of Sakiadis [ 1 ] to the **flow** caused by an elastic sheet moving in its own plane with a velocity varying linearly with the distance from a fixed point. Also, heat and mass transfer aspects with Newtonian/non-Newtonian fluids are studied by several authors [ 5–11 ] under different physical situations.

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