Three-Dimensional Unsteady Flow With Heat and Mass Transfer Over a Continuous Stretching Surface

A numerical solution of the unsteady boundary layer equations under similarity assumptions is obtained. The solution represents the three-dimensional unsteady fluid motion caused by the time-dependent stretching of a flat boundary. It has been shown that a self-similar solution exists when either the rate of stretching is decreasing with time or it is constant. Three different numerical techniques are applied and a comparison is made among them as well as with earlier results. Analysis is made for various situations like deceleration in stretching of the boundary, mass transfer at the surface, saddle and nodal point flows, and the effect of a magnetic field. Both the constant temperature and constant heat flux conditions at the wall have been studied.

Second-order boundary-layer effects for the unsteady laminar incompressible three-dimensional stagnation-point flow

All the second-order boundary-layer effects on the unsteady laminar incompressible flow at the stagnation-point of a three-dimensional body for both nodal and saddle point regions have been studied. It has been assumed that the free-stream velocity, wall temperature and mass transfer vary arbitrarily with time. The effect of the Prandtl number has been taken into account. The partial differential equations governing the flow have been derived for the first time and then solved numerically unsteady free-stream velocity distributions, the nature of the using an implicit finite-difference scheme. It is found that the stagnation point and the mass transfer strongly affect the skin friction and heat transfer whereas the effects of the Prandtl number and the variation of the wall temperature with time are only on the heat transfer. The skin friction due to the combined effects of first- and second-order boundary layers is less than the skin friction due to, the first-order boundary layers whereas the heat transfer has the opposite behaviour. Suction increases the skin friction and heat transfer but injection does the opposite

Interrelations between Dry Eye Syndrome and Tear Fluid Phospholipid Transfer Protein

The simplified model of human tear fluid (TF) is a three-layered structure composed of a homogenous gel-like layer of hydrated mucins, an aqueous phase, and a lipid-rich outermost layer found in the tear-air interface. It is assumed that amphiphilic phospholipids are found adjacent to the aqueous-mucin layer and externally to this a layer composed of non-polar lipids face the tear-air interface. The lipid layer prevents evaporation of the TF and protects the eye, but excess accumulation of lipids may lead to drying of the corneal epithelium. Thus the lipid layer must be controlled and maintained by some molecular mechanisms. In the circulation, phospholipid transfer protein (PLTP) and cholesteryl ester transfer protein (CETP) mediate lipid transfers. The aim of this thesis was to investigate the presence and molecular mechanisms of lipid transfer proteins in human TF. The purpose was also to study the role of these proteins in the development of dry eye syndrome (DES). The presence of TF PLTP and CETP was studied by western blotting and mass spectrometry. The concentration of these proteins was determined by ELISA. The activities of the enzymes were determined by specific lipid transfer assays. To study the molecular mechanisms involved in PLTP mediated lipid transfer Langmuir monolayers and asymmetrical flow field-flow fractionation (AsFlFFF) was used. Ocular tissue samples were stained with monoclonal antibodies against PLTP to study the secretion route of PLTP. Heparin-Sepharose affinity chromatography was used for PLTP pull-down experiments and co-eluted proteins were identified with MALDI-TOF mass spectrometry or Western blot analysis. To study whether PLTP plays any functional role in TF PLTP-deficient mice were examined. The activity of PLTP was also studied in dry eye patients. PLTP is a component of normal human TF, whereas CETP is not. TF PLTP concentration was about 2-fold higher than that in human plasma. Inactivation of PLTP by heat treatment or immunoinhibition abolished the phospholipid transfer activity in tear fluid. PLTP was found to be secreted from lacrimal glands. PLTP seems to be surface active and is capable of accepting lipid molecules without the presence of lipid-protein complexes. The active movement of radioactively labeled lipids and high activity form of PLTP to acceptor particles suggested a shuttle model of PLTP-mediated lipid transfer. In this model, PLTP physically transports lipids between the donor and acceptor. Protein-protein interaction assays revealed ocular mucins as PLTP interaction partners in TF. In mice with a full deficiency of functional PLTP enhanced corneal epithelial damage, increased corneal permeability to carboxyfluorescein, and decreased corneal epithelial occludin expression was demonstrated. Increased tear fluid PLTP activity was observed among human DES patients. These results together suggest a scavenger property of TF PLTP: if the corneal epithelium is contaminated by hydrophobic material, PLTP could remove them and transport them to the superficial layer of the TF or, alternatively, transport them through the naso-lacrimal duct. Thus, PLTP might play an integral role in tear lipid trafficking and in the protection of the corneal epithelium. The increased PLTP activity in human DES patients suggests an ocular surface protective role for this lipid transfer protein.

Unsteady laminar compressible boundary-layer flow at a three-dimensional stagnation point

Unsteady laminar compressible boundary-layer flow with variable properties at a three-dimensional stagnation point for both cold and hot walls has been studied for the case when the velocity of the incident stream varies arbitrarily with time. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. Computations have been carried out for two particular unsteady free-stream velocity distributions: (i) an accelerating stream and (ii) a fluctuating stream. The results indicate that the variation of the density-viscosity product across the boundary layer, the wall temperature and the nature of stagnation point significantly affect the skin friction and heat transfer.

A mathematical analysis of nonlinear waves in a fluid filled visco-elastic tube

Our investigations in this paper are centred around the mathematical analysis of a ldquomodal waverdquo problem. We have considered the axisymmetric flow of an inviscid liquid in a thinwalled viscoelastic tube under certain simplifying assumptions. We have first derived the propagation space equations in the long wave limit and also given a general procedure to derive these equations for arbitrary wave length, when the flow is irrotational. We have used the method of operators of multiple scales to derive the nonlinear Schrödinger equation governing the modulation of periodic waves and we have elaborated on the ldquolong modulated wavesrdquo and the ldquomodulated long wavesrdquo. We have also examined the existence and stability of Stokes waves in this system. This is followed by a discussion of the progressive wave solutions of the long wave equations. One of the most important results of our paper is that the propagation space equations are no longer partial differential equations but they are in terms of pseudo-differential operators.Die vorliegenden Untersuchungen beziehen sich auf die mathematische Behandlung des ldquorModalwellenrdquo-Problems. Die achsensymmetrische Strömung einer nichtviskosen Flüssigkeit in einem dünnwandigen viskoelastischen Rohr, unter bestimmten vereinfachenden Annahmen, wird betrachtet. Zuerst werden die Gleichungen des Ausbreitungsraumes im Langwellenbereich abgeleitet und eine allgemeine Methode zur Herleitung dieser Gleichungen für beliebige Wellenlängen bei nichtrotierender Strömung angegeben. Eine Operatorenmethode mit multiplem Maßstab wird verwendet zur Herleitung der nichtlinearen Schrödinger-Gleichung für die Modulation der periodischen Wellen, und die ldquorlangmodulierten Wellenrdquo sowie die ldquormodulierten Langwellenrdquo werden aufgezeigt. Weiters wird die Existenz und die Stabilität der Stokes-Wellen im System untersucht. Anschließend werden die progressiven Wellenlösungen der Langwellengleichungen diskutiert. Eines der wichtigsten Ergebnisse dieser Arbeit ist, daß die Gleichungen des Ausbreitungsraumes keine partiellen Differentialgleichungen mehr sind, sondern Ausdrücke von Pseudo-Differentialoperatoren.

Low reynolds number flow of a dilute suspension in slowly varying tubes

We have discussed here the flow of a dilute suspension of rigid particles in Newtonian fluid in slowly varying tubes characterized by a small parameter ε. Solutions are presented in the form of asymptotic expansions in powers of ε. The effect of the suspension on the fluid is described by two parameters β and γ which depend on the volume fraction of the particles which we assume to be small. It is found that the presence of the particles accelerate the process of eddy formation near the constriction and shifts the point of separation.

Unsteady mixed convection flow in stagnation region adjacent to a vertical surface

The unsteady two-dimensional laminar mixed convection flow in the stagnation region of a vertical surface has been studied where the buoyancy forces are due to both the temperature and concentration gradients. The unsteadiness in the flow and temperature fields is caused by the time-dependent free stream velocity. Both arbitrary wall temperature and concentration, and arbitrary surface heat and mass flux variations have been considered. The Navier-Stokes equations, the energy equation and the concentration equation, which are coupled nonlinear partial differential equations with three independent variables, have been reduced to a set of nonlinear ordinary differential equations. The analysis has also been done using boundary layer approximations and the difference between the solutions has been discussed. The governing ordinary differential equations for buoyancy assisting and buoyancy opposing regions have been solved numerically using a shooting method. The skin friction, heat transfer and mass transfer coefficients increase with the buoyancy parameter. However, the skin friction coefficient increases with the parameter lambda, which represents the unsteadiness in the free stream velocity, but the heat and mass transfer coefficients decrease. In the case of buoyancy opposed flow, the solution does not exist beyond a certain critical value of the buoyancy parameter. Also, for a certain range of the buoyancy parameter dual solutions exist.

Boundary layer swirling flow through a conical hydrocyclone

The paper deals with the flow and heat-transfer problem of a steady axisymmetric laminar incompressible boundary layer swirling flow of a fluid through a conical hydrocyclone. The implicit finitedifference scheme is used to solve the partial differential equations governing the flow. The effect of swirl is found to be more pronounced on the longitudinal skin friction than on the tangential skin friction and heat transfer. The skin friction and heat transfer increase with swirl or with longitudinal distance. Swirl also gives rise to velocity overshoot in the longitudinal velocity profiles and the magnitude of the velocity overshoot increases as the swirl parameter increases. The results are found to be in good agreement with those of the local nonsimilarity and momentum integral methods but they differ appreciably from those of the local similarity method except for the longitudinal skin friction which is fairly in good agreement with that of the local similarity method.Die Arbeit beschäftigt sich mit der Strömung und dem Wärmeübergang in einem konischen Zyklon unter der Voraussetzung stationärer, achsensymmetrischer, laminarer, inkompressibler Grenzschichtströmung. Ein implizites Differenzenverfahren wird benutzt, um die partiellen Differentialgleichungen zu lösen. Der Einfluß des Dralls ist besonders ausgeprägt auf die longitudinale Komponente der Oberflächenreibung, weniger dagegen bei der tangentialen Komponente und beim Wärmeübergang. Die Oberflächenreibung und der Wärmeübergang nehmen zu mit dem Drall, sowie mit dem longitudinalen Abstand. Der Drall erzeugt ein Überschießen der Geschwindigkeit in der longitudinalen Abstand. Der Drall erzeugt ein Überschießen der Geschwindigkeit in der Längsrichtung. Die Größe des Überschusses nimmt mit wachsendem Drallparameter zu. Die Resultate stimmen gut mit den Ergebnissen der Theorie der lokalen Nichtähnlichkeit und der Impulsintegralmethode überein. Dagegen weichen sie mit Ausnahme der longitudinalen Komponente der Oberflächenreibung beträchtlich von den Resultaten der Theorie der lokalen Ähnlichkeit ab.

Comparative study of different formulations and solution methods for two phase flow in saturated porous media

Six models (Simulators) are formulated and developed with all possible combinations of pressure and saturation of the phases as primary variables. A comparative study between six simulators with two numerical methods, conventional simultaneous and modified sequential methods are carried out. The results of the numerical models are compared with the laboratory experimental results to study the accuracy of the model especially in heterogeneous porous media. From the study it is observed that the simulator using pressure and saturation of the wetting fluid (PW, SW formulation) is the best among the models tested. Many simulators with nonwetting phase as one of the primary variables did not converge when used along with simultaneous method. Based on simulator 1 (PW, SW formulation), a comparison of different solution methods such as simultaneous method, modified sequential and adaptive solution modified sequential method are carried out on 4 test problems including heterogeneous and randomly heterogeneous problems. It is found that the modified sequential and adaptive solution modified sequential methods could save the memory by half and as also the CPU time required by these methods is very less when compared with that using simultaneous method. It is also found that the simulator with PNW and PW as the primary variable which had problem of convergence using the simultaneous method, converged using both the modified sequential method and also using adaptive solution modified sequential method. The present study indicates that pressure and saturation formulation along with adaptive solution modified sequential method is the best among the different simulators and methods tested.

Computational Fluid Dynamics in Combustion

Computational fluid dynamics has reached a stage where flow field in practical situation can be predicted to aid the design and to probe into the fundamental flow physics to understand and resolve the issues in fundamental fluid mechanics The study examines the computation of reacting flows After exploring the conservation equations for species and energy, the methods of closing the reaction rate terms in turbulent flow have been examined briefly Two cases of computation where combustion-flow interaction plays important role, have been discussed to illustrate the computational aspects and the physical insight that can be gained by the reacting flow computation

Dense granular flow down an inclined plane A comparison between the hard particle model and soft particle simulations

The granular flow down an inclined plane is simulated using the discrete element (DE) technique to examine the extent to which the dynamics of an unconfined dense granular flow can be well described by a hard particle model First, we examine the average coordination number for the particles in the flow down an inclined plane using the DE technique using the linear contact model with and without friction, and the Hertzian contact model with friction The simulations show that the average coordination number decreases below 1 for values of the spring stiffness corresponding to real materials, such as sand and glass, even when the angle of inclination is only 10 larger than the angle of repose Additional measures of correlations in the system, such as the fraction of particles with multibody contact, the force ratio (average ratio of the magnitudes of the largest and the second largest force on a particle), and the angle between the two largest forces on the particle, show no evidence of force chains or other correlated motions in the system An analysis of the bond-orientational order parameter indicates that the flow is in the random state, as in event-driven (ED) simulations V Kumaran, J Fluid Mech 632, 107 (2009), J Fluid Mech 632, 145 (2009)] The results of the two simulation techniques for the Bagnold coefficients (ratio of stress and square of the strain rate) and the granular temperature (mean square of the fluctuating velocity) are compared with the theory V Kumaran, J Fluid Mech 632, 107 (2009), J Fluid Mech 632, 145 (2009)] and are found to be in quantitative agreement In addition, we also conduct a comparison of the collision frequency and the distribution of the precollisional relative velocities of particles in contact The strong correlation effects exhibited by these two quantities in event-driven simulations V Kumaran, J Fluid Mech 632, 145 (2009)] are also found in the DE simulations (C) 2010 American Institute of Physics doi 10 1063/1 3504660]

A simple method for potential flow simulation of cascades

A simple method using a combination of conformal mapping and vortex panel method to simulate potential flow in cascades is presented. The cascade is first transformed to a single body using a conformal mapping, and the potential flow over this body is solved using a simple higher order vortex panel method. The advantage of this method over existing methodologies is that it enables the use of higher order panel methods, as are used to solve flow past an isolated airfoil, to solve the cascade problem without the need for any numerical integrations or iterations. The fluid loading on the blades, such as the normal force and pitching moment, may be easily calculated from the resultant velocity field. The coefficient of pressure on cascade blades calculated with this methodology shows good agreement with previous numerical and experimental results.

A note on the slow rotation of a disc in a bounded fluid with a surfactant surface layer

A method involving eigenfunction expansion and collocation is employed to solve the axisymmetric problem of a slowly and steadily rotating circular disc in a fluid of finite extent whose surface is covered with a surfactant film. The present method (originally described by Wang (Acta Mech. 94, 97, 1992)) is observed to produce results of practical importance associated with the problem more quickly and more easily than the one used earlier by Shail and Gooden (Int. J. Multiphase Flow 7, 245, 1992). (C) 1994 Academic Press, Inc.

Conjugate MHD flow past a flat plate

A boundary layer solution for the conjugate forced convection flow of an electrically conducting fluid over a semi-infinite flat plate in the presence of a transverse magnetic field is presented. The governing nonsimilar partial differential equations are solved numerically using the Keller box method. Values of the temperature profiles of the plate are obtained for various values of the parameters entering the problem and are given in a table and shown on graphs.

Nonlinear effects on rotating disk flow in a cylindrical casing

The flow due to a finite disk rotating in an incompressible viscous fluid has been studied. A modified Newton-gradient finite difference scheme is used to obtain the solution of full Navier-Stokes equations numerically for different disk and cylinder sizes for a wide range of Reynolds numbers. The introduction of the aspect ratio and the disk-shroud gap, significantly alters the flow characteristics in the region under consideration, The frictional torque calculated from the flow data reveals that the contribution due to nonlinear terms is not negligible even at a low Reynolds number. For large Reynolds numbers, the flow structure reveals a strong boundary layer character.