The assessment of time dependent flow of Williamson fluid with radiative blood flow against a wedge

The present pagination reports both Brownian diffusion and thermophoresis aspects subject to magneto hydrodynamic Williamson fluid model.Assuming the flow is unsteady and blood is treated as Williamson fluid over a wedge with radiation.The governing equations are transformed into ordinary differential equations by using similarity variables.The analytical solutions of the transformed governing equations are obtained by using the RK 4th order method along with shooting technique solver.The effects of various physical parameters such as Hartmann number,local Weissenberg number,radiation parameter,unsteadiness parameter,Prandtl number,Lewis number,Brownian diffusion,thermophoresis,wedge angle parameter,moving wedge parameter,on velocity,temperature,concentration,skin friction,heat transfer rate and mass transfer rate have been discussed in detail.The velocity and temperature profile deprives for larger We and an opposite trend is observed for concentration.The radiation parameter is propositional to temperature and a counter behaviour is observed for Pr.

Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

Oxidation Kinetics of Aluminum Powders in a Gas Fluidized Bed Reactor in the Potential Application of Surge Arresting Materials

In this technical paper, the oxidation mechanism and kinetics of aluminum powders are discussed in great details. The potential applications of spherical aluminum powders after oxidation to be part of the surging arresting materials are discussed. Theoretical calculations of oxidation of spherical aluminum powders in a typical gas fluidization bed are demonstrated. Computer software written by the author is used to carry out the basic calculations of important parameters of a gas fluidization bed at different temperatures. A mathematical model of the dynamic system in a gas fluidization bed is developed and the analytical solution is obtained. The mathematical model can be used to estimate aluminum oxide thickness at a defined temperature. The mathematical model created in this study is evaluated and confirmed consistently with the experimental results on a gas fluidization bed. Detail technical discussion of the oxidation mechanism of aluminum is carried out. The mathematical deviations of the mathematical modeling have demonstrated in great details. This mathematical model developed in this study and validated with experimental results can bring a great value for the quantitative analysis of a gas fluidization bed in general from a theoretical point of view. It can be applied for the oxidation not only for aluminum spherical powders, but also for other spherical metal powders. The mathematical model developed can further enhance the applications of gas fluidization technology. In addition to the development of mathematical modeling of a gas fluidization bed reactor, the formation of oxide film through diffusion on both planar and spherical aluminum surfaces is analyzed through a thorough mathematical deviation using diffusion theory and Laplace transformation. The dominant defects and their impact to oxidation of aluminum are also discussed in detail. The well-controlled oxidation film on spherical metal powders such as aluminum and other metal spherical powders can potentially become an important part of switch devices of surge arresting materials, in general.

Flow-Induced Stream-Wise Vibration of Circular Cylinders

Results from a series of studies on the stream-wise vibration of a circular cylinder verifying Japan Society of Mechanical Engineers Standard S012-1998, Guideline for Evaluation of Flow-induced Vibration of a Cylindrical Structure in a Pipe, are summarized and discussed in this paper. Experiments were carried out in a water tunnel and in a wind tunnel using a two-dimensional cylinder model elastically supported at both ends of the cylinder and a cantilevered cylinder model with a finite span length that was elastically supported at one end. These cylinder models were allowed to vibrate with one degree of freedom in the stream-wise direction. In addition, we adopted a cantilevered cylinder model that vibrated with two degrees of freedom in both the stream-wise and cross-flow directions under the same vibration conditions as an actual thermocouple well. The value of the Scruton number (structural damping parameter) was changed over a wide range, so as to evaluate the value of the critical Scruton number that suppressed vibration of the cylinder. For the two-dimensional cylinder, two different types of stream-wise excitations appeared in the reduced velocity range of approximately half of the resonance-reduced velocity. For the stream-wise vibration in the first excitation region, due to a symmetric vortex flow, the response amplitudes were sensitive to the Scruton number, while the shedding frequency of alternating vortex flow was locked-in to half of the Strouhal number of vibrating frequency of a cylinder in the second excitation region. In addition, the effects of the aspect ratio of a cantilevered cylinder on the flow-induced vibration characteristics were clarified and compared with the results of a two-dimensional cylinder. When a cantilevered circular cylinder with a finite length vibrates with one degree of freedom in the stream-wise di-rection, it is found that acylinder with a small aspect ratio has a single excitation region, whereas a cylinder with a large aspect ratio has two excitation regions. Furthermore, the vibration mechanism of a symmetric vortex flow was investigated by installing a splitter plate in the wake to prevent shedding of alternating vortices. The vibration amplitude of acylinder with a splitter plate increased surprisingly more than the amplitude of a cylinder without a splitter plate. For a cantilevered cylinder vibrating with two degrees of freedom, the Lissajous figure of vibration of the first excitation region shows the trajectories of elongated elliptical shapes, and in the second excitation region, the Lissajous trajectories draw a figure “8”. The results and information from these experimental studies proved that Standard S012-1998 provides sufficient design methods for suppressing hazardous vibrations of cylinders in liquid flows.

Augmenting the Heat Sink for Better Heat Dissipation

Heat sinks were invented to absorb heat from an electronic circuit conduct, and then to dissipate or radiate this heat to the surrounding supposedly, ventilated space, at a rate equal to or faster than that of its buildup. Ventilation was not initially recognized as an essential factor to thermal dispersion. However, as electronic circuit-boards continued to heat up, circuit failure became a problem, forcing the inclusion of miniaturized high speed fans. Later, heat sinks with fins and quiet fans were incorporated in most manufactured circuits. Now heat sinks come in the form of a fan with fans made to function as fins to disperse heat. Heat sinks absorb and radiate excess heat from circuit-boards in order to prolong the circuit’s life span. The higher the thermal conductivity of the material used the more efficient and effective the heat sink is. This paper is an attempt to theoretically design a heat sink with a temperature gradient lower than that of the circuit board’s excess heat.

A Mathematical Model for Magnetohydrodynamic Convection Flow in a Rotating Horizontal Channel with Inclined Magnetic Field, Magnetic Induction and Hall Current Effects

Closed-form and asymptotic solutions are derived for the steady, fully-developed hydromagnetic free and forced convection flow in a rotating horizontal parallel-plate channel under the action of an inclined magnetic field and constant pressure gradient along the longitudinal axis of the channel. The magnetic field is strong enough to generate Hall current effects and the magnetic Reynolds number of sufficient magnitude that induced magnetic field effects are also present. Secondary flow is present owing to the Hall current effect. The channel plates are also taken to be electrically-conducting. The conservation equations are formulated in an (x, y, z) coordinate system and non-dimensionalized using appropriate transformations. The resulting non-dimensional coupled ordinary differential equations for primary and secondary velocity components and primary and secondary induced magnetic field components and transformed boundary conditions are shown to be controlled by the dimensionless pressure gradient parameter (px), Hartmann number (M2), Grashof number (G), Hall current parameter (m), rotational parameter (K2), magnetic field inclination (&#920), and the electrical conductance ratios of the upper (&#9201) and lower (&#9202) plates. Solutions are derived using the method of complex variables. Asymptotic solutions are also presented for very high rotation parameter and Hartmann number of order equal to unity, for which Ekman-Hartmann boundary layers are identified at the plates. A parametric study of the evolution of velocity and induced magnetic field distributions is undertaken. It is shown that generally increasing Hall current effect (m) serves to accentuate the secondary (cross) flow but oppose the primary flow. An increase in rotational parameter (K2) is also found to counteract primary flow intensity. An elevation in the Grashof number i.e. free convection parameter (G) is shown to aid the secondary induced magnetic field component (Hz);however there is a decrease in magnitudes of the primary induced magnetic field component (Hx) with increasing Grashof number. Increasing inclination of the applied magnetic field (&#920, is also found to oppose the primary flow (u1) but conversely to strongly assist the secondary flow (w1). Both critical primary (Gcx) and secondary (Gcz)Grashof numbers are shown to be reduced with increasing inclination of the magnetic field (&#920), increasing Hall parameter (m) and rotational parameter (K2). Applications of the study arise in rotating MHD induction power generators and also astrophysical flows.

A new constitutive theory for extrusion-extensional flow of anisotropic liquid crystalline polymer fluid

A new continuum theory of the constitutive equation of co-rotational derivative type was developed by the author for anisotropic viscoelastic fluid-liquid crystalline (LC) polymers (S.F. Han, 2008, 2010) . This paper is a continuation of the recent publication [1] to study extrusion-extensional flow of the fluid. A new concept of simple anisotropic fluid is introduced. On the basis of anisotropic simple fluid, stress behavior is described by velocity gradient tensor F and spin tensor W instead of the velocity gradient tensor D in the classic Leslie?Ericksen continuum theory. A special form of the constitutive equation of the co-rotational type is established for the fluid. Using the special form of the constitutive equation in components a computational analytical theory of the extrusion-extensional flow is developed for the LC polymer liquids - anisotropic viscoelastic fluid. Application of the constitutive theory to the flow is successful in predicting bifurcation of elongational viscosity and contraction of extrudate for LC polymer liquids–anisotropic viscoelastic fluid. The contraction of extrudate of LC polymer liquids may be associated with the stored elastic energy conversion into that necessary for bifurcation of elongational viscosity in extrusion extensional flow of the fluid.

Performance of a Horizontal Flow Constructed Reed Bed Filter for Municipal Wastewater Treatment: The Case Study of the Prototype Installed at Gaston Berger University, Saint-Louis, Senegal

In Saint-Louis, Senegal, a constructed wetland with horizontal flow reed beds (FHa and FHb) has demonstrated significant efficacy in treating municipal wastewater. Analyzing various treatment stages, the system showed only a slight temperature variation, from an influent average of 26.3°C to an effluent of 24.7°C. Electrical conductivity decreased from 1331 mS/cm to 974.5 mS/cm post-primary treatment, with suspended solids (SS) dramatically reduced from 718.9 mg/L to 5.7 mg/L in the final effluent. Biochemical oxygen demand (BOD5) and chemical oxygen demand (COD) saw a notable decrease, from initial levels of 655.6 mg/L and 1240 mg/L to 2.3 mg/L and 71.3 mg/L, respectively. Nitrogenous compounds (N-TN) and phosphates () also decreased significantly, indicating the system’s nutrient removal capacity. Microbiological analysis revealed a reduction in fecal coliforms from 7.5 Ulog/100ml to 1.8 Ulog/100ml and a complete elimination of helminth eggs. The presence of Phragmites and Typha was instrumental in enhancing these reductions. The system’s compliance with the Senegalese standards for disposal into natural environments, WHO recommendations for unrestricted water reuse in irrigation, and the European legislation for water reuse was established. The effluent quality met the stringent criteria for various classes of agricultural reuse, illustrating the system’s potential for sustainable water management. This wetland model presents a robust solution for water-stressed regions, ensuring environmental protection while supporting agricultural needs. The study calls for ongoing research to further refine the system for optimal, reliable wastewater treatment and water resource sustainability.

Four-dimensional flow magnetic resonance imaging incirrhosis

Since its introduction in the 1970’s,magnetic resonance imaging(MRI)has become a standard imaging modality.With its broad and standardized application,it is firmly established in the clinical routine and an essential element in cardiovascular and abdominal imaging.In addition to sonography and computer tomography,MRI is a valuable tool for diagnosing cardiovascular and abdominal diseases,for determining disease severity,and for assessing therapeutic success.MRI techniques have improved over the last few decades,revealing not just morphologic information,but functional information about perfusion,diffusion and hemodynamics as well.Four-dimensional(4D)flow MRI,a time-resolved phase contrast-MRI with three-dimensional(3D)anatomic coverage and velocity encoding along all three flow directions has been used to comprehensively assess complex cardiovascular hemodynamics in multiple regions of the body.The technique enables visualization of 3D blood flow patterns and retrospective quantification of blood flow parameters in a region of interest.Over the last few years,4D flow MRI has been increasingly performed in the abdominal region.By applying different acceleration techniques,taking 4D flow MRI measurements has dropped to a reasonable scanning time of 8 to 12 min.These new developments have encouraged a growing number of patient studies in the literature validating the technique’s potential for enhanced evaluation of blood flow parameters within the liver’s complex vascular system.The purpose of this review article is to broaden our understanding of 4D flow MRI for the assessment of liver hemodynamics by providing insights into acquisition,data analysis,visualization and quantification.Furthermore,in this article we highlight its development,focussing on the clinical application of the technique.

Pressure Drop of Liquid–Solid Two-Phase Flow in the Vertical Tube Bundle of a Cold-Model Circulating Fluidized Bed Evaporator

A cold-model vertical multi-tube circulating fluidized bed evaporator was designed and built to conduct a visualization study on the pressure drop of a liquid–solid two-phase flow and the corresponding particle distribution.Water and polyformaldehyde particle(POM)were used as the liquid and solid phases,respectively.The effects of operating parameters such as the amount of added particles,circulating flow rate,and particle size were systematically investigated.The results showed that the addition of the particles increased the pressure drop in the vertical tube bundle.The maximum pressure drop ratios were 18.65%,21.15%,18.00%,and 21.15%within the experimental range of the amount of added particles for POM1,POM2,POM3,and POM4,respectively.The pressure drop ratio basically decreased with the increase in the circulating flow rate but fluctuated with the increase in the amount of added particles and particle size.The difference in pressure drop ratio decreased with the increase in the circulating flow rate.As the amount of added particles increased,the difference in pressure drop ratio fluctuated at low circulating flow rate but basically decreased at high circulating flow rate.The pressure drop in the vertical tube bundle accounted for about 70%of the overall pressure drop in the up-flow heating chamber and was the main component of the overall pressure within the experimental range.Three-dimensional phase diagrams were established to display the variation ranges of the pressure drop and pressure drop ratio in the vertical tube bundle corresponding to the operating parameters.The research results can provide some reference for the application of the fluidized bed heat transfer technology in the industry.

Algebraic Calculation Method of One-Dimensional Steady Compressible Gas Flow

This paper describes a new method of calculation of one-dimensional steady compressible gas flows in channels with possible heat and mass exchange through perforated sidewalls. The channel is divided into small elements of a finite size for which mass, energy and momentum conservation laws are written in the integral form, assuming linear distribution of the parameters along the length. As a result, the calculation is reduced to finding the roots of a quadratic algebraic equation, thus providing an alternative to numerical methods based on differential equations. The advantage of this method is its high tolerance to coarse discretization of the calculation area as well as its good applicability for transonic flow calculations.

Numerical Solution of MHD Flow of Micropolar Fluid with Heat and Mass Transfer towards a Stagnation Point on a Vertical Plate

The paper investigates the numerical solution of problem of magnetohydrodynamic (MHD) micropolar fluid flow with heat and mass transfer towards a stagnation point on a vertical plate. In this study, we consider both strong concentrations (n = 0) and weak concentrations (n = 1/2). The governing equations have been transformed into nonlinear ordinary differential equations by applying the similarity transformation and have been solved numerically by using the finite difference method (FDM) and analytically by using (DTM). The effects of various governing parameters, namely, material parameter, radiation parameter, magnetic parameter, Prandtl number, Schmidt number, chemical reaction parameter and Soret number on the velocity, microrotation, temperature and concentration have been computed and discussed in detail through some figures and tables. In order to verify the accuracy of the present results, we have compared these results with the analytical solutions by using the differential transform method (DTM) and the multi-step differential transform method (MDTM). It is observed that this approximate numerical solution is in good agreement with the analytical solution.

The Construction Method for Solving Radial Flow Problem through the Homogeneous Reservoir

On the basis of similar structure of solutions of ordinary differential equation (ODE) boundary value problem, the similar construction method was put forward by solving problems of fluid flow in porous media through the homogeneous reservoir. It is indicate that the pressure distribution of dimensionless reservoir and bottom hole in Laplace space, which take on the radial flow, also shows similar structure, and the internal relationship between the above solutions were illustrated in detail.

Trans-Thoracic Echocardiographic Aortic Blood Flow Peak Velocity Variation, Distance Minute, Aortic Velocity Time Integral and Postoperative Outcome in Pediatric Surgical Patients—An Observational Pilot Study Protocol

Background: A Randomized Controlled Trial (RCT) has been elaborated where goal directed fluid and hemodynamic therapy (GDFHT) will be realized with trans-thoracic echocardiographic aortic blood flow peak velocity variation (ΔVpeak) and distance minute (DM) to guide fluid therapy and hemodynamics in high risk pediatric surgical patients. This RCT will clarify the impact of GDFHT with ΔVpeak and DM on postoperative outcome in terms of morbidity, length of stay in the intensive care unit (LOSICU), length of mechanical ventilation (LMV) and length of hospital stay (LOS) in children. To determine values of ΔVpeak, DM and VTI predictive of these postoperative outcomes, an observational pilot study will be realized. This pilot study is described here. The primary objective of this study is to determine values of ΔVpeak, DM and ITV predictive of postoperative outcome in children in terms of morbidity. The secondary objectives are to determine values of ΔVpeak, DM and ITV predictive of LOSICU, LMV, LOS, intraoperative, postoperative fluid administration and vasoactive-inotropic therapy. Methods: 500 - 1000 children aged less than 18 years will be included prospectively. Statistic analysis will be realized with XLSTAT 2019.4.2 software or plus. Results and Conclusions: This trial protocol will determine values of ΔVpeak, DM and ITV with echocardiography predictive of postoperative outcome in children.

A Thermal-Hydraulic Coolant Channel Module (CCM) for Single- and Two-Phase Flow

A theoretical “drift-flux based thermal-hydraulic mixture-fluid coolant channel model” is presented. It is the basis to a corresponding digital “Coolant Channel Module (CCM)”. This purpose derived “Separate-Region Mixture Fluid Approach” should yield an alternative platform to the currently dominant “Separate-Phase Models” where each phase is treated separately. Contrary to it, a direct procedure could be established with the objective to simulate in an as general as possible way the steady state and transient behaviour of characteristic parameters of single- and/or (now non-separated) two-phase fluids flowing within any type of heated or non-heated coolant channels. Their validity could be confirmed by a wide range of verification and validation runs, showing very satisfactory results. The resulting universally applicable code package CCM should provide a fundamental element for the simulation of thermal-hydraulic situations over a wide range of complex systems (such as different types of heat exchangers and steam generators as being applied in both conventional but also nuclear power stations, 1D and 3D nuclear reactor cores etc). Thereby the derived set of equations for different coolant channels (distinguished by their key numbers) as appearing in these systems can be combined with other ODE-s and non-linear algebraic relations from additional parts of such an overall model. And these can then to be solved by applying an appropriate integration routine. Within the solution procedure, however, mathematical discontinuities can arise. This due to the fact that along such a coolant channel transitions from single- to two-phase flow regimes and vice versa could take place. To circumvent these difficulties it will in the presented approach be proposed that the basic coolant channel (BC) is subdivided into a number of sub-channels (SC-s), each of them being occupied exclusively by only a single or a two-phase flow regime. After an appropriate nodalization of the BC (and thus its SC-s) and after applying a “modified finite volume method” together with other special activities the fundamental set of non-linear thermal-hydraulic partial differential equations together with corresponding constitutive relations can be solved for each SC separately. As a result of such a spatial discretization for each SC type (and thus the entire BC) the wanted set of non-linear ordinary differential equations of 1st order could be established. Obviously, special attention had to be given to the varying SC entrance or outlet positions, describing the movement of boiling boundaries or mixture levels along the channel. Including even the possibility of SC-s to disappear or be created anew during a transient.

Modeling of Unsteady Flow through Junction in Rectangular Channels: Impact of Model Junction in the Downstream Channel Hydrograph

Open channel junctions are encountered in urban water treatment plants, irrigation and drainage canals, and natural river systems. Junctions are very important in municipal sewerage systems and river engineering. Adequate theoretical description of flow through an open channel junction is difficult because numerous variables are to be considered. Equations of junction models are based on mass and momentum or mass and energy conservation. The objective of this study is to compare two junction models for subcritical flows. In channel branches, we solve numerically the Saint-Venant hyperbolic system by combining Preissmann scheme and double sweep method. We validate our results with HEC-RAS using Nash and Sutcliffe efficiency. In junction models, equality of water stage and complete energy conservation equation from HEC-RAS are compared. Outcome of the research clearly indicates that the complete conservation energy model is more suitable in flow through junction than equality of water stage model in serious situations.

Analysis of Nonlinear Stochastic Systems with Jumps Generated by Erlang Flow of Events

In this paper we consider the stochastic systems with jumps (random impulses) generated by Erlang flow of events that lead to discontinuities in paths. These systems may be used in various applications such as a control of complex technical systems, financial mathematics, mathematical biology and medicine. We propose to use a spectral method formalism to the probabilistic analysis problem for the stochastic systems with jumps. This method allows to get a solution of the analysis problem in an explicit form.

Clinical Efficacy of Modified Erchen Decoction on Cervical Spondylotic Vertebral Arteriopathy with Stagnation and Blockade of Phlegm-dampness Syndrome and Effects on Cerebral Blood Flow Parameters

OBJECTIVE: To observe the effect of Modified Erchen Decoction on cervical spondylotic vertebral arteriopathy with stagnation and blockade of phlegm-dampness syndrome and effects on cerebral blood flow parameters. METHODS: A total of 80 cervical spondylotic vertebral arteriopathy(CSA) patients with stagnation and blockade of phlegmdampness syndrome admitted to our hospital from October 2016 to April 2017 were selected and randomly divided into observation group and control group, with 40 cases in each group. The observation group was treated with Modified Erchen Decoction and the control group was given conventional treatment with Western medicine. After 4 weeks of treatment, the main clinical symptoms and signs(vertigo, neck and shoulder pain, headache, psychological and social adjustment, daily life and work) and cerebral blood flow parameters [the peak values of intracranial vertebral-basal artery diastolic blood flow velocity(Vd) and systolic blood flow velocity(Vp)] were compared between the 2 groups. The total clinical effective rate and adverse reactions during treatment were also compared. RESULTS: After treatment, the total effective rate of the observation group was 90.0%, which was significantly higher than that of the control group(77.5%). The difference between the two groups was statistically significant(P < 0.05). After treatment, The scores of vertigo, neck and shoulder pain, headache, psychology and society adaptation, daily life and work were significantly increased(P < 0.05), and the above scores of the observation group were increased more obviously. The difference between the groups was statistically significant(P < 0.05). After treatment, the levels of Vd and Vp were significantly increased(P < 0.05), and the increase of the above indexes was more obvious in the observation group. The difference between the 2 groups was statistically significant(P < 0.05). There were no significant abnormalities in blood routine, urine routine, liver function and renal function. There was no significant difference in the incidence of adverse reactions between the 2 groups.(P > 0.05). CONCLUSION: The treatment of vertebral artery type cervical spondylopathy with stagnation and blockade of phlegm-dampness syndrome by Modified Erchen Decoction can effectively relieve the main clinical symptoms and signs, improve cerebral blood flow parameters, and improve the peak values of vertebral-basal artery diastolic blood flow velocity(Vd) and systolic blood flow velocity(Vp), which is safe and effective, and helps to promote the recovery of cervical function.

液相物性对气液两相管流流型和压降影响的研究

通过实验研究了不同液相介质(水相和油相)对气液两相管流中流型和压降的影响.实验管线为内径50mm的透明有机玻璃管,管线从入口到分离器长约35m,实验管段由一个高3.3m、宽0.72m的垂直倒U型管和一个长3m的水平管组成.实验结果表明对于较低液相粘度的气液两相流动,液相物性对水平管中塞状流向弹状流的转化以及倒U型管中下降管内的环状液膜流动向间歇流动的转化有一定的影响,但对水平管中分层波状流动向间歇流动的转化以及倒U型管中上升管内的流型转化影响很小.通过分析压降数据得出,对于倒U型管中的上升段,液相流动状态对于压降起着主导作用,但在下降管内液相和气相的流动状态都对压降有重要影响.

GALERKIN METHOD FOR COMPRESSIBLE FLOW OF CONTAMINATION FROM NUCLEAR WASTE WITH MOLECULAR DIFFUSION AND DISPERSION

Abstract A system of quasilinear coupled equations which arise from simulation of contamination of geologic nulear waste in porous media is studied. We’ll discuss Galerkin method for the model of compressible flow with molecular diffusion and dispersion. Some new techniques are introcued to error analysis. Only one dimensional case is considered. The optimal error estimate in both L^2 and H^1 is proved. A contribution of this paper is how the dispersion term can be handled,