Laminar Flow

Nonmodal transient growth studies and estimation of optimal perturbations have been made for the compressible plane Couette flow with three-dimensional disturbances. The steady mean flow is characterized by a non-uniform shear-rate and a varying temperature across the wall-normal direction for an appropriate perfect gas model. The maximum amplification of perturbation energy over time, G max , is found to increase with increasing Reynolds number Re, but decreases with increasing Mach number M. More specifically, the optimal energy amplification G opt (the supremum of G max over both the streamwise and spanwise wavenumbers) is maximum in the incompressible limit and decreases monotonically as M increases. The corresponding optimal streamwise wavenumber, α opt , is non-zero at M = 0, increases with increasing M , reaching a maximum for some value of M and then decreases, eventually becoming zero at high Mach numbers. While the pure streamwise vortices are the optimal

This paper reports an experimental investigation into force convective heat transfer of nanofluids flowing through a cylindrical minichannel under laminar flow and constant wall heat flux conditions. Sample nanofluids were prepared by dispersing different volumetric concentrations (0.2-0.8%) of nanoparticles in deionized water. The results showed that both the convective heat transfer coefficient and the Nusselt number of the nanofluid increase considerably with the nanoparticle volume fraction as well as the Reynolds number. Along with the enhanced thermal conductivity of nanofluids, the migration, interactions, and Brownian motion of nanoparticles and the resulting disturbance of the boundary layer are responsible for the observed enhancement of heat transfer coefficients of nanofluids.

Pulsatile action can be used to mix two streams entering a tube from two separate branches of a bifurcation at low Reynolds numbers. The pulsatile action is provided by two pinch valves, which deform flexible tubing immediately upstream of the connection. The pinch valve action is controlled using a master-slave pulse generator setup. The quality of mixing is evaluated directly by measuring the fluorescence that results from the chemical reaction of species transported in the two streams, one containing native biotin and the other, fluorescein biotin bound to streptavidin. The reaction kinetics are accounted for by normalization using fluorescence measurements on well mixed solutions at the same residence time. The results show that the pulsatile micromixer provides almost complete mixing. Furthermore, the present measurements match results obtained in a previous experiment where flow visualization and image analysis were used to measure mixing quality in a scaled-up model.

A numerical study has been carried out to understand and highlight the effects of axial wall conduction in a conjugate heat transfer situation involving simultaneously developing laminar flow and heat transfer in a square microchannel with constant flux boundary condition imposed on bottom of the substrate wall. All the remaining walls of the substrate exposed to the surroundings are kept adiabatic. Simulations have been carried out for a wide range of substrate wall to fluid conductivity ratio (k sf $ 0.17-703), substrate thickness to channel depth (d sf $ 1-24), and flow rate (Re $ 100-1000). These parametric variations cover the typical range of applications encountered in microfluids/microscale heat transfer domains. The results show that the conductivity ratio, k sf is the key factor in affecting the extent of axial conduction on the heat transport characteristics at the fluid-solid interface. Higher k sf leads to severe axial back conduction, thus decreasing the average Nusselt number (Nu). Very low k sf leads to a situation which is qualitatively similar to the case of zero-thickness substrate with constant heat flux applied to only one side, all the three remaining sides being kept adiabatic; this again leads to lower the average Nusselt number (Nu). Between these two asymptotic limits of k sf , it is shown that, all other parameters remaining the same (d sf and Re), there exists an optimum value of k sf which maximizes the average Nusselt number (Nu). Such a phenomenon also exists for the case of circular microtubes.

Numerical predictions are reported for buoyancy-induced circulations in a 2D closed cavity with internal heat sources. Two cases are considered: (A) two vertical plates with uniform heat generation, forming a short vertical channel within the enclosure; and, (B) a rectangular heating block with uniform wall temperature, placed central in the enclosure. Air, with a Prandtl number 0.71, is considered as the working¯uid. The vertical enclosure walls are isothermal, while the horizontal enclosure walls are adiabatic. Results are presented for two values of the Grashof number, one below the stability limit for laminar ow, and one well above it. In those latter cases, the longterm behaviour of the numerical solution is time-dependent, i.e. no steady-state can be reached. Heat transfer results are compared with predictions from standard correlations for isolated surfaces.

Numerical calculations of the 2-D steady incompressible driven cavity flow are presented. The Navier-Stokes equations in streamfunction and vorticity formulation are solved numerically using a fine uniform grid mesh of 601 × 601. The steady driven cavity solutions are computed for Re ≤ 21,000 with a maximum absolute residuals of the governing equations that were less than 10 −10. A new quaternary vortex at the bottom left corner and a new tertiary vortex at the top left corner of the cavity are observed in the flow field as the Reynolds number increases. Detailed results are presented and comparisons are made with benchmark solutions found in the literature.

This is a preprint or i paper intended for publication in a journal or proceedings. Since changes may he made before publication, this preprint is made available with the un derstanding that it will not be cited or reproduced without the permission of the author.

A series of experiments was conducted to study the effect of twisted-tape width on the heat transfer and pressure drop with laminar flow in tubes. Data for three twisted-tape wavelengths, each with five different widths, have been collected with constant wall temperature boundary condition. Correlations for the friction factor and Nusselt number are also available. The correlations predict the experimental data to within 10 to 15 percent for the heat transfer and friction factor, respectively. The presence of the twisted tape has caused the friction factor to increase by a factor of 3 to 7 depending on Reynolds number and the twisted-tape geometry. Heat transfer results have shown an increase of 1.5 to 3 times that of plain tubes depending on the flow conditions and the twisted-tape geometry. The width shows no effect on friction factor and heat transfer in the low range of Reynolds number but has a more pronounced effect on heat transfer at the higher range of Reynolds number. It i...

The purpose of the present work is to investigate the effect of magnetic field on laminar natural-convection heat transfer inside a partitioned enclosure. In our formulation of non linear governing equations, mass, momentum, and energy are applied to the partitioned enclosure. A finite volume code based on PATANKAR's SIMPLER method is utilized. Results are obtained for different Rayleigh numbers (Ra), Hartmann numbers (Ha) and baffle positions while the Prandtl number is constant (Pr = 0 733). Results show that as Ra increases the maximum absolute value of the stream function increases and causes the flow to move faster. Also, as Hartman number increases (magnetic field intensifies) the natural convection suppresses and therefore the maximum absolute value of the stream function and Nusselt number reduces. Furthermore the partition causes the flow to separate and to form two vortexes inside the enclosure.

Numerical simulations were used to investigate natural radiation and convection interactions in small rooms with three-dimensional geometry. The opposite vertical walls are heated and cooled, while the other walls are supposed to be fixed. Governance flow, momentum equations, and radiative conversion are solved using Ansys Fluent CFD. In estimating thermal terminology, a second-degree wind diagram and a dual solution algorithm are used. The cubic box is filled with air and the flow is considered protective. Air characteristics are assumed to be constant, except for the difference in density in which a Bosnic approximation is used. The surface heat model (S2S) is used as the radiation transfer model. The arithmetic field is a square container Length of the edge = 0.225 m In a surrounding environment at T = 293 K. One of the walls of the case is heated up to 473 K. Note that the radiation from the opposite wall is high, with the improved model. Radiant heat transfer is reduced. I. INTRODUCTION Natural convection and heat transfer by heat radiation in fluid-filled cavities have received much attention in recent years due to its relationship to the thermal performance of engineering applications such as cooling electronic components, electrical boxes, assembler designs, solar designs, heat exchangers, etc.. Therefore, the common characteristics of natural convection and heat transfer by heat radiation are more important. The study of heat transfer in the room was the main topic of the researchers due to a wide range of applications in engineering and working life. It finds its application from cooling the nuclear reactor to removing heat from the micro-electronic components as well as for designing the room air conditioning, thermal design for commercial buildings, cold storage, oven and many more. In addition to a wide range of applications, the simultaneous thought of wall conduction and convection in fluid flow remains an exciting area of research in recent decades. Several articles can be found in the literature to study natural convection in the can. There are many boundary conditions that can be taken into consideration, but the most complex and practically applicable area of least study has been found in the literature. Most of the areas already studied are bottom warming or lateral warming. But in this study, we studied a viable limit state with associated heat transfer. Energy has long been a major topic of discussion among researchers. During any development program for any technology, energy consumption has always been of great importance. An important part of the total energy consumed in the useful life of any building is the operating capacity. This involves maintenance and, most importantly, the energy involved in maintaining the building in comfortable thermal and visual conditions. The building energy analysis tool used before starting any project aims to reduce this operating capacity. It is important to understand that this decrease in energy consumption must be achieved without regard to low performance. Therefore, the building should provide a comfortable environment compared to its external environment. Previous studies have shown the fact that the passenger quickly responds to any discomfort to restore his comfort, but this can negatively affect energy consumption. Therefore, accurate prediction of thermal comfort is very important when designing a building to maintain less energy consumption.

The initiation of turbulent non-premixed combustion of gaseous fuels through autoignition and through spark ignition is reviewed, motivated by the increasing relevance of these phenomena for new combustion technologies. The fundamentals of the associated turbulent-chemistry interactions are emphasized. Background information from corresponding laminar flow problems, relevant turbulent combustion modelling approaches, and the ignition of turbulent sprays are included. For both autoignition and spark ignition, examination of the reaction zones in mixture fraction space is revealing. We review experimental and numerical data on the stochastic nature of the emergence of autoignition kernels and of the creation of kernels and subsequent flame establishment following spark ignition, aiming to reveal the particular facet of the turbulence causing the stochasticity. In contrast to fullyfledged turbulent combustion where the effects of turbulence on the reaction are reasonably wellestablished, at least qualitatively, here the turbulence can cause trends that are not straightforward. Autoignition occurs usually away from stoichiometry at a ''most reactive mixture fraction'', which can be approximately determined from homogeneous or laminar flow autoignition calculations, and at locations in the turbulent flow with low scalar dissipation. Such locations may be the cores of vortices. Once autoignition has occurred at a time that is mostly affected by the history of the conditional scalar dissipation, the relative magnitudes of convection, diffusion and reaction can affect the stabilisation height of flames in sprays or jets. Modelling efforts based on the Conditional Moment Closure, advanced flamelet approaches, and the transported PDF method seem suitable for capturing many, but not yet all, of the trends observed in DNS or experiment. Further experiments and DNS of realistic fuels and at conditions demonstrating chemical complexities must be performed to examine more fully the effects of scalar dissipation and its fluctuations on pre-ignition reaction zones. The statistics of the first appearance of autoignition in transient problems and its connection with the mixing field must also be studied. Ignition from a localised spark has a stochastic character that depends on the mixture fraction sampled at the spark location and duration and the local scalar dissipation. The success or not of the subsequent flame depends on the development of turbulent edge or stratified flames. Only preliminary data exist on the propagation speed of such flames and on their quenching. A lot remains to be done on turbulent edge flame propagation in unreacted and partially-reacted mixtures with inhomogeneities, turbulent flame propagation in non-uniformly dispersed droplet mists, and the transient stabilisation process of recirculating flames. The nature of the flame generation process at very short timescales, i.e. before any appreciable propagation, by sparking in inhomogeneous mixtures needs also to be examined. The development of high repetition rate diagnostics, for single-and two-phase flows, and the development of modelling approaches capturing both premixed and non-premixed reaction zones in gaseous and spray combustion are necessary.

In this paper, roughness was modelled as a pattern of parallelepipedic elements of height k periodically distributed on the plane walls of a microchannel of height H and of infinite span. Two different approaches were used to predict the influence of roughness on heat transfer in laminar flows through this microchannel. Three-dimensional numerical simulations were conducted in a computational domain based on the wavelength l. A one-dimensional model (RLM model) was also developed on the basis of a discrete-element approach and the volume averaging technique. The numerical simulations and the rough-layer model agree to show that the Poiseuille number Po and the Nusselt number Nu increase with the relative roughness. The RLM model shows that the roughness effect may be interpreted by using effective roughness heights k eff and k effq for predicting Po and Nu respectively. k eff and k effq depend on two dimensionless local parameters: the porosity of the rough-layer and the roughness height normalized with the distance between the rough elements. The present results show that roughness increases the friction factor more than the heat transfer coefficient (performance evaluation criteria < 1), for a relative roughness height expected in the fabrication of microchannels (k/(H/2) < 0.46) or k/D h < 0.11).

An experimental investigation on natural convection in air in vertical convergent channels with wall uniform heat flux is presented. Wall temperatures show that by increasing the spacing the effect of the convergence angle decreases. For the lowest spacing, a significant decrease of maximum wall temperature occurs passing from the parallel vertical plate configurations to convergence angles h P 2 .

The concept of permeability of porous media is discussed, and a modification of Kozeny's permeability equation to include the effect of effective porosity is introduced. An analytical expression for the specific surface area of a system constructed of randomly placed identical obstacles with unrestricted overlap is derived, and a lattice-gas cellular automaton method is then used to simulate the dependence on porosity of permeability, tortuosity, and effective porosity for a flow of Newtonian uncompressible fluid in this twodimensional porous substance. The simulated permeabilities can well be explained by the concept of effective porosity, and the exact form of the specific surface area. The critical exponent of the permeability near the percolation threshold is also determined from the simulations.

This work describes a novel bioreactor system for the cultivation of animal, insect, and plant cells using wave agitation induced by a rocking motion. This agitation system provides good nutrient distribution, off-bottom suspension, and excellent oxygen transfer without damaging fluid shear or gas bubbles. Unlike other cell culture systems, such as spinners, hollow-fiber bioreactors, and roller bottles, scale-up is simple, and has been demonstrated up to 100 L of culture volume. The bioreactor is disposable, and therefore requires no cleaning or sterilization. Additions and sampling are possible without the need for a laminar flow cabinet. The unit can be placed in an incubator requiring minimal instrumentation. These features dramatically lower the purchase cost, and operating expenses of this laboratory/pilot scale cell cultivation system. Results are presented for various model systems: 1) recombinant NS0 cells in suspension; 2) adenovirus production using human 293 cells in suspension; 3) Sf9 insect cell/baculovirus system; and 4) human 293 cells on microcarrier. These examples show the general suitability of the system for cells in suspension, anchorage-dependent culture, and virus production in research and GMP applications.

In this presentation we analyzed and compared the software packages Eclipse 2004A, NGT BOS v.2.1 and ANSYS CFX v11.0 for the task of the oil and gas flows simulation in a porous medium. We identified the common features, examined the differences and explored recommended fields of application.

The current study investigates the augmentation in the laminar forced convection characteristics of the backward-facing step flow in a two-dimensional channel by means of introducing an adiabatic circular cylinder in the domain. The effects of various cross-stream positions (i.e., y c ¼ 0e1.5) of the circular cylinder on the flow and heat transfer characteristics of the backward-facing step flow has been numerically explored for the Reynolds number range 1e200 and Prandtl number of 0.71 (air). The governing continuity, NaviereStokes and energy equations along with appropriate boundary conditions are solved by using FLUENT. The flow and thermal fields have been explained by streamline and isotherm profiles, respectively; however, no temperature dependency effects are considered for the flow viscosity and thermal conductivity. The engineering parameters like wake/recirculation length, total drag coefficient and average Nusselt number, etc. are calculated for the above range of conditions. The present results show an enhancement in the peak Nusselt value of up to 155% using a circular cylinder as compared to the unobstructed case (i.e., without cylinder). Finally, simple correlations for total drag coefficient and peak Nusselt number are obtained for the above range of conditions.

The stability of the incompressible attachment-line boundary layer is studied by solving a partial-differential eigenvalue problem. The basic flow near the leading edge is taken to be the swept Hiemenz flow which represents an exact solution of the Navier-Stokes (N-S) equations. Previous theoretical investigations considered a special class of two-dimensional disturbances in which the chordwise variation of disturbance velocities mimics the basic flow and renders a system of ordinarydifferential equations of the Orr-Sommerfeld type. The solution of this sixth-order system by showed that the two-dimensional disturbance is stable provided that the Reynolds number R < 583.1. In the present study, the restrictive assumptions on the disturbance field are relaxed to allow for more general solutions. Results of the present analysis indicate that unstable perturbations other than the special symmetric two-dimensional mode referred to above do exist in the attachment-line boundary layer provided R > 646. Both symmetric and antisymmetric two-and three-dimensional eigenmodes can be amplified. These unstable modes with the same spanwise wavenumber travel with almost identical phase speeds, but the eigenfunctions show very distinct features. Nevertheless, the symmetric twodimensional mode always has the highest growth rate and dictates the instability. As far as the special two-dimensional mode is concerned, the present results are in complete agreement with previous investigations. One of the major advantages of the present approach is that it can be extended to study the stability of compressible attachment-line flows where no satisfactory simplified approaches are known to exist.

A one-dimensional model to determine the laminar ow of a uid in a porous channel with wall suction or injection is proposed. The approach is based on the integration of the Navier-Stokes equations using the analytical solutions for the two-dimensional local velocity and pressure ÿelds obtained from the asymptotic developments at low ÿltration Reynolds number proposed by Berman (J. Appl. Phys. 24 (1953) 1232) and Yuan and Finkelstein (Trans. ASME 74 . It is noticeable that the resulting one-dimensional model preserves the whole ow properties, in particular the inertial terms which can a ect the wall suction conditions and the spatial distribution of the growing particle cake layer at the wall encountered in ÿltration processes. The model is validated in the case of a single porous channel of rectangular or circular cross-section with uniform or variable wall suction. Then the model is applied to a two-dimensional multi-channel system which consists of a great number of adjacent entrance and exit channels connected by a ÿlter porous medium. It is shown that the e ect of non-uniform boundary conditions and the in uence of heterogeneous geometrical characteristics on the heterogeneity of the uid ow structure can be studied using such a model. ?

Pressure gradients and the corresponding mass¯ow rates of ®ve dierent non-Newtonian¯uid foods: 1% solutions of sodium alginate and CMC, 1.5% CMC solution, two dierent tomato ketchups, oyster sauce, in four dierent diameter stainless steel tubes ranging from 7.51 to 16.34 mm i.d. were recorded using a continuous recording type tube¯ow viscometer capable of operating in both transient and continuous¯ow modes. The¯uids were pseudoplastic in nature and followed the power law model. The¯ow was con®ned to the laminar¯ow regime and appreciable slippage occurred in all cases. Commercially available arti®cial neural networks based on back-propagation and generalized regression algorithm were applied to predict the pressure gradients in tube¯ow providing mass¯ow rate, consistency coecients and¯ow behavior indices obtained from a low shear rate rotational viscometer, mass density and tube diameters as inputs. The net predicted values closely followed the experimental ones with an average absolute error below 5.44%.

Laser-Doppler measurements are reported for laminar and turbulent flow through a 90° bend of circular cross-section with mean radius of curvature equal to 2.8 times the diameter. The measurements were made in cross-stream planes 0.58 diameters upstream of the bend inlet plane, in 30, 60 and 75° planes in the bend and in planes one and six diameters downstream of the exit plane. Three sets of data were obtained: for laminar flow at Reynolds numbers of 500 and 1093 and for turbulent flow at the maximum obtainable Reynolds number of 43 000. The results show the development of strong pressure-driven secondary flows in the form of a pair of counter-rotating vortices in the streamwise direction. The strength and character of the secondary flows were found to depend on the thickness and nature of the inlet boundary layers, inlet conditions which could not be varied independently of Reynolds number. The quantitative anemometer measurements are supported by flow visualization studies. Refrac...

Hypoxia can influence fish growth, survival and on larger scales, population structure. These effects may be influenced by water temperature, and may vary intra-specifically with genotype. In Atlantic cod (Gadus morhua L.), the two haemoglobin homozygotes (Hb-I⁎11 and Hb-I⁎22) vary in oxygen affinity at different temperatures, which is thought to correspond to variation in hypoxia tolerance. We therefore tested if hypoxic avoidance behaviour in cod 1) depends on ambient temperature and 2) is modified by haemoglobin genotype. In a laminar flow choice box, we subjected juvenile cod to an initial phase of non-escapable hypoxia, and a subsequent recovery phase, where one habitat was kept at 20% O 2 saturation while the other was raised in steps to full saturation. The experiment was performed at 5 and 15°C with Hb-I⁎11 and Hb-I⁎22 cod. Cod responded to inescapable hypoxia by reducing their overall swimming speed and then, at the initial levels of the recovery phase, avoiding the most hypoxic habitat, irrespective of temperature or genotype. Fish recovered quickly as O 2 levels increased, as evidenced by increased swimming speed and time spent in the most hypoxic habitat. The avoidance response depended strongly on temperature: the relative reduction in speed and avoidance of the most hypoxic habitat was more pronounced at 15 than at 5°C. During the recovery phase, stressed fish initially maintained a higher swimming speed in the most hypoxic habitat. However, as O 2 increased, swimming speed in both habitats converged. This point of convergence occurred at a lower O 2 saturation at 5°C. Fish ventilation rate in inescapable hypoxia was also higher at 15°C. Haemoglobin genotype did not influence either ventilation rates or the nature of the hypoxic avoidance response at either temperature, but Hb-I⁎11 cod swam faster than Hb-I⁎22 cod in normoxia at 15°C. Our results indicate that increased temperature limits the ability of cod of both haemoglobin genotypes to exploit hypoxic habitats. This may have negative future consequences for coastal cod stocks in light of increasing global temperatures and eutrophication in coastal waters.

Reçu le 4 juin 2002 ; accepté le 5 mars 2003 Résumé L'objectif de ce travail est de déterminer l'influence de la forme du profil de vitesse à l'entrée d'un canal, périodiquement chauffé par le bas, sur le transfert thermique. On considère la convection mixte, bidimensionnelle, laminaire, pour un fluide Newtonien. Une solution analytique est obtenue dans le cas de faibles valeurs du nombre de Rayleigh Ra. La solution numérique est en accord avec la solution analytique dans le cas de faibles valeurs du nombre de Peclet Pe.  2003 Éditions scientifiques et médicales Elsevier SAS. Tous droits réservés.

Experimental data are reported for fully developed laminar flow of a shear-thinning liquid through both a concentric and an 80% eccentric annulus with and without centrebody rotation. The working fluid was an aqueous solution of 0.1% xanthan gum and 0.1% carboxymethylcellulose for which the flow curve is well represented by the Cross model. Comparisons are reported between numerical calculations and the flow data, as well as with other laminar annular-flow data for a variety of shear-thinning liquids previously reported in the litera- ture. In general, the calculations are in good quantitative agreement with the experimental data, even in situations where viscoelastic effects, neglected in the calculations, would be expected to play a role.

We investigate how the pseudo-Coriolis force can be employed for the hydrodynamic control of flow through straight and radial microchannels of rectangular cross section on a rotating disk. The key impact parameters are the channel geometry, the angular velocity and the radial downstream position. On the basis of the Coriolis effect, we demonstrate two novel types of hydrodynamically controlled devices for lab-on-a-disk platforms which do neither require hydrophobic structuring of the substrate nor external actuators other than a fixed rotational drive unit. The first device is a flow switch constituted by a symmetric fork structure. Above a certain threshold frequency, the flow is diverted into one particular outlet selected by the sense of rotation. The second device is a hydrodynamically controlled split-and-recombine mixer represented by a simple, 2-dimensional network of low-aspect-ratio channels in parallel. The multilamination of flow which is required to enable rapid mixing under laminar conditions is enforced by the transversal currents resulting from the Coriolis force. By cascading a sequence of such laminators, mixing times can be reduced by more than one order of magnitude!

This paper focuses on the demonstration of an integrated aerostructural method for the design of aerospace vehicles. Both aerodynamics and structures are represented using high-fidelity models such as the Euler equations for the aerodynamics and a detailed finite element model for the primary structure. The aerodynamic outer-mold line and a structure of fixed topology are parameterized using a large number of design variables. The aerostructural sensitivities of aerodynamic and structural cost functions with respect to both outer-mold line shape and structural variables are computed using an accurate and efficient coupled-adjoint procedure. Kreisselmeier-Steinhauser functions are used to reduce the number of structural constraints in the problem. Results of the aerodynamic shape and structural optimization of a natural laminar-flow supersonic business jet are presented together with an assessment of the accuracy of the sensitivity information obtained using the coupled-adjoint procedure.

Excited state lifetimes have been measured for the A-states of CH, OH, and NO in a number of low-pressure, premixed, laminar flow methane flames. From these lifetimes, collisional quenching rates were determined as a function of height above the burner and thus as a function of flame temperature and composition. The results were compared with values calculated using a model of the flame chemistry to predict collider mole fractions, together with parameterizations of quenching rate coefficients for each collider. Measured OH and NO quenching rates agree well with those calculated from these quenching rate coefficients and modeled flame composition data. This indicates that collisional quenching corrections for laser-induced fluorescence measurements can be calculated from knowledge of major species mole fractions and gas temperature. Predicted quenching rates for CH range from agreement with measured values to 27% higher than measured values. This discrepancies suggest insufficient knowledge of high temperature quenching by H 2 O and N 2 .

The fully developed laminar flow in a heated curved pipe under the influence of both centrifugal and buoyancy forces is studied analytically. The pipe is assumed to be heated so as to maintain a constant axial temperature gradient. Both horizontal and vertical pipes are considered. Solutions for these two cases are obtained by regular perturbations in the Dean number and the product of the Reynolds and Rayleigh numbers; the solutions are therefore limited to small values of these parameters. Predictions of the axial and secondary flow velocities, streamlines, shear stress, temperature distribution and heat transfer are given for a representative case. 12-2 VAN DYKE, M.

Two-dimensional periodically fully developed laminar forced convection fluid flow and heat transfer characteristics in a horizontal channel with staggered fins are investigated numerically under constant wall heat flux boundary condition. Study is performed using ANSYS Fluent 6.3.26 which uses finite volume method. Air (Pr 0.7) and Freon-12 (Pr 3.5) are used as working fluids. Effects of Reynolds number, Prandtl number, fin height, and distances between two fins on heat transfer and friction factor are examined. Results are given in the form of non-dimensional average Nusselt number and average Darcy friction factor as a function of Reynolds number for different fin distances and Prandtl numbers. The velocity and temperature profiles are also obtained. It is seen that as the fin distance increases, behavior approaches the finless channel, as expected. Also, thermal enhancement factors are given graphically for working fluids. It is seen that heat transfer dominates the friction as b...

A new mathematical model is proposed for time-independent laminar flow through a rigid isotropic and consolidated porous medium of spatially varying porosity. The model is based upon volumetric averaging concepts. Explicit assumptions regarding the mean-geometric properties of the porous microstructure lead to a relationship between tortuosity and porosity. Microscopic inertial effects are introduced through consideration of flow development within the pores. A momentum transport equation is derived in terms of the fluid properties, the porous medium porosity and a characteristic length of the microstructure. In the limiting cases of porosity unity and zero, the model yields the required Navier-Stokes equation for free flow and no flow in a solid, respectively.

Detailed numerical computations for laminar and turbulent natural convection within a square cavity filled with a fluid saturated porous medium are presented. Heated vertical walls are maintained at constant but different temperatures, while horizontal surfaces are kept insulated. The macroscopic j-e turbulence model with wall function is used to handle turbulent flows in porous media. In this work, the turbulence model is first switched off and the laminar branch of the solution is found when increasing the Rayleigh number, Ra m . Computations covered the range 10 < Ra m < 10 6 and 10 À7 < Da < 10 À10 and made use of the finite volume method. Subsequently, the turbulence model is included and calculations start at high Ra m , merging to the laminar branch for a reducing Ra m and for Ra m less than a certain critical Rayleigh number, Ra cr . This convergence of results as Ra m decreases can be seen as a characterization of the laminarization phenomenon. For Ra m values less than around 10 4 , both laminar and turbulent flow solutions merge, indicating that such critical value for Ra m was reached. Results further indicate that when the parameters porosity, Pr, conductivity ratio between the fluid and the solid matrix and the Ra m are kept fixed, the lower the Darcy number, the higher the average Nusselt number at the hot wall.

An algorithm based on the finite element modified method of characteristics (FEMMC) is presented to solve convection-diffusion, Burgers and unsteady incompressible Navier-Stokes equations for laminar flow. Solutions for these progressively more involved problems are presented so as to give numerical evidence for the robustness, good error characteristics and accuracy of our method. To solve the Navier-Stokes equations, an approach that

The two-dimensional and unsteady free stream flow of power law fluids past a long square cylinder has been investigated numerically in the range of conditions 60 ≤ Re ≤ 160 and 0.5 ≤ n ≤ 2.0. Over this range of Reynolds numbers, the flow is periodic in time. A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. The global quantities such as drag coefficients, Strouhal number and the detailed kinematic variables like stream function, vorticity and so on, have been obtained for the above range of conditions. While, over this range of Reynolds number, the flow is known to be periodic in time for Newtonian fluids, a pseudo-periodic flow regime displaying more than one dominant frequency in the lift is observed for shear-thinning fluids. This seems to occur at Reynolds numbers of 120 and 140 for n = 0.5 and 0.6, respectively. Broadly speaking, the smaller the value of the power law index, lower is the Reynolds number of the onset of the pseudoperiodic regime. This work is concerned only with the fully periodic regime and, therefore, the range of Reynolds numbers studied varies with the value of the power law index. Not withstanding this aspect, in particular here, the effects of Reynolds number and of the power law index have been elucidated in the unsteady laminar flow regime. The leading edge separation in shear-thinning fluids produces an increase in drag values with the increasing Reynolds number, while shear-thickening fluid behaviour delays this separation and shows the lowering of the drag coefficient with the Reynolds number. Also, the preliminary results suggest the transition from the steady to unsteady flow conditions to occur at lower Reynolds numbers in shear-thinning fluids than that in Newtonian fluids.

This work describes a novel bioreactor system for the cultivation of animal, insect, and plant cells using wave agitation induced by a rocking motion. This agitation system provides good nutrient distribution, off-bottom suspension, and excellent oxygen transfer without damaging fluid shear or gas bubbles. Unlike other cell culture systems, such as spinners, hollow-fiber bioreactors, and roller bottles, scale-up is simple, and has been demonstrated up to 100 L of culture volume. The bioreactor is disposable, and therefore requires no cleaning or sterilization. Additions and sampling are possible without the need for a laminar flow cabinet. The unit can be placed in an incubator requiring minimal instrumentation. These features dramatically lower the purchase cost, and operating expenses of this laboratory/pilot scale cell cultivation system. Results are presented for various model systems: 1) recombinant NS0 cells in suspension; 2) adenovirus production using human 293 cells in suspension; 3) Sf9 insect cell/baculovirus system; and 4) human 293 cells on microcarrier. These examples show the general suitability of the system for cells in suspension, anchorage-dependent culture, and virus production in research and GMP applications.

Effect of copper-water nanofluid has been studied as a cooling medium to simulate the heat transfer behaviour in a two-dimensional (infinite depth) horizontal rectangular duct, where top and bottom walls are two isothermal symmetric heat sources. The governing continuity, momentum and energy equations for a laminar flow are being discretized using a finite volume approach using a power law profile approximation and has been solved iteratively, through alternate direction implicit, using the SIMPLER algorithm. The thermal conductivity of nanofluid has been determined by model proposed by Patel et al. Study has been conducted considering the fluid as Newtonian as well as non-Newtonian for a wide range of Reynolds number (Re = 5 to 1500) and solid volume fraction (0.00 φ 0.050). It has been observed that the heat transfer augmentation is possible using nanofluid in comparison to conventional fluids for both the cases. The rate of heat transfer increases with the increase in flow as well as increase in solid volume fraction of the nanofluid. Unlike natural convection the increase in heat transfer is almost same for both the cases.

The transient cooling of a fluid initially at rest inside a storage tank submitted to heat losses to the ambient is studied. The study is restricted to laminar flow conditions. In order to identify the relevant non-dimensional groups that define the transient natural convection phenomenon that occurs, a non-dimensional analysis is carried out. The long-term behaviour of the fluid is modeled by formulating a prediction model based on global balances. A parametric study by means of several multidimensional numerical simulations led to correlate the Nusselt number and the transient mean fluid temperature, to feed the global model proposed. Special attention is given to the appropriateness of the spatial and time discretisation adopted, the verification of the numerical solutions and the post-processing tasks in order to obtain the correlations. The most relevant particularities of the numerical model developed are also pointed out.

We study the effects of localized instabilities on the behavior of inviscid fluids. We place geometric optics techniques independently developed by Friedlander -Vishik and Lifschitz -Hameiri in the framework of the general stability / instability problem of fluid dynamics. We show that, broadly put, all laminar flows are unstable with respect to localized perturbations.

The fully developed steady flow of a fluid through a curved tube with elliptic cross-section is studied, the cross-sectional area varying slowly with longitudinal distance. Using a perturbation scheme in terms of two small parameters (geometric parameter and curvature parameter), complete analytical solutions are obtained to the first order. The effects of constriction combined with constant curvature of the centre line are discussed. The phenomenon of secondary flow, shear stress and the increased impedance (due to the constriction) are calculated. The possibility of the application of the results to various engineering problems and physiological flows is indicated.