In the current letter we present a numerical study to review the impacts of homogeneous–heterogeneous reactions on the stagnation point flow of Carreau fluid. In addition, an investigation is considered for the flow impelled by a shrinking sheet along with uniform suction on the wall. We explored the prototype model of homogeneous–heterogeneous reactions in which the diffusion coefficients of reactant and catalyst are identical. With the aid of non-dimensional variables, we get a non-linear system of differential equations which is integrated numerically using MATLAB builtin routine bvp4c. The flow and concentration are exceptionally impacted by the pertinent parameters, like, the Weissenberg number, shrinking parameter, mass transfer parameter, homogeneous/heterogeneous reactions parameter and Schmidt number. Likewise, we inspected that dual solutions for the velocity and concentration fields exist in the case of a shrinking sheet and for a fixed range of other parameters. Our review indicates that the momentum boundary layer thickness rises significantly with an increase in the shrinking parameter for the second solution. Besides, the strength of homogeneous reaction is extremely useful to reduce the concentration of reaction. Under some special assumptions, the consequences of the present study demonstrate a splendid relationship with prior works.
In this numerical work, mixed convection and entropy generation of Cu–water nanofluid and pure water in a lid-driven square cavity have been studied. Horizontal walls of the cavity are adiabatic and vertical walls have constant temperature but different values. The top wall has been considered as moving from left to right at a constant speed, . Rayleigh numbers of and and Reynolds numbers of 1, 10 and 100 have been considered. The results have shown that addition of nanoparticles to the base fluid affects the entropy generation, flow pattern and thermal behavior especially at higher Rayleigh and low Reynolds numbers. For pure fluid as well as nanofluid, increasing Reynolds number increases the average Nusselt number, linearly. The maximum entropy generation occurs in nanofluid at low Rayleigh number but high Reynolds number. The minimum entropy generation occurs in pure fluid at low Rayleigh and low Reynolds numbers. For the cases studied, at Rayleigh numbers greater than , most of the entropy generation is due to heat transfer effects, thus the Bejan number converges to a constant value. A proper choice of Reynolds number is important, if enhanced heat transfer and minimum increased entropy generation is expected. ► Lack of investigations on entropy generation of nanofluid mixed convection in cavities. ► Verification of models used in this study for conductivity and viscosity of nanofluids. ► Use of nanofluid has similar effect on both terms of entropy generation, thus remains constant. ► Maximum entropy generation occurs for low and high , minimum occurs for low and low . ► Proper choice of at any enhances heat transfer with minimum entropy generation.
In this paper, an analysis is made for the fully developed mixed bioconvection flow in a horizontal channel filled with a nanofluid that contains both nanoparticles and gyrotactic microorganisms. The passively controlled nanofluid model proposed by Kuznetsov and Nield (2013) is then introduced for modeling this flow problem, which is found to be more physically realistic than previous nanofluid models. Analytical approximations with high precision are obtained by the improved homotopy analysis technique for complicated boundary conditions. Besides, the influences of various physical parameters on the distributions of temperature, the nanoparticle volume fraction, as well as the density of motile microorganisms are investigated in detail.
In the present study, entropy generation in the porous square cavity filled with nanofluid in natural convection using lattice Boltzmann method considering wide range parameters of natural convection and effect of different porosities in constant Darcy numbers with various volume fractions of nanofluid has been investigated. Nanofluid comprises of water as base fluid and solid Al O , TiO and CuO as nanoparticles. Effect of these nanofluid in entropy generation, average Nusselt number and heat lines are studied while horizontal walls are adiabatic, temperature of the Left wall changes according to sinusoidal behavior and right wall is maintained at constant temperature According to prediction, maximum total entropy is generated in the vicinity of high temperature walls in the present study. Also the results indicate that average Nusselt number and entropy generation are the increasing function of porosity but the entropy generation is a decreasing function of volume fractions of nanofluid.
The formation and amplification of streamwise velocity perturbations induced by cross-stream disturbances is ubiquitous in shear flows. This disturbance growth mechanism, so neatly identified by Ellingsen and Palm in 1975, is a key process in transition to turbulence and self-sustained turbulence. In this review, we first present the original derivation and early studies and then discuss the non-modal growth of streaks, the result of the lift-up process, in transitional and turbulent shear flows. In the second part, the effects on the lift-up process of additives in the fluid and of a second phase are discussed and new results presented with emphasis on particle-laden shear flows. For all cases considered, we see the lift-up process to be a very robust process, always present as a first step in subcritical transition.
Oyster is a surface-piercing flap-type device designed to harvest wave energy in the nearshore environment. Established mathematical theories of wave energy conversion, such as 3D point-absorber and 2D terminator theory, are inadequate to accurately describe the behaviour of Oyster, historically resulting in distorted conclusions regarding the potential of such a concept to harness the power of ocean waves. Accurately reproducing the dynamics of Oyster requires the introduction of a new reference mathematical model, the “flap-type absorber”. A flap-type absorber is a large thin device which extracts energy by pitching about a horizontal axis parallel to the ocean bottom. This paper unravels the mathematics of Oyster as a flap-type absorber. The main goals of this work are to provide a simple–yet accurate–physical interpretation of the laws governing the mechanism of wave power absorption by Oyster and to emphasise why some other, more established, mathematical theories cannot be expected to accurately describe its behaviour.
A numerical study of the steady free convection in a right-angle porous trapezoidal cavity filled by a nanofluid using Buongiorno's mathematical model has been performed. The analysis has been done for different values of the governing parameters Nb, Nt, Nr, Le, A and Rayleigh number Ra in the range 50≤Ra≤1000 using a finite difference method. It is found that single cell is formed inside the cavity independent of the governing parameters. An addition of the nanoparticles can lead to both an intensification and attenuation of the convective flow and heat transfer in dependence on Nb, Nt, Nr, Le, A and Ra. The results indicate that there exist significant changes in the flow and temperature fields as compared with those of a differentially heated square porous cavity. These results lead, in particular, to the prediction of a position of minimum heat transfer across the cavity, which is of interest in the thermal insulation of buildings and other areas of technology.
In this paper, the overall heat transfer coefficient of water based iron oxide nanofluid in a compact air-cooled heat exchanger has been measured experimentally under laminar flow conditions. The concentrations of 0.15, 0.4 and 0.65 vol.% of stabilized Fe O /water nanofluid have been examined with variation of flow rates in the range of 0.2–0.5 m /h. For better dispersion of iron (III) oxide nanoparticles in water, 0.8 wt% polyethylene glycol has been added and pH has been adjusted to 11.1. The air-cooled heat exchanger is consisted of 34 vertical tubes with stadium-shaped cross section and air makes a cross flow through the tube bank with variable flow rates ranging from 740 to 1009 m /h. Also, hot working fluid enters the heat exchanger at different temperatures including 50, 65, and 80 °C. The results demonstrate that increasing the nanofluid flow rate and concentration and the air Reynolds number can improve the overall heat transfer coefficient and heat transfer rate whereas enhancing the inlet temperature has a negative effect on the overall heat transfer coefficient and a positive effect on the heat transfer rate. Meanwhile, the maximum enhancements of the overall heat transfer coefficient and heat transfer rate compared with base fluid (distilled water) are respectively equal to 13% and 11.5% which is occurred at the concentration of 0.65 vol.%.
The majority of Antarctic ice is discharged via long and narrow fast-flowing ice streams. At ice stream margins, the rapid transition from the vertical shearing flow in the ice ridges surrounding the stream to a rapidly sliding plug flow in the stream itself leads to high stress concentrations and a velocity field whose form is non-trivial to determine. In this paper, we develop a boundary layer theory for this narrow region separating a lubrication-type ice ridge flow and a membrane-type ice stream flow. This allows us to derive jump conditions for the outer models describing ridge and stream self-consistently. Much of our focus is, however, on determining the velocity and shear heating fields in the margin itself. Ice stream margins have been observed to change position over time, with potentially significant implications for ice stream discharge. Our boundary layer model allows us to extend previous work that has determined rates of margin migration from a balance between shear heating in the margin and the cooling effect of margin migration into the colder ice of the surrounding ice ridge. Solving for the transverse velocity field in the margin allows us to include the effect of advection due to lateral inflow of ice from the ridge on margin migration, and we demonstrate that this reduces the rate of margin migration, as previously speculated.
The MHD peristaltic motion of a compressible and electrically conducting Jeffrey fluid induced by a surface acoustic wave in a confined parallel-plane microchannel through a porous medium is analytically investigated. A proper attention is given to the combined effects of physical parameters and magnetic field on the rheological aspects of the considered flow. The slip velocity is considered and the problem is discussed for free pumping case. The wave amplitude is related to the power output of an acoustic source. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. The critical value of the magnetic parameter is discussed such that an optimum is shown where some physical variables are obtained maximum. It is noticed that, for the Jeffrey fluid, oscillations decay rapidly as we move from the hydrodynamic to the hydromagnetic fluid, and the effect of retardation time becomes weak. It is inferred that increasing the magnetic parameter makes the fluid less prone to nonlinear effects. Several results of other fluid models are deduced as the limiting cases of our problem. This work is the most general model of peristalsis created to date with wide-ranging applications in biological microfluidic networks.
The structural response of a rectangular cantilevered flexible hydrofoil submitted to various flow regimes is analyzed through an original experiment carried out in a hydrodynamic tunnel at a Reynolds number of . The experiment considers static and transient regimes. The latter consists of transient pitching motions at low and fast pitching velocities. The experiments are also performed for cavitating flow. The structural response is analyzed through the measurement of the free foil tip section displacement using a high speed video camera and surface velocity vibrations using a laser doppler vibrometer. In non cavitating flows, it is shown that the structural response is linked to the hydrodynamic loading, which is governed by viscous effects such as laminar to turbulent transition induced by Laminar Separation Bubble (LSB), and stall. It is also observed that the foil elastic displacement depends strongly on the pitching velocity. Large overshoots and hysteresis effect are observed as the pitching velocity increases. Cavitation induces a large increase of the vibration level due to hydrodynamic loading unsteadiness and change of modal response for specific frequencies. The experimental results presented in this paper will help to develop high fidelity fluid–structure interaction models in naval applications.
In recent years Discontinuous Galerkin (DG) methods have emerged as one of the most promising high-order discretization techniques for CFD. DG methods have been successfully applied to the simulation of turbulent flows by solving the Reynolds averaged Navier–Stokes (RANS) equations with first-moment closures. More recently, due to their favorable dispersion and dissipation properties, DG discretizations have also been found very well suited for the Direct Numerical Simulation (DNS) and Implicit Large Eddy Simulation (ILES) of turbulent flows. The growing interest in the implementation of DG methods for DNS and ILES is motivated by their attractive features. In particular, these methods can easily achieve high-order accuracy on arbitrarily shaped elements and are perfectly suited to -adaptation techniques. Moreover, their compact stencil is independent of the degree of polynomial approximation and is thus well suited for implicit time discretization and for massively parallel implementations. In this paper we focus on recent developments and applications of an implicit high-order DG method for the DNS and ILES of both compressible and incompressible flows. High-order spatial and temporal accuracy has been achieved using the same numerical technology in both cases. Numerical inviscid flux formulations are based on the exact solution of Riemann problems (suitably perturbed in the incompressible case), and viscous flux discretizations rely on the BR2 scheme. Several types of high-order (up to order six) implicit schemes, suited also for DAEs, can be employed for accurate time integration. In particular, linearly implicit Rosenbrock-type Runge–Kutta schemes have been used for all the simulations presented in this work. The massively separated incompressible flow past a sphere at , with transition to turbulence in the wake region, is considered as a DNS test case, while the potential of the ILES is demonstrated by computing the compressible transitional flow at , and , around the Selig–Donovan 7003 airfoil. The computed solutions are compared with experimental data and numerical results available in the literature, showing good agreement.
A recent database from direct numerical simulation (DNS) of a turbulent boundary layer up to (Schlatter and Örlü, 2010) is analysed to extract the dominant flow structures in the near-wall region. In particular, the question of whether hairpin vortices are significant features of near-wall turbulence is addressed. A number of different methods based on the criterion (Jeong and Hussain, 1995) is used to extract turbulent coherent structures: three-dimensional flow visualisation with quantitative estimates of hairpin population, conditional averaging and planar hairpin vortex signatures (HVS). First, visualisations show that during the initial phase of laminar–turbulent transition induced via tripping, hairpin vortices evolving from transitional vortices are numerous and can be considered as the dominant structure of the immediate post-transition stage of the boundary layer. This is in agreement with previous experiments and low-Reynolds-number simulations such as Wu & Moin (2009). When the Reynolds number is increased, the fraction of hairpin vortices decreases to less than 2% for . Second, conditional ensemble averages (Jeong et al., 1997) find hairpins close to the wall at low Reynolds number, while at a sufficient distance downstream from transition, the flow close to the wall is dominated by single quasi-streamwise vortices; even quantitatively, no major differences between boundary layer and channel can be detected. Moreover, three-dimensional visualisations of the neighbourhood of regions of strong swirling motion in planar cuts through the layer (the HVS) do not reveal hairpin vortices, thereby impairing statistical evidences based on HVS. The present results thus clearly confirm that transitional hairpin vortices do not persist in fully developed turbulent boundary layers, and that their dominant appearance as instantaneous flow structures in the outer boundary-layer region is very unlikely.
Dynamic mode decomposition (DMD) has been extensively utilized to analyze the coherent structures in many complex flows. Although specific flow patterns with dominant frequency and growth rate can be captured, extracting dominant DMD modes for flow reconstruction and dynamic modeling still needs a priori knowledge on flow physics, especially for some transient states of unstable flows. In this paper, a criterion to select dominant modes from DMD technique is developed. The unsteady flow can be described by the superposition of each normalized DMD mode multiplied by its time coefficient. The dominance of each DMD mode can be ordered by time integration of its time coefficient. Compared with standard DMD approach, which decides the dominance of DMD modes from the order of amplitude or mode norm, this criterion considers the evolution of each mode within the whole sampling space, and ranks them according to their contribution to all samples. The proposed mode selection strategy is evaluated by test cases including both equilibrium and transient states of a cylinder at Reynolds number of 60 and a transient state of a NACA0012 airfoil buffeting in transonic flow. Results indicate that using this criterion, dominant DMD modes can be identified and flow dynamics in unstable or transient systems can be reconstructed accurately with fewer modes. Besides, this approach has better convergence against mode number and lower sensitivity to the initial condition than standard DMD method.
The classical Neumann–Kelvin (NK) linear potential flow theory of ship waves in calm water and the related Neumann–Michell (NM) theory are considered. Five alternative boundary integral representations are given: (1) the classical NK integro-differential representation, called “classical NK formulation”, which corresponds to an inconsistent linear flow model, (2) a modification of the classical NK flow formulation that corresponds to a consistent linear flow model and is called “consistent NK formulation”, (3) a flow representation, called “NM potential and velocity formulation”, that involves the flow potential and the velocity components and along two unit vectors and tangent to the ship hull surface, and yields an integro-differential equation for determining (4) a flow representation, called “NM velocity formulation”, that only involves and and yields a pair of coupled integral equations for determining and (5) a flow representation called “NM potential formulation” that only involves the flow potential and yields an integral equation for determining The two NK formulations involve both a surface integral over the ship hull surface and a line integral around the ship waterline, whereas the three NM formulations do not involve a waterline integral. All flow representations other than the classical NK representation are based on a consistent linear flow model.
Electrokinetic peristaltic multi-layered transport is considered in a micro-channel under the action of an axial electrical field. Three different layers i.e. the are simulated with three different viscosities for each fluid layer. The unsteady two-dimensional conservation equations for mass and momentum with electrokinetic body forces, are transformed from the wave frame to the laboratory frame and the electrical field terms are rendered into electrical potential terms via the Poisson–Boltzmann equation, Debye length approximation and ionic Nernst–Planck equation. The dimensionless emerging linearized electrokinetic boundary value problem is solved using integral methods. Closed-form expressions are derived for stream functions in the core, intermediate and peripheral layers. Expressions are also derived for the core–intermediate interface shape and the intermediate–peripheral interface shape. Maximum pressures are also computed. To study bolus migration, the range of the trapping limit is also determined in the peripheral layer. It is found that in the core layer larger boluses are computed in the case of lower intermediate layer viscosity relative to peripheral layer viscosity although the number of boluses is greater when the intermediate layer viscosity exceeds the peripheral layer viscosity. Furthermore, in the intermediate layer, stronger concentration of streamlines is computed in the lower half space with positive Helmholtz–Smoluchowski velocity. Also negative Helmholtz–Smoluchowski velocity reduces the core layer (H ) interface shape whereas it enhances the peripheral layer (H) and intermediate layer (H ) shapes. At lower values of volume flow rate ratio, hydromechanical efficiency is positive Helmholtz–Smoluchowski velocity whether intermediate layer viscosity is less or greater than peripheral layer viscosity. Finally, greater with greater peristaltic wave amplitude and also for positive Helmholtz–Smoluchowski velocity there is an increase in time-averaged flow rate, whether intermediate layer viscosity is less or greater than peripheral layer viscosity. The analysis is relevant to electro-kinetic hemodynamics and bio-micro-fluidics.
This paper is devoted to the study of peristaltic flow of a non-Newtonian fluid in a curved channel. The constitutive relationship between stress and shear rate for a non-Newtonian third grade fluid is used. The problem is governed by a set of two nonlinear partial differential equations. These equations are then transformed into a single nonlinear ordinary differential equation in the stream function under long wavelength and low Reynolds number assumptions. This nonlinear ordinary differential equation is solved for stream function by the shooting method using Mathematica. The important phenomenon of pumping and trapping is presented graphically and discussed in detail. It is found that for a non-Newtonian third grade fluid an increase in the curvature of the channel helps in reducing the pressure rise over one wavelength in pumping region. This result is in contrast to the previous result obtained for the pressure rise over one wavelength for a Newtonian fluid. For a Newtonian fluid, the pressure rise over one wavelength increases with an increase in the curvature. The trapping phenomenon is also altered with the presence of curvature and as a result the symmetry observed for a bolus of the trapped fluid in the case of a straight channel is destroyed and splits into two asymmetrical parts for the curved channel. The outer bolus suppresses the inner bolus towards the lower wall. It is also noted that an increase in size and circulation of boluses achieve a maximum for large values of the shear thickening parameter . Moreover, the size of two boluses in a third grade fluid is larger in comparison with their counterparts in a Newtonian fluid. Further, the lower trapping limit of the flow rate is also changed in the curved channel. In fact the lower trapping limit of the curved channel exceeds that of the straight channel.
In this paper, a simulation of the steady flow in a pipe of square cross-section has been performed when the pipe is filled with a Bingham fluid. The problem has been solved employing the Bingham model without any regularisation. An innovative approach based on a modification of the Lattice Boltzmann Method (LBM) has been applied to solve the problem. Yield stress effects on momentum transport using the Bingham model are investigated for certain pertinent parameters of the Oldroyd number, , and the hydraulic diameter, = 1 and 2.