Momentum Boundary Layer Thickness Research Articles

Fluorescent particle image velocimetry using atomized liquid particles

Aerosolized fluorescent particles of Kiton Red 620 dye in a water/glycol fluid are generated using a Venturi-type atomizer and shown to provide effective flow seeding for fluorescent particle image velocimetry (PIV), which can mitigate the detrimental effects of laser reflections from surfaces. Ninety two percent of particles by number concentration were found to be <1 μm in diameter, an acceptable size threshold for gas-flow PIV purposes. A PIV application was conducted in a wind tunnel (freestream velocity U ∞ = 27 m s−1), using the particles for measurement of the boundary layer flow approaching a forward-facing step (approach boundary layer momentum thickness Reynolds number of . Particles were generated from solutions with dye molar concentrations of and mol l−1, and PIV images were obtained for both elastic Mie scattering and filtered, Stokes-shifted fluorescent light. Raw images indicate that the fluorescence yield of the mol l−1 solution provides PIV images with high contrast, even in the near-surface regions where Mie scattering image contrast is highly affected by surface reflections. Boundary layer profiles are processed in the region of adverse pressure gradient leading up to the forward-facing step, where the fluorescent PIV was found to perform comparably to the most optimized Mie scattering PIV; both approaches obtained data as near to the wall as 30 μm, or two viscous wall units in our flow of interest. These results indicate that the new seeding method holds promise for near-surface measurement applications with more complicated three-dimensional geometries, where it is impossible to arrange PIV cameras to reject surface-scattered light.

Thermal radiation effect on unsteady three-dimensional MHD flow of micropolar fluid over a horizontal surface of a parabola of revolution

This paper explores the time-dependent magnetohydrodynamics (MHD) micropolar fluid flow over a three-dimensional variable stretching surface in the occurrence of radiation effect. The model time-dependent partial differential equations (PDE's) in three independent variables are transformed into ordinary differential equations (ODE's) by the suitable self-similarity variables. Homotopy perturbation method (HPM) and Runge-Kutta (RK) 4th order method along with shooting technique are used in the present model. And also, HPM results are compared with Runge-Kutta (RK) 4th order method along with the shooting technique. The velocity, micro rotation in x and y directions, temperature, skin friction factor and heat transfer rates are examined for the emerging parameters. The velocity profiles and momentum boundary layer thickness intensification with increasing values of the vortex viscosity parameter. The higher value of a magnetic parameter declines the skin friction coefficient. This type of investigation may be profitable to the polymer fluids, exotic lubricants, electronic chips, artificial fibers, drawing of copper wires, etc.

Bödewadt Flow and Heat Transfer in Nanofluid over a Permeable and Radially Stretching Disk

A Bödewadt boundary layer flow and heat transfer problem in nanofluid was investigated in this study for suction/injection as well as combined effects of suction/injection and radial stretching disk. Similarity variables were introduced to transform the three-dimensional flow into a system of ordinary differential equations. Moreover, similar to the Bödewadt heat transfer problem in a viscous fluid, adequate suction is also required so that similarity solutions exist for nanofluid problems with no other boundary effects such as a partial slip or stretching disk. Both the suction and stretching disk effects can suppress the natural oscillatory behavior of flow apart from reducing the momentum and thermal boundary layer thicknesses. As expected, injection acts oppositely. However, the skin friction coefficient and heat transfer rate for Bödewadt flow increase with the increasing suction and stretching parameters. As for stagnant disk, increasing the nanoparticle volume fraction can enhance the wall shear stress, whereas nanofluid can only enhance the heat transfer when both the suction and nanoparticle volume fraction are sufficiently small. For radially stretching disk, both the local skin friction coefficient and local Nusselt number increase as the nanoparticle volume fraction increases. However, for larger suction, a smaller volume fraction of nanoparticles yielded enhanced heat transfer than the larger volume fraction of nanoparticles.

Heat and mass transfer exploration of non-Newtonian fluid flow induced by the exponentially stretching Riga surface with the application of Generalized Fourier’s and Fick’s law

In the present article, the analysis of the transportation of thermal and solutal energy of a3D flow on second- grade fluid with porous medium by an exponentially stretching surface is presented. The chemical reaction and heat generation/absorption are considered the dominating agents for the transportation of mass and heat in the second-order fluid. Furthermore, slip boundary conditions are considered on the boundary of the surface. A novel concept of the Cattaneo-Christov heat flux theory of the flow of second-order fluid is used under the effects of the Joule heating across the Riga surface for this research examination. The prevailing nonlinear PDEs are changed into the nonlinear coupled ordinary differential equations by choosing the suitable similarity transformations. The Matlab approach Bvp4c is applied to solve the nonlinear ODEs. Physical consequences of the different emerging parameters on the thermal, concentration, and momentum boundary layer thickness are examined by graphs. The thermal and concentration profiles are decreased by enhancing the values of (thermal relaxation parameter of time) and the (parameter of solutal relaxation time), respectively.

Fluorescent Particle Image Velocimetry using Atomized Liquid Particles

Abstract Aerosolized fluorescent particles of Kiton Red 620 dye in a water/glycol fluid are generated using a Venturi-type atomizer and shown to provide effective flow seeding for fluorescent PIV, which can mitigate the detrimental effects of laser reflections from surfaces. 92% of particles by number concentration were found to be &lt; 1 μm in diameter, an acceptable size threshold for gas-flow PIV purposes. A PIV application was conducted in a wind tunnel (freestream velocity U∞ = 27 m/s), using the particles for measurement of the boundary layer flow approaching a forward-facing step (approach boundary layer momentum thickness Reynolds number of Re_θ=5930). Particles were generated from solutions with dye molar concentrations of 2.5×10^(-3) and 1.0×10^(-2) mol/L, and PIV images were obtained for both elastic Mie scattering and filtered, Stokes-shifted fluorescent light. Raw images indicate that the fluorescence yield of the 1.0×10^(-2) mol/L solution provides PIV images with high contrast, even in the near-surface regions where Mie scattering image contrast is highly affected by surface reflections. Boundary layer profiles are processed in the region of adverse pressure gradient leading up to the forward-facing step, where the fluorescent PIV was found to perform comparably to the most optimized Mie scattering PIV; both approaches obtained data as near to the wall as 30 μm, or 2 viscous wall units in our flow of interest. These results indicate that the new seeding method holds promise for near-surface measurement applications with more complicated three-dimensional geometries, where it is impossible to arrange PIV cameras to reject surface-scattered light.

Blasius-Rayleigh-Stokes Flow of Hybrid Nanomaterial Liquid Past a Stretching Surface with Generalized Fourier's and Fick's Law.

The effect of Stefan blowing on the Cattaneo–Christov characteristics of the Blasius–Rayleigh–Stokes flow of self-motive Ag-MgO/water hybrid nanofluids, with convective boundary conditions and a microorganism density, are examined in this study. Further, the impact of the transitive magnetic field, ablation/accretion, melting heat, and viscous dissipation effects are also discussed. By performing appropriate transformations, the mathematical models are turned into a couple of self-similarity equations. The bvp4c approach is used to solve the modified similarity equations numerically. The fluid flow, microorganism density, energy, and mass transfer features are investigated for dissimilar values of different variables including magnetic parameter, volume fraction parameter, Stefan blowing parameter, thermal and concentration Biot number, Eckert number, thermal and concentration relaxation parameter, bio-convection Lewis parameter, and Peclet number, to obtain a better understanding of the problem. The liquid velocity is improved for higher values of the volume fraction parameter and magnetic characteristic, due to the retardation effect. Further, a higher value of the Stefan blowing parameter improves the liquid momentum and velocity boundary layer thickness.

Double Stratified MHD Stagnation Point Slip Flow Over a Permeable Shrinking/Stretching Surface in A Porous Medium

The intention of this article is to investigate the impact of slip of MHD stagnation point flow over a permeable shrinking/stretching sheet with double stratification in a porous medium. Employing the appropriate similarity transformations and non-dimensional variables, the governing partial differential equations were reduced into a set of nonlinear ordinary differential equations. These equations were solved using shooting method and influence of pertinent variables on velocity, temperature and concentration are computed and analyzed. It was found that the slips have the propensity to control boundary layer flow and as the velocity slip increases, the momentum, thermal, and concentration boundary layer thickness become thinner for velocity slip. Therefore, velocity slip acts as a boost for enhancement of the velocity profile in the boundary layer region, whereas temperature and concentration profiles decelerate with the velocity slip. It is also shown that the skin friction coefficient has decreased as the values of velocity slip increase while the It was found that the slips have the propensity to control boundary layer flow and as the velocity slip increases, the momentum, thermal, and concentration boundary layer thickness become thinner for velocity slip. Therefore, velocity slip acts as a boost for enhancement of the velocity profile in the boundary layer region, whereas temperature and concentration profiles decelerate with the velocity slip. It is also shown that the skin friction coefficient has decreased as the values of velocity slip increase while the local Nusselt number and the local Sherwood number are increasing. A comparison with previous studies available in the literature has been done and found an excellent agreement by comparing the numerical results in two decimal places which supports the validity of the present analysis.

Unsteady magnetohydrodynamic couple stress fluid flow from a shrinking porous sheet: Variational iteration method study

AbstractMotivated by magnetic polymer manufacturing applications, the present research article examines theoretically the hydromagnetic boundary layer flow of an electrically conducting non‐Newtonian couple stress fluid due to a transient shrinking (contracting) porous sheet. The conservation partial differential equations for mass and momentum are rendered into a fifth‐order nonlinear ordinary differential equation via similarity transformations with associated boundary conditions. A semi‐analytical/numerical scheme employing Lagrangian multipliers and known as the variational iteration method (VIM) is implemented to solve the ordinary differential boundary value problem. Validation of the solutions is conducted by benchmarking against earlier Newtonian studies and very good agreement is achieved. A detailed assessment of the impact of couple stress (rheological), unsteadiness, magnetic body force parameter, and wall transpiration (suction/injection) parameter on flow characteristics is conducted with the aid of graphs. A significant deceleration in the flow is computed with increasing injection (acceleration is caused with greater suction) and acceleration is induced with higher unsteadiness parameter values. Increasing magnetic field (higher magnetic number) generates flow acceleration, rather than the customary deceleration, due to the shrinking sheet dynamics. A stronger couple stress effect manifests in strong retardation in the boundary layer flow and an increase in momentum (hydrodynamic|) boundary layer thickness. VIM demonstrates excellent convergence and accuracy and shows significant promise in studying further magnetic polymer fabrication flow problems.

Melting heat transfer of a magnetized water-based hybrid nanofluid flow past over a stretching/shrinking wedge

This research presents the stagnation point flow with heat transfer of water-based hybrid nanofluid over a stretching/shrinking wedge. Magnetic field is applied normal to the wedge with melting heat transfer effect. The wall of the boundary with slip effect on the surface. Water as base fluid with two different nanoparticles (Al2O3 and Cu) is considered. The Navier-Stokes and heat equation are first simplified through similarity variables to convert the partial differential equations (PDEs) into non-dimensional ordinary differential equations (ODEs). The numerical solutions are obtained with the help of bvp4c technique in MATLAB programming. This study is focused on the impacts of different dimensionless parameters on the velocity field, temperature distribution, skin friction coefficient and Nusselt number. It is seen that the solution of governing ODEs has two branches, first and second branch solutions in some specific range of supervising parameters. It is found that heat transfer rate enhances against melting parameter in the first branch solution and converse behavior can be observed for second branch solution. It is also uncovered that in hybrid nanofluid, the momentum and thermal boundary layer thickness enhances in first solution while reduces in the second solution with the advancement of angle of wedge parameter.

Conjugate heat transfer numerical study of the ejector by means of SU2 solver

In this paper, the test supersonic ejector with conjugate heat transfer in solid bodies has been studied numerically. An extensive numerical campaign by means of open-source SU2 solver is performed to analyze the fluid dynamics of the ejector flowfield accounting for the heat conduction in solids. The fluid domain simulation is carried out by employing compressible RANS treatment whilst the heat distribution in solids is predicted by simultaneous solving the steady heat conduction equation. The working fluid is R245fa and all simulations are performed accounting for real gas properties of the refrigerant. Experimental data against numerical results comparison showed close agreement both in terms mass flow rates and static pressure distribution along the walls. Within the CFD trials, the most valuable flow parameters at a wall vicinity are compared: distribution across the boundary layer of the temperature and the turbulent kinetic energy specific dissipation rate, boundary layer displacement and momentum thicknesses. A comprehensive analysis of the simulation results cases with adiabatic walls against cases with heat permeable walls revealed the actual differences of the flow properties in the wall vicinity. However, the ejector performance has not changed noticeably while accounting for the heat conduction in solids.

Numerical study of axisymmetric magneto-gyrotactic bioconvection in non-Fourier tangent hyperbolic nano-functional reactive coating flow of a cylindrical body in porous media

Modern functional nanomaterials coating processes feature an increasing range of intelligent properties including rheology, biological (bio-inspired) modifications, elaborate thermophysical behaviour and complex chemical reactions which are needed for the precise synthesis of bespoke designs. Such manufacturing flow processes are extremely complex and involve both heat and multiple mass transfer (species diffusion) phenomena. Intelligent nano-coatings are particularly attractive since they exploit magnetic nanoparticles which can be manipulated by external magnetic fields. Recently, Boeing Aerospace have explored the use of micro-organisms for intelligent aircraft coatings. Mathematical models provide an excellent analysis for elucidating the response characteristics of such coating dynamics processes. With this motivation, the present analysis is indented to develop a new mathematical model to examine the axisymmetric, magnetohydrodynamic, chemically reactive, gyrotactic bioconvection flow of a tangent hyperbolic nanofluid past a cylinder saturated with Darcy porous medium, as a model of smart-coating enrobing flow. The influence of Cattaneo–Christov heat flux (non-Fourier thermal relaxation parameter), thermophoresis and Brownian motion are taken into consideration. The steady-state, boundary layer, partial differential conservation equations are rendered dimensionless via appropriate transformations, and the subsequent nonlinear, coupled, system of governing equations is numerically solved by employing implicit Keller box method. The impact of various factors such as Hartmann magnetic number, Weissenberg viscoelastic parameter, Prandtl number, non-Fourier thermal relaxation parameter, thermophoresis, Brownian motion, micro-organisms concentration difference variable, chemical reaction, bioconvection Peclet number, Schmidt number and bio-convection Schmidt number on the flow, heat transfer, mass transfer, motile density, local friction factor, local heat transfer rate, local mass transfer rate and local microorganism density number wall gradient is visualized graphically. Validation with earlier studies is included. Further validation with a finite element method (FEM) code (SMART-FEM) is presented. Results reveal that the heat transfer upsurges for amplifying the Weissenberg number and Hartmann magnetic number. Microorganism concentration distribution of the non-Newtonian nanofluid coating diminishes for amplifying the bioconvection Schmidt number and Peclet number. Magnifying the power law index parameter reduces the momentum boundary layer thickness of tangent hyperbolic nanofluid, while there is an acceleration in the fluid flow near the surface of the cylinder. Local Sherwood number rises with higher values of homogenous destructive chemical reaction parameter. The computations provide a solid benchmark for further CFD modelling.

Spectral computation of reactive bi-directional hydromagnetic non-Newtonian convection flow from a stretching upper parabolic surface in non-Darcyporous medium

This paper presents a mathematical model for bi-directional convection magnetohydrodynamic (MHD) tangent hyperbolic nanofluid flow from the upper horizontal subsurface of a stretching parabolic surface to a non-Darcian porous medium, as a simulation of nanocoating. Chemical reaction, activation energy and thermo solutal buoyancy effects are included. The Darcy–Brinkman–Forchheimer model is deployed which permits the analysis of inertial (second order) porous drag effects. The Buongiorno nanoscale model is deployed which includes Brownian motion and thermophoresis effects. The dimensionless, transformed, nonlinear, coupled ordinary differential equations are solved by implementing the spectral relaxation method (SRM). Validation with previous studies is included. The numerical influence of key parameters on transport characteristics is evaluated and visualized graphically. Velocity is elevated (and momentum boundary layer thickness is reduced) with increasing wall thickness parameter, permeability parameter, Forchheimer parameter, Weissenberg (rheological) parameter and modified Hartmann (magnetic body force) number. Velocity enhancement is also computed with increment in stretching rate parameter, rheological power-law index, thermal Grashof number, and species (solutal) Grashof number, and momentum boundary layer thickness diminishes. Temperature is suppressed with increasing stretching rate index and Prandtl number whereas it is substantially elevated with increasing Brownian motion and thermophoresis parameters. Velocity and temperature profiles are reduced adjacent to the parabolic surface with larger wall thickness parameter for stretching rate index [Formula: see text]1, whereas the reverse behavior is observed for stretching rate index [Formula: see text]1. Nanoparticle concentration magnitude is depleted with larger numeric of Lewis number and the Brownian motion parameter, whereas it is enhanced with greater values of the stretching index and thermophoresis parameter. The nanoparticle concentration magnitude is reduced with an increase in chemical reaction rate parameter whereas it is boosted with activation energy parameter. Skin friction, Nusselt number and Sherwood number are also computed. The study is relevant to electromagnetic nanomaterials coating processes with complex chemical reactions.

Hall and ion‐slip effects on MHD natural convective flow past an unbounded vertical porous channel with thermodiffusion

AbstractThe consequences of Soret in addition to Dufour of natural convection heat and mass transfer for the unsteady three‐dimensional boundary layer flow through a perpendicular condition of the existence of viscous dissipation, invariable suction, Hall as well as ion slip consequences into relation. The prevailing partial differential equation is dissolved digitally utilizing the implicit Crank–Nicolson finite difference method. The velocity, temperature, as well as concentration dispensations, is addressed computationally and demonstrated by the graphs. Numerical values of the Nusselt number, skin friction as well as Sherwoods numbers nearby the plate are discussed for a choice of values of substantial parameters and are displayed in a tabular manner. It is noticed that the temperature of the fluid diminishes with higher Prandtl numbers. The resulting velocity diminishes with the growing Hartmann number. Rotation, Soret, and Dufour parameters strengthen the velocity and momentum boundary layer thickness. The velocity intensifies through growing Hall and ion‐slip parameters and the revoke trend is acquired with enhancement in suction parameter.

Numerical Study on Generalized Heat and Mass in Casson Fluid with Hybrid Nanostructures.

The rheological model for yield stress exhibiting fluid and the basic laws for fluid flow and transport of heat and mass are used for the formulation of problems associated with the enhancement of heat and mass due to dispersion of nanoparticles in Casson. The heat and mass transfer obey non-Fourier’s laws and the generalized Fick’s law, respectively. Model problems are incorporated by thermal relaxation times for heat and mass. Transfer of heat energy and relaxation time are inversely proportional, and the same is the case for mass transport and concentration relaxation time. A porous medium force is responsible for controlling the momentum thickness. The yield stress parameter and diffusion of momentum in Casson fluid are noticed to be inversely proportional with each other. The concentration gradient enhances the energy transfer, and temperature gradient causes an enhancement diffusion of solute in Casson fluid. FEM provides convergent solutions. The relaxation time phenomenon is responsible for the restoration of thermal and solutal changes. Due to that, the thermal and solutal equilibrium states can be restored. The phenomenon of yield stress is responsible for controlling the momentum boundary layer thickness. A porous medium exerts a retarding force on the flow, and therefore, a deceleration in flow is observed. The thermal efficiency of Casson fluid is greater than the thermal efficiency of Casson fluid.

Heat Transport Phenomena for the Darcy–Forchheimer Flow of Casson Fluid over Stretching Sheets with Electro-Osmosis Forces and Newtonian Heating

In this study, an investigation has been carried out to analyze the impact of electro-osmotic effects on the Darcy–Forchheimer flow of Casson nanofluid past a stretching sheet. The energy equation was modelled with the inclusion of electro-osmotic effects with viscous and Joule dissipations. The governing system of partial differential equations were transformed by using the suitable similarity transformations to a system of ordinary differential equations and then numerically solved by using the Runge–Kutta–Fehlberg method with a shooting scheme. The effects of various parameters of interest on dimensionless velocity and temperature distributions, as well as skin friction and heat transfer coefficient, have been adequately delineated via graphs and tables. A comparison with previous published results was performed, and good agreement was found. The results suggested that the electric and Forchheimer parameters have the tendency to enhance the fluid velocity as well as momentum boundary layer thickness. Enhancements in temperature distribution were observed for growing values of Eckert number. It was also observed that higher values of electric field parameter diminished the wall shear stress and local Nusselt number.

Three dimensional heat transfer in the Carreau-Yasuda hybrid nanofluid with Hall and ion slip effects

For enhancement of heat and mass transfer, the use of hybrid nano-particles in shear rate-dependent viscous fluid is of great significance given applications. In this study, we have considered the impacts of Hall and ion-slip currents on the three-dimensional (3D) flow of shear rate-dependent viscous fluid. The shear rate-dependent rheology is characterized by the Carreau-Yasuda model. Ethylene glycol is found in plasma and rheological characteristics are best described by the power-law constitutive model which is a special case of the Carreau-Yasuda rheological model, Therefore, the most generalized model is considered to examine the rheological characteristics. Further, Al 2 O 3 − ethylene glycol and TiC − Al 2 O 3 − ethylene glycol are termed as Carreau-Yasuda nanofluid and Carreau-Yasuda hybrid nanofluids respectively. Specifically, here in the considered problem, Titanium carbide and aluminum oxide (TiC and Al 2 O 3) hybrid nano-particles which are source materials for MXenes, are dispersed in the Ethylene glycol (C 2 H 6 O 2) as a base fluid. The finite element method (FEM) is implemented to find the numerical solution of the boundary value problems. The thermal performance of both types of fluids is analyzed under the influence of related parameters. The thermal performance of both types of fluids is compared. Hall and ion-slip currents are induced to the ion and electron collisions and cause Hall and ion-slip forces which have the opposite direction to the magnetic force induced due to the magnetic field interaction. Thus Hall and ion-slip forces are favorable forces and result in to increase in momentum boundary layer thickness (MBLT). It is also discovered that the Hall and ion-slip forces in TiC − Al 2 O 3 − ethylene glycol flow are greater than those in Al 2 O 3 − ethylene glycol flow. Furthermore, Hall and ion-slip currents play an important role in decreasing Ohmic dissipation, which has a negative impact on the thermal performance of the working fluid. The role of generative chemical reaction on the transport of mass is opposite to the role of the destructive chemical reaction. Joule heating (Ohmic dissipation) directly affects the temperature of fluid particles and their kinetic energy increases and hence thermal boundary layer thickness (TBLT) becomes wider. Thus Ohmic dissipation has adverse effects on thermal performance. Thus fluids with no dissipation behave better as coolants.

Effects of Pressure Gradient on Convective Heat Transfer in a Boundary Layer Flow of a Maxwell Fluid Past a Stretching Sheet

The pressure gradient term plays a vital role in convective heat transfer in the boundary layer flow of a Maxwell fluid over a stretching sheet. The importance of the effects of the term can be monitored by developing Maxwell’s equation of momentum and energy with the pressure gradient term. To achieve this goal, an approximation technique, i.e. Homotopy Perturbation Method (HPM) is employed with an application of algorithms of Adams Method (AM) and Gear Method (GM). With this approximation method we can study the effects of the pressure gradient (&lt;i&gt;m&lt;/i&gt;), Deborah number (β), the ratio of the free stream velocity parameter to the stretching sheet parameter (ɛ) and Prandtl number (Pr) on both the momentum and thermal boundary layer thicknesses. The results have been compared in the absence and presence of the pressure gradient term &lt;i&gt;m&lt;/i&gt; . It has an impact of thinning of the momentum and boundary layer thickness for non-zero values of the pressure gradient. The convergence of the system has been taken into account for the stretching sheet parameter ɛ. The result of the system indicates the significant thinning of the momentum and thermal boundary layer thickness in velocity and temperature profiles. On the other hand, some results show negative values of &lt;i&gt;f&lt;/i&gt; '(η) and θ (η) which indicates the case of fluid cooling.

Three Dimensional MHD Hybrid Nanofluid Flow with Rotating Stretching/Shrinking Sheet and Joule Heating

A three-dimensional hybrid nanofluid flow over a stretching/shrinking sheet is numerically studied. The hybrid nanofluid being considered in this study used water as the base fluid and mixed with two types of solid nanoparticles, namely alumina (Al2O3) and copper (Cu). The main focus of the current study is to examine the effect of magnetic field, Joule heating, and rotating sheet on the velocity, and temperature profiles. In addition, the impact of suction and stretching sheet on the variations of reduced skin friction, , and reduced heat transfer are studied as well. The fluid flow and heat transfer problem presented in this study is governed by a system of nonlinear partial differential equations (PDEs), which is then transformed into the corresponding system of high order nonlinear ordinary differential equations (ODEs) using similarity variables. The resulting system of higher order nonlinear ODEs is solved numerically using a boundary value solver known as bvp4c, which operates on the MATLAB computational platform. Results revealed that dual solutions exist for shrinking sheet while unique solutions are observed for stretching sheet with various values of Cu nanoparticles volume fraction and magnetic parameter. Dual solutions also exist for the value of the suction parameter greater than its critical point with various values of Cu nanoparticles volume fraction. Velocity profile of the hybrid nanofluid increases alongside with the value of magnetic parameter but declination was observed in the profile of and temperature, for both solutions as the value of Cu nanoparticles volume fraction increases. When the value of rotational parameter increases, both velocity and profiles increase for both solutions. This indicates that the momentum boundary layer thickness increases with increasing values of for both solutions, but thermal boundary layer thickness decreases for the first solution and increases for the second solution. Finally, an increment in the value of Eckert number causes the temperature of the hybrid nanofluid to rise as well for both first and second solutions.

Wake Width: Discussion of Several Methods How to Estimate It by Using Measured Experimental Data

Several methods of defining and estimating the width of a turbulent wake are presented and tested on the experimental data obtained in the wake past an asymmetric prismatic airfoil NACA 64(3)-618, which is often used as tip profile of the wind turbines. Instantaneous velocities are measured by using the Particle Image Velocimetry (PIV) technique. All suggested methods of wake width estimation are based on the statistics of a stream-wise velocity component. First, the expansion of boundary layer (BL) thickness is tested, showing that both displacement BL thickness and momentum BL thickness do not represent the width of the wake. The equivalent of 99% BL thickness is used in the literature, but with different threshold value. It is shown that a lower threshold of 50% gives more stable results. The ensemble average velocity profile is fitted by Gauss function and its σ-parameter is used as another definition of wake width. The profiles of stream-wise velocity standard deviation display a two-peak shape; the distance of those peaks serves as wake width for Norberg, while another tested option is to include the widths of such peaks. Skewness (the third statistical moment) of stream-wise velocity displays a pair of sharp peaks in the wake boundary, but their position is heavily affected by the statistical quality of the data. Flatness (the fourth statistical moment) of the stream-wise velocity refers to the occurrence of rare events, and therefore the distance, where turbulent events ejected from the wake become rare and can be considered as another definition of wake width. The repeatability of the mentioned methods and their sensitivity to Reynolds’ number and model quality are discussed as well.

Fluorescent PIV using Atomized Liquid Particles

It is shown that aerosolized fluorescent particles generated using a Venturi-type atomizer, from a solution of fluorescent Kiton Red 620 dye in a water/glycol fluid, provide effective flow seeding for fluorescent PIV. The atomized liquid particles were found to be of acceptable size for PIV purposes, with 92% of detected particles by number concentration measuring &lt; 1 μm in diameter. A PIV application was conducted in a wind tunnel (freestream velocity U∞ = 27 m/s), using the particles for measurement of the boundary layer flow approaching a forward-facing step (approach boundary layer momentum thickness Reynolds number of Reθ = 5930), to identify potential benefits in near-wall regions normally affected by unwanted laser reflections from tunnel surfaces. Particles were generated from solutions with dye molar concentrations of 2.5 × 10−3 and 1.0 × 10−2 mol/L, and PIV images were obtained for both elastic Mie scattering and filtered, Stokes-shifted fluorescent light. Raw images indicate that the fluorescence yield of the 1.0 × 10−2 mol/L solution provides PIV images with high contrast, even in the near-surface regions where Mie scattering images are highly affected by surface reflections. Boundary layer profiles are processed in the adverse pressure gradient region leading up to the forward-facing step, where the fluorescent PIV performed comparably to the most optimized Mie scattering PIV; both obtained data as near to the wall as 30 μm, or 2 viscous wall units in our flow of interest. These results indicate that the new seeding method holds excellent promise for near-surface measurement applications with more complicated three-dimensional geometries, where it is impossible to arrange PIV cameras to reject surface-scattered light.