Averaged Velocity Profiles Research Articles

Low Shear Stress Increases Recombinant Protein Production and High Shear Stress Increases Apoptosis in Human Cells.

SummaryHuman embryonic kidney cells HEK293 can be used for the production of therapeutic glycoproteins requiring human post-translational modifications. High cell density perfusion processes are advantageous for such production but are challenging due to the shear sensitivity of HEK293 cells. To understand the impact of hollow filter cell separation devices, cells were cultured in bioreactors operated with tangential flow filtration (TFF) or alternating tangential flow filtration (ATF) at various flow rates. The average theoretical velocity profile in these devices showed a lower shear stress for ATF by a factor 0.637 compared to TFF. This was experimentally validated and, furthermore, transcriptomic evaluation provided insights into the underlying cellular processes. High shear caused cellular stress leading to apoptosis by three pathways, i.e. endoplasmic reticulum stress, cytoskeleton reorganization, and extrinsic signaling pathways. Positive effects of mild shear stress were observed, with increased recombinant erythropoietin production and increased gene expression associated with transcription and protein phosphorylation.

Numerical simulations of Newtonian fluid flow through a suddenly contracted rectangular channel with two different types of baffle plates

Numerical analysis of turbulent air flow structure through a rectangular channel along with multiple and different types of baffle plates has been performed, which is an important issue for heat exchangers and for that the flow characteristics and pressure drop are need to be identified. Finite Volume Method are employed to solve the governing equations using FLUENT with the Standard $$k-\epsilon $$ turbulence model. The present study has been validated at $$\text {Re}=87{,}300$$ with the studies of Dermitini et al. The aim of this study is to investigate the dynamic behavior of turbulent air flow, baffle height, baffle thickness and arrangement of baffle in different locations for high values of $$\text {Re}=88{,}000$$ . Moreover, flow structure and pressure drop characteristics are discussed in the presence of trapezoidal and plane shape baffles. Normalized velocity profiles and skin friction coefficients have been studied at different locations for trapezoidal and plane baffle plates. Finally, it has been concluded that pressure drop attains its maximum value at the upstream of the channel and minimum value at the downstream of the channel for both the plane and trapezoidal shape baffles. It is ensured that in trapezoidal case axial velocity is higher than plane baffle when four baffles are alternately placed at lower and upper walls. Furthermore, it has also been revealed that the separation of boundary layer is influenced by baffle height (h) and baffle thickness (b). At $$x=0.170 \ \mathrm{m}$$ , normalized velocity profiles $$(u/u_{0})$$ are presented for wide range of Reynolds number, $$\text {Re}\in [44{,}000-176{,}000]$$ to reveal that increase of $$\text {Re}$$ causes the increase in vortexes.

Experimental study of the flow structure around Taylor bubbles in the presence of dispersed bubbles

This work presents an experimental study focusing on the interactions between the dispersed and Taylor bubbles in a slug flow pattern. In order to better investigate these interactions, a quasi-real slug flow was studied, where a single Taylor bubble is injected in a bubbly flow background stream, under controlled and repeatable conditions, controlling the bubbly flow superficial gas and liquid velocity, and also the Taylor bubble length. In this way, ensemble averaged results can be obtained over several Taylor bubbles. The flow was analyzed through the laser diode photocell, high-speed camera imaging and PIV techniques. Results revealed that the terminal Taylor bubble velocity is affected by the gas volume fraction of the bubbly background flow. Ensemble average velocity profiles are presented for Taylor bubble nose and tail regions. Since the experimental apparatus used in the present work allowed a large number of instantaneous PIV acquisitions, the turbulent statistics around the Taylor bubble can also be calculated. These experimental results can be used for the implementation and validation of multidimensional CFD models for flows with different interface length scales.

IMPROVEMENT OF APPROACHES AND METHODS OF TURBULENT FLOW THEORY IN THE PIPES

Abstract. The article consideres the analysis of the literature about the development of the water turbulent flow theory in the pipes. According to the results of analysis and theoretical studies, we obtained mathematical models. These models described the kinematic structure of the water turbulent flow in the pipes for different regions of turbulence. For the first time, the hypothesis was accepted that the dependence obtained from the Navier-Stokes differential equation for constructing the velocity profile in the laminar regime is suitable for calculating the average velocities in the turbulent regime of flow, but for this, it is necessary to replace the molecular kinematic viscosity with the total turbulent kinematic viscosity, which includes kinematic viscosity on the inner surface of the pipe and turbulent kinematic viscosity , which occurs due to the movement of masses from one layer into another, as recommended in J.V. Boussinesq. Based on experimental data I. Nikuradze and F.O. Shevelev, we obtained a distribution of the total kinematic viscosity in the pipes, including the kinematic viscosity on the pipe inner surface and the kinematic turbulent viscosity. For the first time, we used the kinematic viscosity distribution equation in the pipes and obtained the averaged velocity profile equation. This equation corresponds to the boundary conditions on the pipe inner surface and on the axis of the pipe. The equation of maximum averaged velocity, the equation of distance from the axis of the pipe to the points having average velocity, the equation of the ratio of maximum velocity to average velocity was obtained. For the first time, the equation of the tangent stresses components ( , ) and the tangent stresses equation in radial coordinates ( ) were obtained. The equation of the maximum value of the tangent stresses located on the inner surface of the pipe was obtained. The tangent stresses assume a zero value on the pipe axis. The equation of the vortex components ( , ) was obtained. We have shown that vortex lines are concentric circles whose centers are located on the pipe axis. The equation of angular velocity of flow particles rotation relative to the vortex lines was obtained. The maximum value of the particle rotation angular velocity on the pipe inner surface is determined. It decreases monotonically to zero on the axis of the pipeline. It is zero on the pipe axis. In this article, all equations reveal the kinematic structure of the water flow. We described these equations by the Reynolds number and the pipe friction factor. Such equations are adopted to show the dependencies between the regimes and the flow kinematic structure. These equations make it possible to calculate the distribution profile of the total kinematic viscosity, averaged velocity, tangential stresses and angular velocity of flow particle rotation.

Wind load prediction on single tree with integrated approach of L-system fractal model, wind tunnel, and tree aerodynamic simulation

In this work, we adopt the integration of the L-system fractal tree generation, 3D printed wind tunnel modeling, and computational fluid dynamics (CFD) simulation approach to model the wind effect on a single tree. We compare the agreement between CFD simulations and wind tunnel measurements of rigid branched structures resembling trees. First, fractal tree mesh models based on species growth and branching patterns are developed to represent tree species for wind–tree modeling. Subsequently, a scaled-down fractal tree is generated with 3D-printing and subjected to tunnel testing with load cell and particle image velocimetry measurement data under the wind speed of 10 m/s and 15 m/s. Finally, CFD based on Reynolds-Average Navier–Stokes (RANS) simulation with a full closure model and Large Eddy Simulation (LES) using appropriate momentum sink and turbulence source terms for the volumetric tree is carried out. We use both the volume-average porous media and the volume-splitting discretized zones (split number 10 × 10 × 10) to reproduce the momentum sink effect in the numerical simulation. Three tree species, namely, Peltophorum pterocarpum (yellow flame), Khaya senegalensis (African mahogany), and Hopea odorata (ironwood), are tested, and a reasonable agreement of drag force prediction and velocity profiles is obtained when comparing the CFD simulation results with wind tunnel data. The RANS modeled drag force results exhibit 20% of over-prediction, while the normalized velocity profiles display a good match of velocity decay at the tree leeward sides. On the other hand, LES produces much better results with only 3% discrepancy with the experimental results. A comparison of experimental results among the tree species is also carried out. Due to the actual random wind direction, tree slenderness representation, and structural flexibility issues, the current methodology still has the limitation for validation with urban on-site measurement. Nonetheless, this integrated approach is the first step in establishing modeling tool applicability to examine the effect of the forest structure and composition on wind loads.

Adult sea lamprey respond to induced turbulence in a low current system

Manipulation of water velocities and turbulence using pumps, propellers, or jets is a promising alternative to physical water control structures to guide fish towards traps or fishways. Sea lamprey (Petromyzon marinus) are a species of concern in much of their native and invasive ranges, and their improved guidance could benefit management actions for both conservation and control. The flow velocity enhancement system (FVES), an emergent technology that uses a Venturi pump to generate a plume of turbulence, has shown promise guiding downstream migrating fish in slow-moving or static water conditions formed by large reservoirs, but is untested for guidance of upstream swimming fish in low current environments. The FVES had minimal impact on depth averaged velocity profiles, but produced elevated levels of turbulence. Changes in spatial distribution and number of turns suggest sea lamprey detect and are mildly attracted to turbulence induced by the FVES. These results demonstrate the potential of induced turbulence as a guidance mechanism for upstream migrating sea lamprey, but more extensive testing is needed to show the full utility of this approach.

Perfil de velocidad promedio entre una capa de fluido y un medio poroso: La capa límite de Brinkman

It has been mentioned that, the existence of some terms in Darcy's law are the result of the up-scaling method applied to the Stokes flow problem at the pore scale. To address this debate, in this work we perform, at the pore-scale, flow simulations in a free fluid/porous medium system using different models of granular porous media. The local velocity obtained from the Stokes equation allows to obtain the Darcy-scale velocity profiles by a direct averaging instead of using the up-scaled model. The results show the existence of a smooth transition zone in the average velocity profiles near the free fluid/porous medium inter-region. The size and shape of such transition zone depend on the size of the averaging domain and they are a result of averaging local quantities and not a result of solving average equations. In this way, we confirm the existence of an average velocity boundary layer (i.e. Brinkman boundary layer); thus the pertinence of considering other terms in Darcy's law can be certainly justified. We have also determined the extension of the influence of the flow in the free fluid inside the porous medium and the perturbation of the flow in porous medium on the flow in the free fluid.

Experimental and numerical shadowgraph in turbulent Rayleigh–Bénard convection with a rough boundary: investigation of plumes

We show that, in the case of turbulent Rayleigh-Benard convection, shadowgraph can be used to have quantitative results on the plumes statistics and their velocity. For this purpose, we compare the experimental shadowgraph of a Rayleigh-Benard cell with the synthetic shadowgraph obtained by calculating the integrated 2D Laplacian of the temperature field from a numerical simulation very similar to the experiment. We use image processing tools to enhance the quality of the shadowgraph image, and obtain quantitative statistics for the thermal plumes, such as plume density, and plume velocity distribution. To highlight the efficiency of this new process of plume counting, we use, both in the experiment and in the numerical simulation, a turbulent Rayleigh-Benard convection cell with a rough bottom surface, and a smooth top surface, where the statistics of the plumes can be influenced (or not) by the roughness. In addition, the distribution of velocity obtained from processing the synthetic shadowgraph images of the DNS or the experimental shadowgraph images, are compared to the velocity fluid at mid plane of the DNS or PIV measurement in the experiment, respectively. It will be shown that the mean velocity profile measured using the advection of the plumes is different from the average eulerian velocity profile.

Thermodynamic analysis of natural convection supercritical water flow past a stretching sheet using an equation of state approach

The present numerical study examines the free convection heat transfer characteristics of supercritical water flow past a stretching sheet. A suitable equation for the thermal expansion coefficient in a supercritical fluid region is derived based on the equation of state (EOS) approach in terms of compressibility factor, pressure, and temperature. In the present study, the Redlich–Kwong equation of state (RK-EOS) is used to calculate the thermal expansion coefficient in the supercritical region. The values of the thermal expansion coefficient calculated through RK-EOS lies close to the NIST data values when compared to the other equations of state like the Van der Waals equation of state and ideal gas EOS. Also, the behaviour of Nusselt number is studied to characterize the heat transfer characteristics of supercritical water. However, the equations governing the supercritical fluid flow past a stretching sheet are coupled and nonlinear in nature. Hence, the Runge–Kutta fourth-order integration scheme with shooting technique is used to solve these equations. Numerical computations are performed for supercritical water under the influence of various control parameters. Similarity solutions are obtained in terms of flow profiles in the supercritical fluid region. The present study reports that the normal velocity profile decreases and the temperature field increases for increasing values of reduced pressure and reduced temperature. Also, the axial velocity profile shows the dual behaviour for increasing values of unsteady parameter, reduced temperature, and reduced pressure in the supercritical boundary layer region. Furthermore, the component of the normal velocity profile decays for increasing values of the unsteady parameter in the supercritical fluid region. The calculated values of the thermal expansion coefficient using RK-EOS lies in the proximity of NIST data values when compared to Van der Waals and ideal gas equations of state. Also, the local skin-friction coefficient decreases for increasing values of reduced pressure and reduced temperature. Furthermore, the magnitude of local heat transfer rate increases with increasing values of unsteady parameter. The RK-EOS is the suitable EOS approach for predicting the free convection properties of water in a supercritical region.

Coherent Vortex in Two-Dimensional Turbulence around a Rotating Disc

We consider the structure of a coherent vortex formed around a solid rotating disc in two-dimensional turbulent flow. We find the average velocity profile of the coherent vortex for different rotation velocities.

A detailed experimental airfoil performance investigation using an equipped wind tunnel

An experimental study is conducted to investigate the impact of different parameters on the performance of CFJ0025-065-196 airfoil. For this purpose, an equipped wind tunnel with the motor capacity of 7 kW as well as high-tech measuring instruments are employed, and the impact of attack angle on the average velocity profiles for different jet flow velocities, in addition to the self-similar velocity profiles for different attack angles, and the wake effect are found and discussed comprehensively. The experiments are done for five different values of the attack angle, which are 0, 5, 12, 20, and 25° as well three magnitude for the jet flow velocity, including 0, 19.7, and 32.2 m s−1. According to the results, the attack angle in which the performance of the airfoil decreases has an upward trend when the jet flow velocity increases, and it reaches from 20 to 25° when jet flow velocity changes from 0 to 19.7 m s−1. Moreover, increasing the attack angle from 0 to 12° makes the jet frountier wider whereas a downward trend happens by chaning the attack angle from 12 to 25°. Additionally, the higher the jet velocity is, the weaker wake stream has.

Toward the GMF for Wind Speed and Surface Stress Retrieval in Hurricanes Based on the Collocated GPS-Dropsonde and Remote Sensing Data

This article describes the first step toward the development of the geophysical model function (GMF) for the retrieval of wind speed and wind stress in hurricanes, based on developing a relation between the cross-polarized satellite SAR data from Sentinel-1 and winds/stress observed from collocated NOAA GPS-dropsondes data. Field measurements and remote sensing data for tropical cyclones in the Atlantic Ocean were analyzed. Using the data measured by GPS-dropsondes, average wind velocity profiles were obtained, while the parameters of the wind boundary layer (drag coefficient and friction velocity) were restored from the “wake” part of the velocity profiles using the self-similarity property. The self-similarity of the velocity profile “defect” in the boundary layer, known from the fluid dynamics, was used to retrieve the parameters of the atmospheric boundary layer (the surface wind velocity, drag coefficient, and friction velocity) from the dropsonde wind velocity profiles in ten major hurricanes. Based on the processing of the measurements in the hurricanes Irma 2017/09/07 and Maria 2017/09/21 and 2017/09/23 at a time close to the time of acquisition of the Sentinel-1 images, the dependencies of the cross-polarized normalized radar cross section on the wind speed and wind friction velocity were obtained and used for constructing the GMFs.

Incipient spallation of high purity copper under non-one-dimensional strain shock waves

A new spallation experimental method by using conical target is proposed. Based on the analysis of wave propagation, the basic principle of spallation experiment of conical target is discussed. Then incipient spallation of high purity (HP) copper under non-one-dimensional strain shock wave is studied experimentally by using a gas gun setup. The damage distribution characteristics and micro-mechanism of conical HP copper target are analyzed. The intrinsic relationship between the characteristics of free surface velocity profiles and damage evolution is explored. The results indicate that 1) continuous damage zones including different damage states appear in the conical HP copper target with initial spallation from the bottom of cone to the top of cone along the direction parallel to the cone surface, which is attributed to the spatial evolution of the amplitude and duration time of tensile stress in the conical target; 2) quantitative statistical analysis of damage inside conical HP copper target reveals that the nucleation and early growth of micro-voids are random, while the coalescence of micro-voids has significant localization characteristics; 3) the normal free surface particle velocity profiles with typical pull-back spallation signals at different locations of conical HP copper target are measured by multi-channel photon Doppler velocimetry. Comparing with the damage distribution characteristics, it is revealed that the spallation strength based on pull-back velocity is independent of damage, and is the critical nucleation stress of micro-voids. But the slope and amplitude of pull-back rebound velocity depend on damage evolution process, which relates to the change of damage evolution rate and stress relaxation caused by damage degree respectively.

Validation of a Discrete Element Method (DEM) Model of the Grinding Media Dynamics within an Attritor Mill Using Positron Emission Particle Tracking (PEPT) Measurements

Positron emission particle tracking (PEPT) was used to investigate the grinding media dynamics in a laboratory-scale attritor mill in the absence of powder. The grinding media motion was analysed as a function of the equipment’s typical operating parameters: impeller speed, impeller clearance and bead fill level. It was observed that the impeller speed had the strongest influence on the media motion. An increase of the impeller speed from 300 rpm to 600 rpm led to a change in the bead recirculation patterns with the increasing formation of well segregated upper and lower recirculation loops that fully developed at the maximum speed of 600 rpm. For a constant impeller speed, an increase of the bead loading did not majorly affect the bead velocity as remarked by minor changes on the flow field. For all the impeller clearance values, the occupancy plots revealed an inefficient dead region at the bottom of the attritor where the beads were moving at very low velocity. In this region the beads were tightly packed under their own weight and, furthermore, there was an absence of direct contact with the impeller arms. The depth of this region increased proportionally to the distance between the bottom of the impeller and the vessel base indicating that a minimum value of clearance should be set to optimise the lower recirculation pattern. For two experimental conditions, the data generated by PEPT measurements were utilised to set-up a friction-adjusted discrete element method (DEM) model. Here, the simulation results were qualitatively and quantitatively compared against the PEPT data by assessing the averaged velocity flow fields and the average velocity profiles at different radial locations inside the vessel. Given the intrinsic uncertainty of the PEPT measurements, the DEM model results were in considerably good agreement with the experimental results. The major discrepancy was observed close to the vessel wall where the simulations overpredicted the velocity by about 10%.

Nature of turbulence inside a cubical lid-driven cavity: Effect of Reynolds number

Large eddy simulation of incompressible flow inside a cubic lid driven cavity for a range of Reynolds number (Re=1000,3200,5000,10000,15000) is carried out using dynamic Smagorinsky model (DSM). Centerline average velocity profiles are compared with the existing experimental and numerical results. Except for Re = 1000, the boundary layer slope at wall remains almost same up to the point of inflexion on the mid-bottom wall and on the mid-upstream wall. With increase in Re, the point of inflexion adjusts in such a way so as to make larger and larger volume of fluid a sluggishly-rotating central core. The turbulent quantities such as turbulent kinetic energy and turbulent dissipation are found to be increasing with increase in Re. The auto and cross-correlation coefficient of velocity components are studied and it is found that low Re (= 3200) flow shows periodic nature and as Re increases it becomes aperiodic and turbulent. The cross-correlation decreases with increase in Re. The Fourier spectra of auto-correlation coefficient follows Kolmogorov’s −53 slope in the inertial subrange irrespective of the Re, but the length of inertial subrange increases as Re increases. Kolmogorov length scale (η) and Taylor micro scale (λ) are calculated and it is found that both decrease towards the wall as dissipation is high at the walls. Anisotropic invariant map (AIM) has been plotted; nature of turbulence is found to be non-homogeneous and anisotropic even at low Re (= 3200) and non-homogeneity increases as Re increases. With increasing Re, the turbulence at the core region of the cavity shifts closer to isotropic.

Highly-resolved large-eddy simulations of combustion stabilization in a scramjet engine model with cavity flameholder

Scramjet engines are high-speed airbreathing propulsion systems that do not require rotating elements to compress the air inlet stream. It is compressed dynamically through a supersonic intake system that is integrated in the forebody, thus leading to the required temperature and pressure levels for combustion to proceed within the combustor length. In such engines, the combustion chamber is crossed by a supersonic flow, which limits the time available to inject fuel, to mix it with oxidizer, to ignite the resulting mixture, and to reach complete combustion. Residence times can be increased thanks to cavities, which have the potential to stabilize combustion without excessive total pressure loss and are therefore used as flameholders in supersonic combustors. In the present study, we perform high-fidelity large-eddy simulations (LES) of a hydrogen jet in a supersonic crossflow (JISCF) of vitiated air, which is located upstream of a wall-mounted squared cavity. The performance of such high-fidelity LES does not only require the use of high-precision numerical schemes and reliable subgrid-scale models relevant to the so-called direct numerical simulation (DNS) limit, it is also strongly dependent on the mesh quality. Therefore, the present study places special emphasis on computational grid assessment through the introduction of a detailed numerical procedure, which aims at analysing mesh reliability. The corresponding procedure combines several verification subsets including (i) the inspection of distributions of the dimensions of the computational cells present at the wall location, (ii) the analysis of normalized velocity profiles and viscosity ratio in boundary layers, and (iii) the check of fields of some mesh quality indexes and associated distributions. For the geometry under consideration, it appears that the level of resolution imposed by a correct description of boundary layers leads to a mesh quality that is close to the one associated to DNS requirements. Combustion stabilization is then studied for two distinct values of the inlet vitiated airstream temperature. Two stabilization modes are recovered from the numerical simulations: cavity-stabilized and jet-wake stabilized regimes.

Direct investigation of methane nanofluidic microstructure and system dynamics in rough silicon nanochannel

The microstructure and system dynamics of methane nanofluidic are important to determine the flow properties. In this study, we use non-equilibrium multiscale molecular dynamics simulation (NEMSMD) to investigate the microstructure and system dynamics of methane nanofluidic confined by rough silicon atomic walls. To capture the detailed atomic microstructure of methane moving in rough nanochannel accurately, the modification of OPLS methane fully atomic model is employed. The average number density distributions of C (H) atom, average velocity profile, velocity autocorrelation function and projection radial distribution function (XOY-, XOZ- and YOZ planes) plots give a clear observation of the impacts of different conditions (roughness, body driving force, fluid–wall interaction strength and cutoff radius) on the methane Poiseuille flow in nanochannel. The projection radial distribution functions and diffusivity appear anisotropic, and seem to be affected more significantly by roughness, fluid–wall interaction strength and cutoff radius than body driving force in the whole channel region. Moreover, the body driving force and cutoff radius also play an important role in methane nanofluidic simulation using NEMSMD. The present simulation results are very meaningful for the design of energy-saving emission reduction nanofluidic devices.

PIV Measurement of Separation Bubble on an Airfoil at Low Reynolds Numbers

A wind tunnel experiment was conducted to measure the flow over a suction side of a DAE51 airfoil at low Reynolds numbers using particle image velocimetry (PIV). Five chord Reynolds numbers ranging from 39,000 to 118,000 were investigated at angles of attack ranging from 0° to 10° at an interval of 1°. The locations of laminar separation, transition onset, transition end, and reattachment were identified by examining the measured averaged and RMS velocity data. The locations determined from the PIV data were in very good agreement with the features of measured surface pressure distribution. A large amplification of the RMS velocity leading to transition of a separated shear layer was observed centered at the inflection point of the averaged velocity profile, which indicates the important role of inflectional instability on the transition onset. The behaviors of those locations with respect to the Reynolds number and angle of attack were analyzed. For a fixed Reynolds number, the size of the separation bubble decreases quickly, and the bubble moves upstream as the angle of attack increases. The transition onset location moves upstream with increasing Reynolds number and angle of attack. The transition length becomes shorter as the Reynolds number increases. The lowest angle of attack at which a separation bubble is formed on the airfoil surface depends significantly on the Reynolds number. The movement of the separation point with respect to the Reynolds number indicates a different tendency depending on the presence of the separation bubble.

Direct Numerical Simulation of the Flow in a Bare Rod Bundle at Different Prandtl Numbers

Abstract A direct numerical simulation (DNS) of bare rod bundles with a low pitch-to-diameter ratio is performed with heat transfer at different Prandtl numbers. Turbulence statistics for temperature and velocity as well as the turbulent budgets have been collected. High-fidelity simulations are performed with the spectral element method (SEM) using Nek5000, a highly scalable code. To pertain to industrial-related flows, a rod bundle model is based on Hooper and Wood's (Hooper, J. D., and Wood, D., 1984, “Fully Developed Rod Bundle Flow Over a Large Range of Reynolds Number,” Nucl. Eng. Des., 83(1), pp. 31–46) experimental setup. Both wall normalized velocity profile and turbulent kinetic energy are validated with a Reynolds number of 22,600. Kolmogorov length scales and time scales are calculated to be within the simulation's spatial–temporal resolution. Moreover, gap vortices and coherent structures are quantified by using Lambda2 vortex criterion, frequency analysis, and two-point correlation. Heat transfer statistics are discussed with a constant heat flux for six different Prandtl numbers ranging from 2 to 0.002. This range shows significantly different characteristics in temperature for both mean and variance. Mean temperature profiles in the subchannel center are very sensitive to the Prandtl number when it becomes small. It is also found that the location of the local maxima for the variance of temperature fluctuations becomes very sensitive at larger Prandtl numbers. The temperature frequency analysis reveals a shift to lower frequencies for low Prandtl numbers. The DNS results provided in this work will contribute as benchmark for the improvement and development of existing and new turbulent heat transfer models at different Prandtl number regimes.

Analysis of thin film flow of generalized Maxwell fluid confronting withdrawal and drainage on non-isothermal cylindrical surfaces

This investigation is concerned with the study of thin film flow of a generalized Maxwell fluid along with slip conditions, confronting withdrawal and drainage on non-isothermal cylindrical surfaces. The governing equations have been formulated from the continuity equation, momentum equation, and energy equation. Analytical solutions for the velocity field, volume flow rate, average film velocity, tangential stress, and temperature are obtained in series form through the Binomial expansion technique in both withdrawal and drainage cases. The well-known solutions for a Newtonian fluid are regained as a particular case of our acquired general solutions in all flow cases. In addition, solutions for the power-law fluid model, executing alike motion, can be recovered as a limiting case of our acquired general solutions. The influence of different dimensionless parameters on all physical quantities (i.e. velocity, volume flow rate, average film velocity, tangential stress, and temperature profile) is examined and discussed graphically for both generalized Maxwell and Newtonian fluids.