Dimensionless Velocity Profiles Research Articles

Thermal and hydrodynamic analysis inside a channel partially filled with porous material

AbstractIn this work, the transfer of heat and changes in fluid pressure within a rectangular channel fairly packed with porous material have been studied numerically for various Darcy numbers and dimensionless porous layers. The model was run with the following assumptions: laminar flow, forced convection, isotropic porous material, local thermodynamic equilibrium, constant wall temperature boundary condition, and no thermal dissipation. The study covers a broad range for the dimensionless porous layer, 0 ≤ hr < 1, and the Darcy number, 10−4 < Da < 10−2. The fully developed and developing flow over the channel is investigated in numerical study. It was observed that the inertia effect may be disregarded when Da < 10−4. The local dimensionless bulk temperature distribution, pressure drop, and velocity profiles were all shown to be impacted by the Darcy number and dimensionless porous layers, according to the numerical analysis results. The maximum heat transfer rate was attained when the ratio of the porous layer inside the channel was 0.8, and the pressure gradient was the highest. Partial packing of the channel with a porous material has two advantages: it increases the rate heat transmission rate and results in a much smaller pressure drop than a filled porous medium.

Extended analytical model of Tesla turbine with advanced modelling of velocity profile in minichannel between corotating disks with consideration of surface roughness

Consideration of roughness effects in the flow in a minichannel has been a major scientific problem for many decades. Roughness can alter the momentum diffusion, heat transfer conditions or laminar-turbulent transition. These effects are even more pronounced in minichannel flows where the roughness can occupy a large part of the cross-section. Modelling methods applied so far usually fall short in internal flows with high relative roughness. The presented paper pertains to the analytical flow model in Tesla turbine components with consideration of roughness on the rotor walls. The model uses the equivalent sand grain approach to modify dynamic viscosity in the governing equations to achieve a desired downward shift of the dimensionless velocity profile. The model solves two-dimensional equations of continuity, momentum and energy. The semi-empirical function was derived to consider the change in the shape of the radial velocity. The applied model incorporates Euler's turbomachinery equation to determine the influence of roughness on the turbine performance under varied operating conditions. Roughness shortens the streamlines inside the rotor, but the overall turbine's performance is improved. The roughness equal to 10−5 m increased the power generated and isentropic efficiency by factors of 3 and 2.5, respectively, compared to the smooth rotor.

Entropy analysis of Darcy-Forchheimer flow of Reiner-Rivlin A12O3–Cu/engine oil based hybrid nanofluid between two rotating disks

This paper analyzes the flow of the Reiner-Rivlin hybrid nanofluid, considering the magnetic field and varying thermal conductivity between two spinning disks. Appropriate similarity variables are used to transform all dimensional equations into dimensionless form. A semi-analytical homotopy analysis approach applied to solve dimensionless equations and velocity profiles, temperature distribution, Nusselt number, skin friction, entropy generation, and Bejan number are presented graphically. Some key outcomes include that axial and tangential velocities decreases when porosity parameters increase. Additionally, higher Eckert number when varying from 1 to 1.3, increases the temperature near the center of the two disks from 1.02 to 1.18. The heat transfer rate goes up from 10.2767 to 10.3043 when thermal conductivity rises from 0.1 to 0.7. The entropy generation grows in proportion to the Brinkman number, Reynolds number, and the porosity parameter values. This research might enhance cooling, lubrication, and thermal management in automotive, aerospace, and biomedical industries.

Investigation of Soret and Dufour Effects on Chemically Reacting Free Convective Fluid Flowing Over a Vertical Plate Along with Viscous Dissipation Using the Laplace Adomian Decomposition Method

This study comprehensively analyses heat and mass transfer phenomena in a chemically reacting free convective fluid flow along a vertically moving plate. The flow is influenced by thermo-diffusion, diffusion-thermo, and viscous dissipation effects. To simplify the analysis, scaling group analysis and appropriate similarity transformations are used to transform the governing equations into nonlinear ordinary differential equations. These equations are then solved using a combination of Laplace transform and the Adomian decomposition method. The study conducts a parametric investigation to explore the impact of various control parameters on the dimensionless velocity, temperature, and concentration profiles. The parameters considered include the Prandtl number, Schmidt number, Eckert number, chemical reaction parameter, Soret parameter, Dufour parameter, solutal Grashof number, and thermal Grashof number. These parameters are depicted graphically and analysed quantitatively. The results reveal that an increase in the Schmidt number leads to a decrease in velocity and concentration profiles while temperature varies monotonically. Elevating the Eckert number enhances velocity and temperature profiles, with a slight decrease in concentration profiles. A rise in the Prandtl number decreases the temperature profile, with minimal effects on velocity and concentration profiles. Increasing the solutal Grashof number decreases temperature and concentration profiles, whereas the thermal Grashof number is directly proportional to the velocity profile. An increase in the Dufour parameter boosts velocity and temperature profiles while reducing the concentration profile. The presence of the Soret parameter increases velocity and concentration profiles but decreases the temperature profile. This study aims to enhance comprehension of the complex interactions within flow characteristics, providing valuable insights into the fundamental mechanisms of such systems. It also highlights their potential applications in various engineering and industrial processes.

Two-relaxation-time lattice Boltzmann model of the velocity profiles and volumetric flow rate of generalized Newtonian fluids in a single-screw extruder

Single-screw extruders and injection molding machines are essential equipment in polymer processing. It is of great importance for the optimization of operating parameters and the design of extrusion screw to predict the throughput of an extruder and the metering time of an injection molding machine according to the geometric parameters of the screw, operating parameters, and the rheological behavior of materials. Most polymer melts exhibit non-Newtonian behavior. The lattice Boltzmann method has many advantages in simulating the flow of non-Newtonian fluids. Herein, the dimensionless velocity profiles and dimensionless volumetric flow rate of generalized Newtonian fluids in a screw channel have been studied using the two-relaxation-time lattice Boltzmann method (TRT–LBM). The numerical results of power-law fluids are in good agreement with the analytical solutions, which verifies the validity of TRT–LBM. Through research, the change rule of the dimensionless volumetric flow rate of Bingham fluids with dimensionless pressure gradient has been obtained. It was found that the rheological properties of polymer melts and the dimensionless pressure gradient significantly affect the dimensionless velocity profiles and dimensionless volumetric flow rate. The dimensionless volume flow rate has some unexpected changes with the increase of the dimensionless pressure gradient. This study can provide theoretical guidance for the optimization of operating parameters and the design of extrusion screws.

Numerical Approach to Thermo-Convective Micro-Polar Fluid with Radiation in Permeable Medium

A steady, incompressible and thermo-convective flow of micro-polar fluid over a stretching permeable sheet with heat and mass transfer under effects of radiation, Soret, Schmidt and Dufour numbers has been analyzed. The modeled governing equations, of the classical Navier-Stokes are coupled with micro rotation, temperature and concentration equations, in the form of Partial Differential Equations (PDE’s), along with initial and boundary conditions, are transformed into a system of nonlinear coupled Ordinary Differential Equations (ODE’s) by using an appropriate transformation. The numerical solution is obtained by using the Parametric Continuation Method (PCM). For the validity of the scheme the results are compared with a numerical package bvp4c. It has been observed that both the results are in their best agreement with each other. The effects of associated parameters on the dimensionless velocity, micro-rotation, temperature and concentration profiles are discussed and depicted graphically. It has been detected that the permeability parameter give rise in micro-rotation profile.

Ion acceleration in expanding plasma in small radio frequency plasma thruster with a magnetic cusp

Ambipolar electric field is formed in the expanding plasma of the small radio frequency plasma thruster using a cusp-shaped magnetic field. A highly energized group of ion energy distribution function is observed in the z-direction, indicating the presence of axial ion acceleration downstream the magnetic nozzle owing to the electric field. The mean velocity profile of the beam ions along the z axis is evaluated using the energy distribution functions along the z axis. The high axial ion velocity profile stretches downstream, although the evaluated dimensionless velocity profile is lower than that calculated using quasi-one-dimensional models. It is suggested that ion momentum loss can result from ion-neutral collision, leading to beam divergence in the magnetic nozzle of the proposed small thruster.

Evaluation of dynamic correction of turbulence wall boundary conditions to simulate roughness effect in minichannel with rotating walls

PurposeThe purpose of this study is an assessment of the existing roughness models to simulate the flow in the narrow gap between corotating and rough disks. A specific configuration of the flow through the gap, which forms a minichannel with variable cross sections and rotating walls, makes it a complex problem and, therefore, worth discussing in more detail.Design/methodology/approachTwo roughness models were examined, the first one was based on the wall function modification by application of the shift in the dimensionless velocity profile, and the second one was based on the correction of turbulence parameters at the wall, proposed by Aupoix. Due to the lack of data to validate that specific case, the approach to deal with was selected after a systematic study of reported test cases. It started with a zero-pressure-gradient boundary layer in the flow over a flat plate, continued with flow through minichannels with stationary walls, and finally, focused on the flow between corotating discs, pertaining each time to smooth and rough surfaces.FindingsThe limitations of the roughness models were highlighted, which make the models not reliable in the application to minichannel flows. It concerns turbulence models, near-wall discretization and roughness approaches. Aupoix’s method to account for roughness was selected, and the influence of minichannel height, mass flow rate, fluid properties and roughness height on the velocity profile between corotating discs in both smooth and rough cases was discussed.Originality/valueThe originality of this study is the evaluation and validation of different methods to account for the roughness in rotating mini channels, where the protrusions can cover a substantial part of the channel. Flow behavior and performance of different turbulence models were analyzed as well.

Application of Bernoulli wavelet method on triple‐diffusive convection in Jeffery–Hamel flow

AbstractIn this article, triple‐diffusive convection in the Jeffery–Hamel flow of viscous fluid is studied. The Jeffery–Hamel flow depends upon the radial component of velocity, while the peripheral velocity is zero. The problem has been articulated as nonlinear coupled partial differential equations (PDEs) together with the pertinent boundary conditions. The reduction of the nonlinear coupled PDEs into new nonlinear coupled ordinary differential equations is achieved via a collection of appropriate transformations, which is solved using the Bernoulli wavelet method. The obtained results were compared with the numerical results, confirming the good agreement between the present and previous numerical results. Dimensionless velocity, temperature, and concentration profiles are discussed for the relevant factors involved. Furthermore, skin friction, heat transfer, and solute diffusions are calculated.

Heat transfer analysis of water-ethylene glycol (50:50) based nanofluid over a cone with the influences of magnetic field and uniform heat generation/absorption

Aim:The novelty of the problem is to examine the heat transfer analysis of H2O–C2H6O2 (50:50) mixture based Al2O3 and Fe3O4 over a heated and spinning down-pointing vertical cone with the effect of heat generation or absorption in the presence of magnetic field. Findings:Results are demonstrated in terms of graphs to examine the influence of various physical parameters that come across such as Magnetic parameter M, Spin parameter ϵ, Nanoparticle volume fraction ϕ, Heat generation or absorption parameter Δ, velocity slip parameter Γ1 and thermal slip parameter Γ2 on dimensionless velocity profile F′(y), G(y) and temperature profile H(y). The effect of M, ϵ, ϕ, Δ,Γ1,Γ2on skin friction and local Nusselt number are examined in tabulation form. Significant outcomes:It is pointed out that enhancement in Magnetic parameter and thermal slip parameter leads to declination of the velocity profile. Influence of Heat generation or absorption parameter magnifies the thermal characteristic of the flow. Moreover, the numerical statistics was triggered and catalogued to analogize the results of existing outcomes with those of previous literature for some special cases and established excellent agreement. Fe3O4 possess 0.78% and 0.92% of high surface drag force and heat transfer rate respectively than Al2O3 with respect to heat generation or absorption parameter. Approach:The system of partial differential equations is transformed into set of nonlinear ordinary differential equations. Solutions for the system of nonlinear Ordinary differential equation are obtained by Numerical method. The numerical scheme is developed based on fourth order Runge Kutta scheme along with shooting techniques. Practical implications:In this current growing scenario, engineers and scientists are making an endeavour to gratify the global needs. Nanofluids are considered as inevitable one for achieving industrial and global needs. The investigation of heat transfer over rotating cone with the effect of magnetic field is of considerable interest due to its presence in industrial and technological applications. Especially in the design of turbines and turbo equipment’s and in understanding the path of flight of rotating wheels.

Numerical investigation of MHD flow of hyperbolic tangent nanofluid over a non-linear stretching sheet

This research investigates two-dimensional MHD incompressible boundary layer Hyperbolic Tangent nanofluid flow across a non-linear stretching plate. Similarity transformations are employed to convert the governing non-linear partial differential equations (PDEs) into coupled non-linear ordinary differential equations (ODEs). The MATLAB built-in routine bvp4c has been used for finding the numerical solutions of the dimensionless velocity, temperature, and concentration profiles. The current findings are validated with already published results. The influence of some important parameters on the velocity, temperature, and concentration profiles are displayed through graphs and tables. It is observed that for increasing values of magnetic parameter M and hyperbolic Tangent parameter We, the boundary layer thickness of the velocity profile decreases while it increases for the temperature profile.

Analysis of assisting and opposing flows of the Eyring-Powell fluid on the wall jet nanoparticles with significant impacts of irregular heat source/sink

Nanofluids are employed in a variety of human endeavors, such as engineering tools in chemical and power engineering, electronics, medicine, and other areas. Thus, this article investigates the wall jet flow (WJF) and heat transfer (HT) by incorporating the Eyring-Powell nanofluid with a significant consequence of erratic heat source/sink and buoyancy. The leading equations are converted by similarity variables and then obtained numerical solutions by the bvp4c technique. The influences of physical influential parameters on the dimensionless velocity and dimensionless temperature distribution profiles are discussed to predict the behavior of the fluid flow and heat transfer. Also, the heat transfer and friction factor were elaborated with the aid of tables for dimensionless emerging parameters. Moreover, the current results are compared with published results in a limiting case to show the accuracy of the present method. Finally, the current study informs us that the relevant parameters have had a considerable impact on the profiles of the boundary layer.

Investigation of radiative MHD Carreau nanofluid over an inclined stretching cylinder with activating energy, Wu’s slip, and convective heating

The influence of radiation, convective heating, second-order velocity slip condition, and activating energy on the magnetohydrodynamic (MHD) Carreau nanofluid and heat/mass transfer are depicted in this study. A mathematical model of the Carreau nanofluid is carried out with the effects of thermophoresis and Brownian motion. The governing equations are transformed into a system of nonlinear coupled differential equations. Solutions of the transformed equations are derived by the Matlab BVP4c solver. Efficiency of the solver is verified by the comparison with the previous literature. Moreover, the impacts of the dimensionless velocity, temperature, and nanoparticle concentration profile are elucidated graphically.

Heat transfer in MHD flow of Carreau ternary-hybrid nanofluid over a curved surface stretched exponentially

This investigation aims to study Magnetohydrodynamics (MHD)two-dimensional incompressible boundary layer performing non-Newtonian Carreau ternary-hybrid nanofluid flow with heat transfer through an exponential stretching curved surface. The ternary-hybrid nanofluid has been synthesized with titanium oxide, aluminum oxide, and silver dispersionin the base fluid water. TheNavier Stokes equation and Carreau ternary-hybrid nanofluid model govern the partial differential equations (PDEs), and appropriate similarity transformations are utilized to transfer these PDEs into ordinary differential equations (ODEs). The effects of the pertinent parameters on the dimensionless velocity and temperature profiles are analyzed withfigures. This study provides new insights and solutions to previously unsolved problems related to heat transfer in the MHD flow of a Carreau Ternary-Hybrid Nanofluid over a curved surface stretched exponentially, or it could contribute to the existing knowledge and literature by refining existing models or methods. The surface drag force and Nusselt numbers are studied for the different values of the governing parameters throughgraphs. It is demonstrated that the heat transfer rate and skin friction increase from base fluid to mono, hybrid, and ternary nanofluids. Both heat transfer rate and skin friction increase with the addition of nanoparticles.

Mathematical modeling and analysis of immiscible metallic based nanofluid flow in a microchannel with non-spherical nanoparticles

The non-spherical shaped nanoparticles have grown in popularity due to their ability to alter the nanofluid thermophysical properties. This nanofluid plays a beneficial role in biomedical imaging, cancer and tumor therapy. In the current study the effect of pressure gradient, transverse magnetic field and electroosmosis on the flow of two immiscible metallic based nanofluids (blood-based Au/Ag Casson nanofluid and water-based Au/Ag Newtonian nanofluid) of different viscosities in separate regions in a microchannel is addressed. The combined impact of electromagnetohydrodynamics (EMHD), modified Darcy’s law, Joule heating and Hall current have been considered into account. The mathematical modeling has been developed with the help of modified Navier Stoke’s equations, and simplified the complex problem using appropriate assumptions and non-dimensional parameters. The complementary function and particular integral concepts have been used to obtain the exact solutions of a non-dimensionalized system of coupled differential equations along with non-dimensionalized conditions. The dimensionless velocity, temperature and concentration profiles of nanofluids have been computed. The influence of numerous relevant fluid transport parameters has been graphically depicted. It is noticed that the magnetic strength declines the nanofluid velocity in both regions. Further, the radiation parameter exhibits an inverse effect on the rate of heat transfer in nanofluids. The heat transfer rate enhanced by 56% and 2% with rising volume fraction [0.01 to 0.02] and zeta potential [0.1 to 0.2], respectively. With increasing strength of magnetic field [2 to 3], thereby 31% increment in shear stress distribution. The results of the current study can be used to enhance the performance of various processes such as surface-enhanced Raman spectroscopy, drug delivery, sensors, and electrochemistry.

Dual Solutions and Stability Analysis of Cu-H2O-Casson Nanofluid Convection past a Heated Stretching/Shrinking Slippery Sheet in a Porous Medium

In this study, we examined the impact of Cu-H2O nanoparticles on two-dimensional Casson nanofluid flows past permeable stretching/shrinking sheet embedded in a Darcy-Forchheimer porous medium in the presence of slipperiness of surface, suction/injection, viscous dissipation, and convective heating. Using some realistic assumptions and appropriate similarity transformations, the governing nonlinear partial differential equations were formulated and transformed into a system of nonlinear ordinary differential equations and then numerically solved by using the shooting technique. Numerical results are displayed for dimensionless fluid velocity and temperature profiles, skin friction, and the local Nusselt number. The impacts of different governing physical parameters on these quantities are presented and discussed using graphs, tables, and a chart. For the specific range of shrinking sheet, the result shows that dual solutions exist, and temporal stability analysis is performed by introducing small disturbances to determine the stable solutions. It is detected that the upper branch solution is hydrodynamically stable and substantially realistic; however, the lower branch solution is unstable and physically unachievable. The fluid flow stability is obtained by enhancing the suction, surface slipperiness, and viscous dissipation parameters. However, augmenting the values of the Casson factor, Cu-H2O nanoparticle volume fraction, porous medium, porous medium inertia, and convective heating parameters increases the blow-up stability of the fluid flow. The rate of heat transfer enhances with the increment in the Casson factor, porous medium, porous medium inertia, suction, velocity ratio, nanoparticle volume fraction, and convective heating parameters, whereas it reduces as the slipperiness of the surface and viscous dissipation parameters rise. Increment of Cu-H2O nanoparticle volume fraction into the Casson fluid boosts the heat transfer enhancement rate higher for the shrinking sheet surface.

Numerical simulation of mass and heat transport phenomena of hydromagnetic flow of Casson fluid with sinusoidal boundary conditions

AbstractA magnetic field might interact with its surroundings, influencing chemical and physical processes in materials processing, heat exchangers, and other scientific study. Therefore, a computational study of non‐Newtonian (Casson) free convective MHD unsteady fluid flow has been highlighted in this article with mass and heat transit property through a vertical infinite porous plate. A sinusoidal boundary conditions as well as chemical reaction and thermal radiation have been considered. Using a collection of nondimensional variables, the flow related equations are also turned into nondimensional form. The EFDM algorithm is employed in order to arrive at a numerical solution via Compaq Visual Fortran. The reliability of the numerical solution has been confirmed using stability testing and convergence analysis. The whole system is convergent when the values of Prandtl number and Lewis number are greater than or equals to 0.075 and 0.025, respectively. A visual depiction of the impact of the pertinent factors on dimensionless velocity, temperature, and concentration profiles are displayed through graphical representation as well as with tabular representation. It has been inspected that when the magnetic component is regarded, it greatly affects the heat transfer factors of Casson nanofluid and the heat also rises when Eckert number, heat source and radiation parameter accelerate. It is also found that the Sherwood number is increased as the impact of chemical reaction parameter and the Lewis number, also the skin friction is decreased as the influence of porosity term got accelerated. The comparison of the current findings with the data that were previously published serves as the final stage in validating the present study.

Influence of an inclined magnetic field and heat and mass transfer on the peristaltic flow of blood in an asymmetric channel

This article presents a theoretical study on heat and mass transfer analysis of the peristaltic flow of blood conveying through an asymmetric channel in the presence of inclined to the magnetic field. The effects of ratio of relaxation to retardation times, non-uniform parameter, the non-dimensional amplitude, Hartman number and phase difference have been taken into account. The governing coupled non-linear partial differential equations representing the flow model are transmuted into linear ones by assuming that the wave is very long with a small Reynolds number. The converted mathematical formulations are solved analytically via the Mathematica software. Analytical expressions for the dimensionless velocity profiles of fluid, temperature, concentration, pressure gradient, increase in pressure, heat transfer coefficient and shear stress of the blood are derived. The velocity, temperature, concentration, pressure gradient, increase in pressure, heat transfer coefficient and shear stress were calculated numerically for different values of the parameters, which were represented graphically and find their physical meaning.

Experimental study of velocity and turbulence fields in a square mixer-settler tank: Comparison of shake the box PTV and 2D2C PIV

The characterization of flows in agitated vessels is essential for a good understanding of physical and chemical processes and to validate computational fluid dynamics code. The hydrodynamics of cylindrical vessels have been well studied at various scales, mostly in the turbulent regime, typically using particle image velocimetry (PIV). Studies of square tanks or at moderate Reynolds numbers are much rarer however, and 3D Shake-The-Box (STB) Lagrangian particle tracking has never been used in this context. The objective of the present work was to compare two-dimensional, two-component PIV (2D2C-PIV) and STB particle tracking in characterizing the hydrodynamics of a stirred 20 cm sided (8 L) square tank at Reynolds numbers ranging from 1700 to 4300. The velocity fields, velocity profiles, turbulent kinetic energy fields and turbulent kinetic energy dissipation rates obtained using the two approaches were compared. The velocity fields measured with the two methods were found to be in good agreement, except for a few discrepancies in the velocity profiles of the turbine discharge at 250 rpm. The dimensionless velocity profiles were similar above 100 rpm and indicated that the flow was turbulent at the Reynolds numbers considered. The turbulent kinetic energy fields obtained with the two approaches were globally similar, although with STB, the energy tended to be underestimated, especially in the jet discharge area. The STB method was also found to have lower spatial resolution and precision in measuring turbulent kinetic energy dissipation rates, a consequence of a too large interrogation window. Recommendations are proposed to improve the precision of STB measurements.

Dual solutions on three-dimensional nanofluid flow and heat transfer over a permeable non-linearly shrinking surface with second-order velocity slips

PurposeThis paper aims to present the steady dual solutions on three-dimensional flow and heat transfer of nanofluid over a permeable non-linearly shrinking surface with two-order velocity slips conditions. Boundary layer assumption is considered in the mathematical modelling. Authors comprehend from previous studies and papers that the shrinking surfaces are extremely important in current engineering and environmental systems.Design/methodology/approachUsing appropriate similarity variables, the full partial differential equations (PDF) are modified into a specific set of ordinary (similar) differential equations (ODE). The resulting non-linear ordinary differential system is then solved both analytically for some particular cases and numerically for the general case using the function bvp4c from MATLAB for characteristic values of the parameters which govern the equations. The transformed mathematical model is analysed using the bvp4c procedure. Based on the given assumptions, this study is able to produce multiple solutions of the problem.FindingsThe ordinary (similarity) differential equations have two branches solutions, upper and lower branch solutions, given some interval of shrinking and velocity slip parameters. The authors consider here a temporal stability analysis, as they want to establish which of the solutions are stable and which are not. In a distinct paragraph, the authors discuss in detail and present in a graphical manner the effects of shrinking and second-order slip flow model on the skin friction coefficient, surface wall heat flux and dimensionless velocity and temperature profiles. The analysis reveals that the second order slip has a big influence on the flow and heat transfer characteristics.Originality/valueThe present discoveries are unique and truly new for the research of the three-dimensional stretching/shrinking forced convection flow and heat transfer nanofluids. The nanofluid is a water-based nanofluid (H2O), which contains one type of nanoparticles, namely, copper (Cu). Of course, the analysis can be further extended considering other types of nanoparticles such as alumina (Al2O3). The authors assume that the thermal equilibrium is reached for the base fluid together with the suspended nanoparticles and that the nanoparticles are uniform in dimension and form.