Drag Formula for a Clas s of Axially Symmetric Particles in a Uniform Flow 10 Viscous Interaction Between a Small Number of Spherical Particle s 26 The Effect of Continuous Solid Boundar[r]

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Permeability decreased with effective pressure as a power law function. Permeability values in the fault zones were 8 × 10 −18 m 2 at site C0004 and 9 × 10 −18 m 2 at site C0007. Stratigraphic variation in **transport** **properties** suggests that the megasplay fault zone may act as a barrier to **fluid** **flow**, but the frontal thrust fault zone might not. Depth variation in permeability at site C0007 is probably controlled by the mechanical compaction of sediment. Hydraulic diffusivity at shallow depths was approximately 1 × 10 −6 m 2 s −1 in both fault zones, which is small enough to lead to pore pressure generation that can cause dynamic fault weakening. However, absence of a very low permeable zone, which may have formed in the Japan Trench subduction zone, might prevent facilitation of huge shallow slips during Nankai subduction zone earthquakes. Porosity tests under dry conditions might have overestimated the porosity.

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The height of the casting was 180 mm, and the upper half of the casting was 25 mm and the lower half was 40 mm in di- ameter, respectively. The physical **properties** used in the cal- culation are shown in the Table 1, and the **fluid** was poured from the upper side with a rate of 100 g/s and pouring finish within 4 s. The results are shown in the Fig. 8. Figure 8(a) is the result of MR1-1.0 at 4.5 s, showing unnatural pressure distribution at the bottom of the casting, and hopping of the casting particles. At the last moment, the **fluid** **flow** was very slow. However the pressure in the casting was unnaturally high under the shoulder. In such shapes with shoulders, posi- tional correction in the correction phase tends to be insuffi- cient, and the pressure under the shoulder will be accumulat- ed unnaturally. As a result, unnatural hopping occurs, and the calculation will result in failure. In the Fig. 8(b), we can find that the proposed method improves the calculation stability. The calculated pressure value at the bottom agreed well with the theoretical value, 4410 Pa. It is possible to improve calcu- lation stability by using smaller Δt. However the pressure or velocity oscillation problem will remain, and also, longer cal- culation time will be required because of higher maximum velocity.

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performance is still going due to effective applications in the field of cooling (transformer cooling, electronics device cooling, silicon mirror cooling, vehicles cooling, controlling fusion), biomedical (magnetic cell separation, drug delivery, cancer therapeutics, cryopreservation, nano cryosurgery) etc. The term “nano **fluid**” can be refers to a class of fluids by suspending nanometre sized (1-100 nm diameters) particles in common base fluids of highly enhanced thermal **properties** (Ferdows et al., 2013; Dogonchi et al., 2016). This type of fluids has highly industrial importance because of its unique chemical and physical **properties**. It has a higher thermal conductivity which controlled significant enhancement due to the rate of heat transfer.

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To study the effect of crude oil **properties** on the **transport** profile inside a pipeline, numerical simulation was tested under laminar unsteady state conditions. The Reynolds number of the **flow** in the pipeline was in the range of 35.63 to 261.16, depending on the condition. It is apparent that the Reynolds number is low for crude oil **flow** due to its high viscosity. The Peclet numbers were in the range of 15,999.00 to 22,752.29, and the Biot number was 1.83. Because the Peclet number was high, the convection was important. In addition, in this study, the Biot number implies that the conduction was much slower than the convection and temperature gradients dominant in the pipeline. A crude oil liquid **flow** was simulated with a 30,000 cell straight pipe model after grid independency testing. The simulation test operated until a steady state was reached. The details about the validation of this study used to develop the computer program code with literature experimental data can be found in Rukthong [15] and Rukthong et al. [16]. In this study, the result trends from the developed computational **fluid** dynamics simulation program were verified with the commercial program, ANSYS FLUENT [17], and theoretical **transport** phenomena concept.

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A mathematical model is presented for analyzing the boundary layer **flow** and heat transfer of dusty **fluid** over a stretching sheet embedded in a porous medium. Temperature dependent **fluid** **properties** are assumed to vary as a function of the temperature. Using a similarity transformation, the governing coupled non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations and solved numerically by the Keller-box method. The numerical solutions are compared with the approximate analytical solutions, obtained by a perturbation technique. The analysis reveals that even in the presence of variable **fluid** **properties** the transverse velocity of the **fluid** is to decrease with an increase in the **fluid**-**particle** interaction parameter. This observation holds even for porous medium. Furthermore, the effects of the physical parameters on the **fluid** velocity, the velocity of the dust **particle**, the density of the dust **particle**, the **fluid** temperature, the dust-phase temperature, the skin friction, and the wall-temperature gradient are assessed through tables and graphs.

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The Analysis of Internal Heat source for **transport** processes of the physical system formulated with Forcheimeir model is studied. The extended Darcy model is used here. For Physical problem considered here, the governing measures are highly coupled. To solve them, initially similarity transformations are used to convert them into ODE and solved approximately. RK method of fifth order followed by Newton-Raphson method is employed. The graphical representations are obtained for **transport** processes, where the features of **fluid** **flow** are discussed. The exponential form of internal heat source enhances melting and impedes freezing. The significance of inertial parameter is highly influenced in decreasing the **flow** field. Besides, skin friction, heat and mass **transport** graphical interpretations are made for different physical parameters. A good agreement is found when interpretation of the effects of various significant parameters are analysed and the results are compared.

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(ii) Distributed Lagrangian Multiplier Method. The distrib- uted Lagrange multiplier (DLM) method is based on the fictitious–domain method. The fictitious domain is derived from the idea that **fluid** fills the space inside of the particles as well as outside. Since **fluid** fills the whole **flow** domain, including **particle** volumes, a simple fixed finite element mesh can be generated to solve for the velocities of the **fluid** and the particles. As the mesh does not need to be refreshed in every time step, it is much more efficient when compared to the ALE method. The **particle** is tracked by using boundary control points that are on the **particle** boundary and move with the **particle**. The grid (see Fig. 4) does not conform to the shape of the **particle**. The nodes that are inside the **particle** boundary have their calculated velocity, i.e., the velocity which at that point in the **particle** would have due to a rigid body motion. Since **fluid** occupies the region of the **particle**, the Navier–Stokes equations must be solved to obtain velocity values for any point inside or on the surface of the **particle**. The body force term in the Navier–Stokes equations is multiplied by a constant corresponding to that particular position that will yield a velocity due to rigid body motion.

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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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become greater at higher **flow** velocities, resulting in larger pressure gradient through the porous media (Antohe & Lage 1997). The mechanism responsible for this turbulence is the drag force imposed on a **fluid** by the pore walls which impede the **flow** (Carman, 1956). In steady viscous or streamline **flow**, the resistance arises solely from viscosity. As the velocity increases, the regular pattern of streamline **flow** becomes unstable, and gives way to a regime where large number of small, randomly distributed local eddies form spontaneously. This results in the dissipation of the kinetic energy of **fluid** motion as heat and hence increases the resistance to **flow**. This resistance can be described as inertial resistance and depends on the kinetic energy per unit volume of the **fluid**, i.e. on ρ f v 2 . Therefore, in general engineering applications, the law governing this **fluid** **flow** is a modified version of Darcy’s equation, with inertial resistance superimposed on the viscous resistance (Dupuit 1863; Forchheimer 1901):

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Pulmonary **flow** is characterized by a series of bifurcations. The laminar flows in this type of bifurcations have been studied by many authors, but few researchers have focused on the efforts of the upstream turbulence. Indeed, although the **flow** is laminar in the bronchi (at least for normal respiration), it is turbulent in the upper airways. This turbulent appearance is paramount, as this significantly alters the **transport** and deposition of particles. In addition, many current research considers a steady **flow** at the entrance and therefore do not reproduce the cycle of breathing. These modeled air flows through an anatomically realistic system conduits and branches, are governed by contraction and expansion movements of the pulmonary system and alveolar sacs. Today, **fluid** dynamics (a science of everyday, but that seems very unknown) is a very active area of research with many unsolved or partially solved problems yet. She always uses numerical methods better known under the name of Computational **Fluid** Dynamics (CFD). In order to understand and characterize the **transport** of inhaled particles in human airways, many authors conducted various experimental and numerical studies that led to relevant results. We will be interested in this study to provide a reliable and comprehensive numerical modeling of **particle** **transport** in pulmonary **flow** without taking into account the movements imposed by breathing with the help of CFD-ACE commercial calculation code.

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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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current effect in oscillatory **flow** of a couple stress **fluid** in an inclined channel. Eldabe et al. [1] studied the effects of heat and mass transfer on the MHD **flow** of an incompressible, electrically conducting couple stress **fluid** through a porous medium in an asymmetric flexible channel over which a traveling wave of contraction and expansion is produced, resulting in a peristaltic motion. Sankad and Radhakrishnamacharya[12] contributed towards the effect of magnetic field on the peristaltic **transport** of couple stress **fluid** in a channel with different wall **properties**. Shit and Roy[14] discussed the effect of slip velocity on peristaltic **transport** of a physiological **fluid** through a porous non-uniform channel under the long wave length and low-Reynolds number assumptions. Kothandapani and Srinivas [7] analysed the effect of elasticity of the flexible walls on the MHD peristaltic **flow** of a Newtonian **fluid** in a two-dimensional porous channel with heat transfer under the assumptions of long wavelength and low- Reynolds number.

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equation (4)# that K muet be 0oro and equation (2) le thuo an Identity. On the other hand# If K la aeeumed to be aero# it can be easily shown that the **fluid** met be bara tropic# Thus# the govei'nlng eqmtlono reduce to three in number# ao expected# namely equatlono (1)# (3) and (9). The temperature at any point can be obtained Imaediately from equation (4)# It should be noted that equation (9) la tho law governing loezi^yropio floi)# which le not the case in the rotational **flow** behliKa a bow shock wave# where the entropy 8# varleo from stream line to otreom lino# although tho otagnatlon enthal]%f for

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The governing equations presented in the previous section are highly nonlinear and exhibited no analytical solutions due to thermal radiation effect. In general analytical solution are very useful in validating computer routines of complicated time dependent two or three-dimensional free convective and radiating conducting **fluid** and comparison with experimental data. It is therefore of interest to reduce the governing equations of the present problem to the form that can be solved analytically. A special case of the present problem that exhibit analytical solution is the problem of steady state MHD natural convection Couette **flow** trapped between two infinite vertical plates in the presence of thermal radiation effects. The resulting steady state equations and boundary

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Analytical solutions to the Navier-Stokes equations are impossible to obtain for any systems but the simplest flows under ideal conditions. For real flows, a numerical approach must be adopted whereby a discretization method involves replacing the Navier- Stokes equations by their algebraic approximations, which can then be solved using a numerical method. The CFD approach uses Navier-Stokes equations and energy balances over control volumes, small volumes within the geometry at a defined location representing the reactor internals. The size and number of control volumes (mesh density) is user determined and will influence the accuracy of the solutions to a degree. After boundary conditions have been introduced in the system the **flow** and energy balances are solved numerically. An iteration process decreases the error in the solution until a satisfactory result has been reached. By using CFD in the simulation of coolant of the nuclear reactors a detailed description of the **flow** behavior within the barrel can be established, which can then be used in more accurate modeling.

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The **Particle** **Flow** (PF) algorithm [1] is based on a concept of global event reconstruction as it performs a correlation of the basic elements (i.e. tracks and clusters) obtained from all subdetector systems, in order to identify all particles in the event and measure their **properties**. An example is shown in Fig. 1 and Fig. 2 where a jet with transverse momentum of 65 GeV, simulated in the CMS detector [2], is made of only five particles: two charged hadrons (a π + and a π − ), two photons (from the decay of a π 0 ) and one neutral hadron (a K 0

The fine particles in air are mainly from the combustion of fossil fuels. They are difficult to be removed completely by conventional dust collector because of the small size [3]. **Particle** agglomeration technology is a potential method to improve the removal efficiency of fine particles using the conventional dust col- lector. Several external fields and some chemical agents were applied to make fine particles to “grow” into large particles agglomeration which can be filtered easily. The agglomeration methods mainly include acoustic agglomeration, How to cite this paper: Yan, P.L., Sun,

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no one was able to prove that the statement is true or no one have ever suggested a systematic procedure to prove MQL’s efficiency. The effectiveness and the working principle of MQL are still questionable with very few explanations provided. The aim of this study is to determine the desirable **flow** pattern of the mist **flow** in order to choose the nozzle distance from the cutting tool for the minimum quantity lubricant in machining process using **Particle** Image Velocimetry (PIV) and Computer **Fluid** Dynamics (CFD).