Showing papers on "Velocity gradient published in 2021"

Impact of Binary Chemical Reaction and Activation Energy on Heat and Mass Transfer of Marangoni Driven Boundary Layer Flow of a Non-Newtonian Nanofluid

Abstract: The flow and heat transfer of non-Newtonian nanofluids has an extensive range of applications in oceanography, the cooling of metallic plates, melt-spinning, the movement of biological fluids, heat exchangers technology, coating and suspensions. In view of these applications, we studied the steady Marangoni driven boundary layer flow, heat and mass transfer characteristics of a nanofluid. A non-Newtonian second-grade liquid model is used to deliberate the effect of activation energy on the chemically reactive non-Newtonian nanofluid. By applying suitable similarity transformations, the system of governing equations is transformed into a set of ordinary differential equations. These reduced equations are tackled numerically using the Runge–Kutta–Fehlberg fourth-fifth order (RKF-45) method. The velocity, concentration, thermal fields and rate of heat transfer are explored for the embedded non-dimensional parameters graphically. Our results revealed that the escalating values of the Marangoni number improve the velocity gradient and reduce the heat transfer. As the values of the porosity parameter increase, the velocity gradient is reduced and the heat transfer is improved. Finally, the Nusselt number is found to decline as the porosity parameter increases.

Computational modelling of nanofluid flow over a curved stretching sheet using Koo–Kleinstreuer and Li (KKL) correlation and modified Fourier heat flux model

Abstract: The objective of the current paper is to study the two-dimensional, incompressible nanofluid flow over a curved stretching sheet coiled in a circle. Further, the impact of dispersion of nanoparticle CuO in base liquid water on the performance of flow, thermal conductivity and mass transfer using KKL model in the presence of Cattaneo-Christov heat flux and activation energy is deliberated. A curvilinear coordinate system is used to develop the mathematical model describing the flow phenomena in the form of partial differential equations. Further, by means of apt similarity transformations the governing boundary value problems are reduced to ordinary differential equations. Mathematical computations are simplified using Runge-Kutta-Fehlberg-45(RKF-45) process by adopting shooting method. Graphical illustrations of velocity, temperature, concentration gradients for various pertinent parameters are presented. The result reveals that, the heightening of porosity parameter heightens the thermal gradient but converse trend is depicted in velocity gradient. The enhancing values of Schmidt number and chemical reaction rate parameter declines concentration gradient whereas converse trend is depicted for upsurge in activation energy parameter.

Slip flow of Casson–Maxwell nanofluid confined through stretchable disks

Abstract: This study reports an incompressible electrically conducting Casson–Maxwell fluid flow confined across two uniformly stretchable disks. Buongiorno nanofluid model is implemented in the fluid flow. Cattaneo–Christov theory of double-diffusion is characterized through the heat and mass equations. Velocity, thermal and concentration slip conditions are executed at the lower stretchable disk. The flow model is dimensionalized through the similarity functions and then numerical solution is attained by RKF-45 scheme combined with shooting technique. The results of physical parameters are discussed by plotting the effects of such parameters on velocity, thermal and concentration fields. The results revealed that the Maxwell liquid is highly effected by Lorentz force than the Casson liquid. Thermal gradient of Maxwell liquid is highly influenced by stretching ratio parameter when compared to Casson fluid. Increase in Casson parameter and Deborah number declines the velocity gradient. Rise in the values of Brownian motion parameter declines the concentration gradient. Finally, the upsurge in thermal relaxation time parameter enhances the thermal gradient quickly in absence of thermal slip parameter.

Two-Phase Darcy-Forchheimer Flow of Dusty Hybrid Nanofluid with Viscous Dissipation Over a Cylinder

Abstract: The current article concerns with the flow of an incompressible dusty hybrid nanofluid over a stretching cylinder by considering Darcy–Forchheimer porous medium and viscous dissipation. Heat transfer and momentum behavior of water-based fluid with suspended nanoparticles (copper and Titania) is scrutinized in this study. The two-phase model which handles the particle phase and the fluid phase is accounted in this study. The modelled equations are reduced to a set of non-linear ordinary differential equations (ODEs) using suitable similarity variables. Later, these reduced equations are solved by adopting the Runge–Kutta Fehlberg-45(RKF-45) technique along with shooting scheme. The graphs are plotted to examine the impact of various dimensionless parameters on velocity and thermal profiles for both dust and fluid phases. For engineering apprehensions, the coefficient of skin friction and Nusselt number are also calculated and scrutinized through graphs. The outcomes reveal that, increase in mass concentration of particles improves the heat transfer but declines velocity gradient. The increase in velocity interaction parameter of the fluid reduces the velocity gradient of fluid phase but increases the velocity of the dust phase. Finally, increasing values of curvature parameter improves the velocity and temperature of both the phases.

An assessment of the mathematical model for estimating of entropy optimized viscous fluid flow towards a rotating cone surface

Abstract: Entropy optimization in convective viscous fluids flow due to a rotating cone is explored. Heat expression with heat source/sink and dissipation is considered. Irreversibility with binary chemical reaction is also deliberated. Nonlinear system is reduced to ODEs by suitable variables. Newton built in shooting procedure is adopted for numerical solution. Salient features velocity filed, Bejan number, entropy rate, concentration and temperature are deliberated. Numerical outcomes for velocity gradient and mass and heat transfer rates are displayed through tables. Assessments between the current and previous published outcomes are in an excellent agreement. It is noted that velocity and temperature show contrasting behavior for larger variable viscosity parameter. Entropy rate and Bejan number have reverse effect against viscosity variable. For rising values of thermal conductivity variable both Bejan number and entropy optimization have similar effect.

Energy transfer structures associated with large-scale motions in a turbulent boundary layer

Abstract: The role of large-scale motions (LSMs) in energy transfer is investigated by analysing wall-parallel velocity fields at low-to-moderate Reynolds number (), which are obtained via a two-dimensional (2-D) particle image velocimetry measurement with large field-of-view. Two types of energy flux, i.e. local interscale energy flux and in-plane spatial energy flux are inspected in detail. Targeting the energy transfer in large-scale regime, an anisotropic filter is designed based on the zero-crossing scale boundary in a 2-D energy transfer spectrum, across which the net energy flux is the maximum. This ‘optimal’ energy flux boundary separates the scale space into an energy donating large-scale part and an energy receiving small-scale one. The crossover energy flux, as well as the associated flow field structures, are studied by conditional statistics and linear stochastic estimation, in which the statistical spanwise symmetry is deliberately broken by designing special velocity gradient conditions for event probing. A strong connection between large-scale energy flux events and LSMs are found. Namely, forward scatter events have higher probability to reside on the wavy flank of low-momentum LSMs, if compared with the scenario of being clamped in the middle of two streamwise-aligned high- and low-momentum LSMs (Natrajan & Christensen, Phys. Fluids, vol. 18, issue 6, 2006, pp. 299–325). Meanwhile, pairs of positive and negative spatial transfer events tend to locate inside LSMs. It is thus argued that the meandering nature of LSMs, which forms the necessary velocity gradient, might play a determining role in the process of large-scale energy transfer. The spatial correlation between them is then schematized in a conceptual model, which explains most of the present observations.

On the Analysis of the Non-Newtonian Fluid Flow Past a Stretching/Shrinking Permeable Surface with Heat and Mass Transfer

Abstract: The 3D Carreau fluid flow through a porous and stretching (shrinking) sheet is examined analytically by taking into account the effects of mass transfer, thermal radiation, and Hall current. The model equations, which consist of coupled partial differential equations (PDEs), are simplified to ordinary differential equations (ODEs) through appropriate similarity relations. The analytical procedure of HAM (homotopy analysis method) is employed to solve the coupled set of ODEs. The functional dependence of the hydromagnetic 3D Carreau fluid flow on the pertinent parameters are displayed through various plots. It is found that the x-component of velocity gradient (f′(η)) enhances with the higher values of the Hall and shrinking parameters (m,ϱ), while it reduces with magnetic parameter and Weissenberg number (M,We). The y-component of fluid velocity (g(η)) rises with the augmenting values of m and M, while it drops with the augmenting viscous nature of the Carreau fluid associated with the varying Weissenberg number. The fluid temperature θ(η) enhances with the increasing values of radiation parameter (Rd) and Dufour number (Du), while it drops with the rising Prandtl number (Pr). The concentration field (ϕ(η)) augments with the rising Soret number (Sr) while drops with the augmenting Schmidt number (Sc). The variation of the skin friction coefficients (Cfx and Cfz), Nusselt number (Nux) and Sherwood number (Shx) with changing values of these governing parameters are described through different tables. The present and previous published results agreement validates the applied analytical procedure.

An inclination in Thermal Energy Using Nanoparticles with Casson Liquid Past an Expanding Porous Surface

Abstract: The physical aspects of inclined MHD nanofluid toward a stretching sheet embedded in a porous medium were visualized, which has numerous applications in industry. Two types of nanoparticles, namely copper and aluminum oxide, were used, with water (limiting case of Casson liquid) as the base fluid. Similarity transformations were used to convert the partial differential equations into a set of ordinary differential equations. Closed solutions were found to examine the velocity and temperature profiles. It was observed that an increment in the magnitude of the Hartmann number, solid volume fraction, and velocity slip parameter brought a reduction in the velocity profile, and the opposite behavior was shown for the permeability parameter in Cu–water and Al2O3–water nanofluids. The temperature field, local skin friction, and local Nusselt number were further examined. Moreover, the study of Cu and Al2O3 is useful to boost the efficiency of thermal conductivity and thermal energy in particles. Reduction was captured in the velocity gradient and temperature gradient against changes in the thermal radiation number. The opposite trend was tabulated into motion with respect to the volume fraction number for both cases (Cu–water and Al2O3–water).

Numerical simulation on the effects of bubble size and internal structure on flow behavior in a DAF tank: A comparative study of CFD and CFD-PBM approach

Abstract: Although dissolved air flotation (DAF) plays a crucial role in wastewater treatment, fluid dynamics in the contact zone (CZ) of a DAF tank are still considered black-box processes, which hampers DAF's optimal design and operation. In this article, we perform a modeling study to further unravel the governing mechanisms occurring in a DAF tank. A computational fluid dynamics (CFD) model coupled with a generic population balance model (PBM) for the DAF system was developed in this work. CFD-PBM results showed that the eddy capture is the dominating mechanism for the bubble coalescence in the most volume of the CZ. Simultaneously, the velocity gradient mechanism and turbulent induced mechanism also play a key role in bubble coalescence in the regions with drastic flow transition and in the nozzle downstream. CFD-PBM simulations reveal that increasing the recirculation rate is better than increasing the volume fraction in the smaller recirculated flow to achieve higher bubble number density and smaller bubble size if the same amount of gas flow rate is injected. The baffle with proper transverse corrugate can equalize and reduce the total coalescence rate. By establishing a synergy between fluid dynamics and bubble size to achieve the best CZ efficiency, the generic CFD-PBM approach developed in this study has laid a solid basis for the optimal design and operation of DAF systems.

Two-and-three-dimensional analysis of Joule and viscous heating effects on MHD nanofluid forced convection in microchannels

Abstract: This paper aims to study viscous heating, Joule heating and their simultaneous impacts on Al2O3-water nanofluid laminar flow and thermal characteristics in the presence of a magnetic field inside microchannels. The flow field and heat transfer are modeled two- and three-dimensionally by employing the finite volume method. To investigate the influence of viscosity variation with temperature on viscous heating, a temperature-dependent viscosity correlation specifically presented for Al2O3-water is employed. Predicted results indicate that viscosity changes due to temperature changes are negligible and although viscous heating can be reasonably ignored in the absence of the magnetic field, it must be taken into account when the magnetic field is applied. At the Hartmann number of 20, near microchannel walls, the velocity gradient rises up to 165% where the viscous dissipation significantly increases the temperature. In addition, when the magnetic field is applied, the 2D model underestimates the temperature compared to the 3D model where the effects of maximum velocity and velocity gradient on the energy equation and heat dissipation exist. The temperature profiles demonstrate that at the Hartmann number of 20, the effects of Joule heating or viscous heating increase the maximum dimensionless temperature by a factor of about 2.5 and by the rise of the Hartmann number, the dimensionless temperature increases and the effects of Joule and viscous heating become more significant. All in all, it is concluded that the heat generated by viscous and Joule heating can remarkably decrease the cooling performance of microchannels in the presence of magnetic fields.

Slip hydrodynamics of combined electroosmotic and pressure driven flows of power law fluids through narrow confinements

Abstract: Electroosmotic flows (EOF) in microfluidic devices can be greatly enhanced over superhydrophobic surfaces because the high shear rates within the electrical double layer can drive large slip velocities at the interface. Using the power law fluid model, we derive a novel formulation for the Helmholtz–Smoluchowski (HS) velocity and use it to examine the effect of slip on the hydrodynamics of a coupled pressure driven and EOF. Semi analytical relations for the velocity gradient are obtained for cases of a favourable pressure gradient but exact solutions of the velocity can be found only for certain power law indices. Cases of adverse pressure gradient and fractional power law indices are investigated using numerically using the Galerkin Finite Element Method. The validity of the semi analytical relations verified by comparison with the numerical method. The presence of velocity slip at the wall leads to an enhancement of the HS velocity that is most pronounced in shear thinning fluids. Adverse pressure gradients are observed to generate an inflection in the velocity profile and even a two-way flow for certain flow parameters. The strength of the adverse pressure gradient needed to setup a reverse flow at the channel centre reduces as the slip length is increased. The location of the point of inflection is found to depend on the channel height, pressure gradient, electric field, slip length, Debye length and non-Newtonian behaviour.

Collision rate of bidisperse, hydrodynamically interacting spheres settling in a turbulent flow

Abstract: The collisions in a dilute polydisperse suspension of sub-Kolmogorov spheres with negligible inertia settling in a turbulent flow and interacting through hydrodynamics including continuum breakdown on close approach are studied. A statistically significant decrease in ideal collision rate without gravity is resolved via a Lagrangian stochastic velocity-gradient model at Taylor microscale Reynolds number larger than those accessible by current direct numerical simulation capabilities. This arises from the difference between the mean inward velocity and the root-mean-square particle relative velocity. Differential sedimentation, comparable to the turbulent shear relative velocity, but minimally influencing the sampling of the velocity gradient, diminishes the Reynolds number dependence and enhances the ideal collision rate i.e. the rate without interactions. The collision rate is retarded by hydrodynamic interactions between sphere pairs and is governed by non-continuum lubrication as well as full continuum hydrodynamic interactions at larger separations. The collision efficiency (ratio of actual to ideal collision rate) depends on the relative strength of differential sedimentation and turbulent shear, the size ratio of the interacting spheres and the Knudsen number (defined as the ratio of the mean-free path of the gas to the mean radius of the interacting spheres). We develop an analytical approximation to concisely report computed results across the parameter space. This accurate closed form expression could be a critical component in computing the evolution of the size distribution in applications such as water droplets in clouds or commercially valuable products in industrial aggregators.

Time dependence of advection-diffusion coupling for nanoparticle ensembles

Abstract: Advection-diffusion coupling can enhance particle and solute dispersion by orders of magnitude as compared to pure diffusion, with a steady state being reached for confined flow regions such as a nanopore or blood vessel. Here, by using evanescent wave microscopy, we measure for the first time the full dynamics of Taylor dispersion, highlighting the crucial role of the initial concentration profile. We make time-dependent, nanometrically-resolved particle dispersion measurements varying nanoparticle size, velocity gradient, and viscosity in sub-micrometric near-surface flows. Such resolution permits a measure of the full dynamical approach and crossover into the steady state, revealing a family of master curves. Remarkably, our results show that the dynamics depend sensitively on the initial spatial distribution of the nanoparticles. These observations are in quantitative agreement with existing analytical models and numerical simulations performed herein. We anticipate that our study will be a first step toward observing and modelling more complex situations at the nanoscale, such as target finding and chemical reactions in nanoconfined flows, dynamical adsorption and capture problems, as well as nanoscale drug delivery systems.

Shear viscosity and electrical conductivity of the relativistic fluid in the presence of a magnetic field: A massless case

Abstract: We have explored the shear viscosity and electrical conductivity calculations for bosonic and fermionic media, without and with presence of an external magnetic field. For numerical visualisation, we have dealt with their simplified massless expressions. In the presence of a magnetic field, five independent velocity gradient tensors can be designed, and so their corresponding proportional coefficients, connected with the viscous stress tensor, provide us five components of the shear viscosity coefficient. In the existing literature, two sets of viscous stress tensors are available. Starting from them, the present work has obtained expressions for two sets of five shear viscosity coefficients, which can be ultimately classified into three basic components – parallel, perpendicular and Hall components as one get similar expression for the electrical conductivity at the finite magnetic field. Our calculations are based on the kinetic theory approach in relaxation time approximation. Repeating the same mathematical steps under finite magnetic field, which is traditionally practiced in the absence of magnetic field, we have obtained two sets of five shear viscosity components, whose final expressions are in good agreements with earlier references, although a difference in methodology or steps can be noticed. In this context, the present work, for the first time, addresses a detailed calculation of relaxation time approximation (RTA)-based kinetic theory calculations of the second set of five shear viscosity components, which was previously done by Denicol et al (Phys. Rev. D 98, 076009 (2018)) in moment method technique. Realising the massless results of viscosity and conductivity for Maxwell–Boltzmann, Fermi–Dirac and Bose–Einstein distribution functions, we have applied them for massless quark gluon plasma and hadronic matter phases, which can provide us a rough order of strength, within which actual results will vary during quark–hadron phase transition. The present work also indicates that the magnetic field might have some role in building perfect fluid nature in RHIC or LHC matter. The lower bound expectation of shear viscosity to entropy density ratio is also discussed. Here, for the first time, we are addressing an analytic expression of temperature- and magnetic field-dependent relaxation time of the massless fluid, for which perpendicular component of shear viscosity to entropy density ratio can reach its lower bound.

Influence of Emitter Structure on Its Hydraulic Performance Based on the Vortex

Abstract: The rectangular labyrinth emitter is taken as the study object in this article, as we added internal teeth to vortex-free and vortex areas in its lateral channel or lengthened the vertical channel, to change the channel structure. Using the computational fluid dynamics (CFD) method simulates the water flow field, to get the relationship between flow rate and pressure, and the vortexes distribution in channel. The aim of this study is to explore the reasons for the influence of structural change on hydraulic performance of the emitter through the analysis of vortex intensity and its distribution from the perspective of the vortex. The results show that the relative error of simulated results and experimental data was 1.02–2.11%. Adding internal teeth to vortex-free areas in lateral channel can improve hydraulic performance of the emitter; adding them to vortex areas can reduce it. The increase in vortex number and intensity in flow field is the internal reason for the improvement of the emitter’s hydraulic performance. The channel structure changes promote the formation of a larger velocity gradient, and the increase in the velocity gradient in flow field exacerbates vortex formation. Changing channel structure to improve the emitter’s hydraulic performance can promote an increase in the number and intensity of vortexes in the channel.

Numerical simulation of mechanical flocculation in water treatment

Abstract: Flocculation plays a very important role in increasing the suspended solids removal and enhancing the phosphorous adsorption in wastewater treatment. In the current work, a combined model of computational fluid dynamics (CFD) and the population balance model (PBM) is proposed to simulate the flow characteristics and flocs behavior in a full scale flocculation. In order to relief computational efforts, the assumption of uniform particle size within the control volume is considered in the PBM model. The model considers the rotating flow in a mechanical flocculator, and the aggregation and breakage in the floc growth dynamics. Both the axial velocity and average floc size are validated with experimental measurements taken from literatures. The typical transportation phenomena of the flow velocity, local velocity gradient and floc size distribution are obtained. The inlet flow rate and initial floc particle size are investigated in the simulation. With the increasing of inlet flow rate, the floc particle size decreases, thus to cause the degradation of flocculation performance. The floc particle size linearly increases with the increasing of initial floc particle size, and the flocculation performance is correspondingly enhanced. These simulation results provide a profound understanding of the flocs growth mechanism, which is critical to the flocculation optimization.