Nanoparticle Concentration Distribution Research Articles

Nanofluid flow through a porous space with convective conditions and heterogeneous–homogeneous reactions

Abstract Present analysis deals with the nanofluid flow due to a cylinder. Heat transfer mechanism is inspected under the physically acceptable convective type conditions. A simple isothermal model of homogeneous–heterogeneous reactions is used to regulate the solute concentration. Thermodynamics processes of homogeneous–heterogeneous reactions analyze the effect of temperature phase changes, such as convection or evaporation. It is assumed that the base fluid (water) is essentially composed of single and multi walled carbon nanotubes. Uniformly valid convergent series expressions are obtained with the help of optimal homotopic approach. Impacts of embedded flow parameters are visualized through graphical illustrations. Fluid velocity displays decreasing trend near the cylinder as the curvature parameter is incremented. Interestingly, such result is not preserved far from the cylinder. The simulations predict that wall heat flux is inversely proportional to both curvature parameter and the convecting heating strength. However, value of heat flux is predicted to be larger in case of larger volume fraction of carbon nanotubes. Moreover heat transfer coefficient is more in single wall carbon nanotubes (SWCNTs) when compared with multi wall carbon nanotubes (MWCNTs). Heterogeneous and homogeneous reactions have opposite behaviors on nanoparticle concentration distribution. Drag coefficient at the cylinder enhances when larger curvature parameter is accounted. Comparison of present study with previous published work is given. The results are found in good agreement.

On magnetohydrodynamic flow of second grade nanofluid over a convectively heated nonlinear stretching surface

Here magnetohydrodynamic (MHD) flow of second grade nanofluid over a nonlinear stretching surface with the convective surface boundary condition is examined. Heat and mass transfer characteristics subject to viscous dissipation, Brownian motion and thermophoresis effects are examined. Second grade fluid is electrically conducted in the presence of non-uniformly applied magnetic field. Mathematical formulation for boundary layer and low magnetic Reynolds number assumptions is presented. Newly proposed condition having a zero nanoparticles mass flux at the surface is employed. The partial differential system has been converted into the nonlinear ordinary differential system by using appropriate transformations. The resulting nonlinear system has been solved via convergent approach. Graphs are sketched to analyze the impacts of various physical parameters on the velocity, temperature and nanoparticles concentration distributions. Numerical values of skin friction coefficient and local Nusselt number are computed and discussed.

Numerical simulation and sensitivity analysis of effective parameters on heat transfer and homogeneity of Al2O3 nanofluid in a channel using DPM and RSM

In this paper, a 2-D numerical study and a sensitivity analysis of convective heat transfer in a channel are investigated using the Discrete Phase Model along with determination of the nanoparticles concentration distribution. Numerical simulations are carried out to investigate the effects of the three parameters, the Reynolds number (250⩽Re⩽650), nanoparticles volume fraction (0.01⩽Ф⩽0.05) and nanoparticles diameter (40nm⩽dp⩽100nm) on the heat transfer performance and nanoparticles distribution. In addition, the effective parameters analysis is performed utilizing the Response Surface Methodology. The results indicated that increasing the Re number and Ф and decreasing of dp, enhances the mean total Nusselt number. Also, an enhancement in dp and Ф and reduction of Re number increases the homogeneity of the nano-fluid. In addition, it is found that the sensitivity of the mean total Nusselt number to Re number, Ф and dp parameters is more than the sensitivity of the nanoparticles concentration ratio to these parameters.

Vortex generators position effect on heat transfer and nanofluid homogeneity: A numerical investigation and sensitivity analysis

A 2-D numerical study and a sensitivity analysis of convective heat transfer in a channel with vortex generators for application in solar heat exchangers are investigated using a Lagrangian-Eulerian model along with determination of the Nanoparticles concentration distribution. Numerical simulations are carried out to study the effects of Reynolds number (50⩽Re⩽250), Nanoparticles volume fraction (0.01⩽Ф⩽0.04), distance between two vortex generators (10mm⩽d⩽20mm) and the angles between them (30°⩽α and β⩽150°) on the heat transfer performance and Nanoparticles distribution. In addition, an analysis on effective parameters is processed utilizing the Response Surface Methodology. The results show a 39.81% increase in the Nusselt number for Re numbers ranged from 150 to 250. Also, it is found that increasing in d and α and reduction of β and Ф increases the mean Nusselt number. Enhancement in d, α and β and also decreasing in Re number and Ф increases the homogeneity of the Nanofluid. Finally, it is shown that the sensitivity of the mean Nusselt number to the Re number, Ф and d parameters is more than the sensitivity of the Nanoparticles concentration ratio to these parameters.

Natural convection in a triangular cavity filled with a nanofluid-saturated porous medium using three heat equation model

The present study aims to examine the local thermal non-equilibrium natural convection heat and mass transfer of nanofluids in a triangular enclosure filled with a porous medium. The effect of the presence of nanoparticles and the thermal interaction between phases on the flow, temperature distribution of phases, the concentration distribution of nanoparticles as well as the Nusselt number of phases is theoretically studied. The interaction between the phases of nanoparticles and the base is taken into account by using a three thermal energy equation model while the concentration distribution of nanoparticles is modeled by Buongiorno’s model. A hot flush element is mounted at the vertical wall of the triangle enclosure to provide a constant temperature of Th while the inclined wall is at a constant temperature of Tc. A three heat equation model by considering the local thermal non-equilibrium model of nanoparticles, the porous medium, and the base fluid is developed and utilized for natural convection of nanofluids in an enclosure. The drift-flux of nanoparticles due to the nano-scale effects of thermophoresis and Brownian motion effects is addressed. The governing equations are represented in a non-dimensional form and solved by employing the finite element method. The results indicate that the increase of Rayleigh number shows a significant increase in the average Nusselt number for the base fluid phase, a less significant increase in the average Nusselt number for the solid matrix phase, and almost an insignificant effect in the average Nusselt number of the nanoparticle phase. Increasing the buoyancy ratio parameter (the ratio of mass transfer buoyancy forces to the thermal buoyancy forces) tends to reduce and increase the average Nusselt number in fluid and porous phases, respectively. An optimum value of buoyancy ratio parameter for the average Nusselt number of the nanoparticle phase is observed.

Analytical solution for peristaltic flow of conducting nanofluids in an asymmetric channel with slip effect of velocity, temperature and concentration

The Peristaltic transport of conducting nanofluids under the effect of slip condition in an asymmetric channel is reported in the present work. The mathematical modelling has been carried out under long wavelength and low Reynolds number approximations. The analytical solutions are obtained for pressure rise, nanoparticle concentration, temperature distribution, velocity profiles and stream function. Influence of various parameters on the flow characteristics has been discussed with the help of graphs. The results showed that the pressure rise increases with increasing magnetic effect and decreases with increasing slip parameter. The effects of thermophoresis parameter and Brownian motion parameter on the nanoparticle concentration and temperature distribution are studied. It is observed that the pressure gradient increases with increasing slip parameter and magnetic effect. The trapping phenomenon for different parameters is presented.

Impact of magnetic field in three-dimensional flow of Sisko nanofluid with convective condition

This communication addresses the magnetohydrodynamic (MHD) three dimensional flow of Sisko nanofluid bounded by a surface stretched bidirectionally. Nanofluid model includes the Brownian motion and thermophoresis. Heat transfer through convective condition is discussed. Developed condition with the zero nanoparticles mass flux at the surface is implemented. The governing problems subject to boundary layer approximations are computed for the convergent series solutions. Effects of interesting flow parameters on the temperature and nanoparticles concentration distributions are studied and discussed. Skin friction coefficients and the local Nusselt number are computed and analyzed.

Free convection in a square cavity filled by a porous medium saturated by a nanofluid: Viscous dissipation and radiation effects

The influence of the viscous dissipation and radiation effects on the natural convection heat transfer in a square cavity filled with porous media saturated with a nanofluid is studied. The vertical walls of the cavity are subject to finite temperature difference while the top and bottom walls of the cavity are insulated. The Buongiorno's nanofluid model, incorporating the Brownian motion and thermophoresis effects, is employed. The governing equations, in nondimensional form, are written in the weak form and solved using the finite element method. The influences of viscous dissipation and radiation effects on the concentration distribution of nanoparticles are discussed. The average and local Nusselt numbers are reported for various values of viscous dissipation (Eckert number) and radiation effects. The results show that the Nusselt numbers at the hot and cold walls are not equal due to the presence of viscous dissipation effects. The raise of Eckert number decreases the Nusselt number at hot wall, but it increases the Nusselt number at the cold wall. It is also found that the increase of Lewis number enhances the heat transfer in the cavity.

On three-dimensional boundary layer flow of Sisko nanofluid with magnetic field effects

This article models the effects of magnetic field and nanoparticles in the three-dimensional flow of Sisko fluid. The flow is caused by a bidirectional stretching surface. Effects of Brownian motion and thermophoresis in the nanofluid model are considered. Sisko fluid is assumed electrically conducted through a constant applied magnetic field. Mathematical formulation in boundary layer regime is presented for a low magnetic Reynolds number. Newly constructed boundary condition subject to zero nanoparticles mass flux at the surface is employed. Nonlinear differential systems are solved for the convergent solutions. Effects of various physical parameters are studied and discussed. Numerical values of skin friction coefficients and Nusselt number are tabulated and analyzed. It is observed that the effects of Brownian motion and thermophoresis parameters on the nanoparticles concentration distribution are quite opposite. Further the temperature and nanoparticles concentration distributions are enhanced for the larger values of magnetic parameter.

On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet

This research article addresses the magnetohydrodynamic (MHD) flow of second grade nanofluid over a nonlinear stretching sheet. Heat and mass transfer aspects are investigated through the thermophoresis and Brownian motion effects. Second grade fluid is assumed electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed subject to small magnetic Reynolds number and boundary layer assumptions. Newly constructed condition having zero mass flux of nanoparticles at the boundary is incorporated. Transformations have been invoked for the reduction of partial differential systems into the set of nonlinear ordinary differential systems. The governing nonlinear systems have been solved for local behavior. Graphical results of different influential parameters are studied and discussed in detail. Computations for skin friction coefficient and local Nusselt number have been carried out. It is observed that the effects of thermophoresis parameter on the temperature and nanoparticles concentration distributions are qualitatively similar. The temperature and nanoparticles concentration distributions are enhanced for the larger magnetic parameter.

Forced Convective Flow of a Nanoliquid due to a Stretching Cylinder with Free Stream

Steady, transverse boundary layer flow and heat transfer caused by an exponentially stretching cylinder of constant radius immersed in an uniform flow of an incompressible, viscous nanoliquid are considered in the present study. The paper discusses a systematic procedure of obtaining a local similarity transformation that reduces the governing partial differential equations into ordinary differential equations. Power series solution is then obtained for velocity, temperature and nanoparticle concentration distributions using the uni-variate differential transform method. Help is sought from Domb-Sykes plots in making a decision on the minimum number of terms required in the power series expansion to ensure convergence. Radius of convergence is quite naturally suggested by these plots. Pad ´ e approximants are then appropriately decided upon to increase the radius of convergence. The algorithm used succeeds in capturing boundary effects, free stream flow effects and nanoparticle effects on flow and heat transfer. An important finding of the paper is the prediction of accelerated cooling of the stretching cylinder due to the nanoparticles in the cooling liquid. In having a desirable property for the extruding cylinder nanoliquid coolant seems an attractive proposition.

Multiphysics Coupling of Dynamic Fluid Flow and Electromagnetic Fields for Subsurface Sensing

Nanoparticles designed with high electric conductivity and magnetic permeability are injected into oil reservoirs to enhance fluid flow monitoring. The movement of nanoparticles with the flow in a porous medium can be modeled by solving the flow transport equation. In this research, the three-dimensional spectral-element time-domain method based on Gauss-Lobatto-Legendre polynomials is employed to solve the fluid flow equation to obtain the nanoparticle (NP) concentration distribution in reservoirs. This method shows spectral accuracy, as the error decreases exponentially with the order of basis functions. The injected fluid with high contrast NPs increases the electric conductivity and magnetic permeability in the flooded zone, thus enhancing the electromagnetic (EM) signals in the receivers. Based on the coupling of the dynamic fluid flow and crosswell EM measurement, we are able to analyze the detection range of EM sensing with the high contrast NPs injection. The EM responses with different types of NPs injection are investigated under both an electric dipole and a magnetic dipole. The magnetic contrast NPs excited by a magnetic dipole source can generate a detectable signal while the electric contrast NPs can generate a detectable signal when excited by an electric dipole. The EM response of an inhomogeneous formation with a low permeable region shows that the signal at the producer near the barrier is lower than the other producers. The proposed multiphysics coupling technique of fluid flow and EM measurements can provide guidance for NPs field application and help monitor the flow movement in reservoirs.

Influence of Magnetic Field in Three-Dimensional Flow of Couple Stress Nanofluid over a Nonlinearly Stretching Surface with Convective Condition.

This article investigates the magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid subject to the convective boundary condition. Flow is generated due to a nonlinear stretching of the surface in two lateral directions. Temperature and nanoparticles concentration distributions are studied through the Brownian motion and thermophoresis effects. Couple stress fluid is considered electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed via boundary layer approach. Nonlinear ordinary differential systems are constructed by employing suitable transformations. The resulting systems have been solved for the convergent series solutions of velocities, temperature and nanoparticles concentration profiles. Graphs are sketched to see the effects of different interesting flow parameters on the temperature and nanoparticles concentration distributions. Numerical values are computed to analyze the values of skin-friction coefficients and Nusselt number.

On squeezing flow of nanofluid in the presence of magnetic field effects

This article investigates the magnetohydrodynamic (MHD) squeezing flow of nanofluid over a porous stretching surface. Constitutive expressions of viscous fluid are employed in the mathematical formulation. Brownian motion and thermophoretic diffusion of nanoparticles are taken into account. Fluid is electrically conducted in the presence of an applied magnetic field. The induced magnetic field is neglected for a small magnetic Reynolds number. Appropriate transformations yield a coupled nonlinear ordinary differential system. The resulting nonlinear system is solved successfully. Graphs are plotted to examine the impacts of physical parameters on the velocity, temperature and nanoparticle concentration distributions. Skin friction coefficient, Nusselt and Sherwood numbers are analyzed numerically.

Modeling of direct conversion of the uranium fission product kinetic energy to laser radiation energy in an argon–xenon dusty plasma with uranium nanoparticles

The process of direct conversion of the uranium fission product kinetic energy to laser radiation (LR) energy in a moving argon–xenon laser-active gas medium containing uranium nanoparticles has been investigated.A model and a method have been developed to solve numerically equations for the model of direct uranium fission product kinetic energy conversion to laser radiation energy in such medium. Spatiotemporal evolutions of the uranium nanoparticle concentration distribution have been calculated for different gas flow velocities and uranium nanoparticle sizes.Kinetic processes in a moving argon–xenon laser-active gas medium containing uranium nanoparticles have been studied.It is the first time that amplifying properties of a laser-active spatially heterogeneous nuclear-excited moving argon–xenon medium, containing uranium nanoparticles and irradiated by neutrons, have been studied. As shown by the investigation results, the LR intensity amplification may be sevenfold and more in steady-state conditions. Such a high value makes it possible to state that this medium can be used not only in a nuclear-pumped laser but also in the mode of a single-pass nuclear-pumped laser amplifier.

Three-Dimensional Flow of Jeffrey Nanofluid with a New Mass Flux Condition

AbstractThe three-dimensional (3D) boundary layer flow of Jeffrey nanofluid subject to the convective boundary condition is analyzed. The flow is induced by a bidirectional stretching surface. Effects of thermophoresis and Brownian motion are considered. Newly developed boundary condition with the zero nanoparticles mass flux is employed. Mathematical modeling is made under boundary layer approach. Similarity variables are used to convert the governing partial differential equations into the nonlinear ordinary differential equations. The resulting nonlinear ordinary differential equations have been solved for the velocities, temperature, and nanoparticles concentration. Graphs are plotted to examine the influence of various physical parameters on the dimensionless temperature and nanoparticles concentration distributions. Numerical values of local Nusselt number are tabulated and discussed. It is found that the effects of the Biot number on the temperature and nanoparticles concentration are quite similar...

Characteristics of formation and growth of atmospheric nanoparticles observed at four regional background sites in Korea

Measurements of the number concentration and size distribution of atmospheric nanoparticles were conducted at four sites on the west coast of the Korean Peninsula by using identical scanning mobility particle sizers (SMPSs) in October 2012. The new particle formation and subsequent growth (NPF) of atmospheric nanoparticles, which were identified by the cyclostationary empirical orthogonal function (CSEOF) analysis technique, was observed on 11 out of 21days at the Baengnyeong-do Comprehensive Monitoring Observatory (BCMO); and on 10 out of 21days at the Korea Global Atmosphere Watch Center (KGAWC) from October 9 to 29, 2012. We also observed NPF events for 9 out of 21days at both the Gosan Climate Observatory (GCO) and the Jeju Comprehensive Monitoring Observatory (JCMO). During the study period, NPF was simultaneously observed for five days at all four sites, which indicates that the NPF event had a spatial extent of at least 540km.A cold, dry and cloud-free continental air mass originated from northern China, formed favorable environmental conditions (e.g., increasing solar insolation at the surface) on simultaneous NPF at the four sites. These synoptic weather patterns were closely associated with an extraordinary typhoon passing over the south of Japan. The mean values of particle formation rates at BCMO (1.26cm−3s−1) and KGAWC (1.49cm−3s−1) were relatively higher than those at GCO (0.39cm−3s−1) and JCMO (0.74cm−3s−1), however, the growth rate showed a similar level among four sites. An increase in the spatial homogeneity and inter-site correlation of atmospheric particles among the four sites was apparent for small particles (diameter<30nm) on simultaneous NPF event days.

Interaction of magnetic field in flow of Maxwell nanofluid with convective effect

Magnetohydrodynamic (MHD) three-dimensional flow of Maxwell nanofluid subject to the convective boundary condition is investigated. The flow is generated by a bidirectional stretching surface. Thermophoresis and Brownian motion effects are present. Fluid is electrically conducted in the presence of a constant applied magnetic field. Unlike the previous cases even in the absence of nanoparticles, the correct formulation for the flow of Maxwell fluid in the presence of a magnetic field is established. Newly proposed boundary condition with the zero nanoparticles mass flux at the boundary is employed. The governing nonlinear boundary layer equations through appropriate transformations are reduced in the nonlinear ordinary differential system. The resulting nonlinear system has been solved for the velocities, temperature and nanoparticles concentration distributions. Convergence of the constructed solutions is verified. Effects of emerging parameters on the temperature and nanoparticles concentration are plotted and discussed. Numerical values of local Nusselt number are computed and analyzed. It is observed that the effects of magnetic parameter and the Biot number on the temperature and nanoparticles concentration are quite similar. Both the temperature and nanoparticles concentration are enhanced for the increasing value of magnetic parameter and Biot number.

Nanoparticles migration effects on magnetohydrodynamic (MHD) laminar mixed convection of alumina/water nanofluid inside microchannels

This is a theoretical study on effects of nanoparticles migration on magnetohydrodynamic mixed convective heat transfer of alumina/water nanofluid inside a vertical microchannel. Walls are subjected to different heat fluxes; q''lw for the left wall and q''rw for the right wall, and nanoparticles are assumed to have a slip velocity relative to the base fluid, induced by Brownian diffusion and thermophoresis. Scale analysis of the governing equations indicates that buoyancy effects due to the temperature distribution is insignificant, however, the buoyancy effects due to concentration distribution of nanoparticles have vast effects on flow and heat transfer characteristics. Further, it is shown that nanoparticles eject themselves from the heated walls and accumulate in the core region, but they are more likely to accumulate near the wall with lower heat flux. Also, the non-uniform nanoparticle distribution causes velocities to move toward the wall with higher heat flux and enhances heat transfer rate there. Moreover, while the nanoparticle volume fraction is smaller than 0.1, the maximum increase in the values of heat transfer rate is 37% for small nanoparticles which drops to 14% for larger nanoparticles. Applying a magnetic field leads to 42% and 30% increase in the values of heat transfer rate for small and large nanoparticles respectively. Additionally, one-sided heating serves as another causing factor for increasing the heat transfer rate which boosts it up to 80% for large nanoparticles.

Transient Boundary Layer Laminar Free Convective Flow of a Nanofluid Over a Vertical Cone/Plate

Two-dimensional transient hydrodynamic boundary layer flow of incompressible Newtonian nanofluid past a cone and plate with constant boundary conditions is investigated numerically. The Newtonian nanofluid model incorporates the effects of Brownian motion and thermophoresis. In order to solve the transformed unsteady, nonlinear coupled boundary layer equations numerically under the conditions, an implicit finite difference scheme of Crank–Nicolson type has been employed. Numerical results obtained for the velocity, temperature and nanoparticle concentration distributions, as well as the skin friction, local Nusselt number and local Sherwood number for several values of the parameters, namely the buoyancy ratio parameter, Prandtl number, Lewis number and nanofluid parameters. The dependency of the thermophysical properties has been discussed on these parameters. The results shown that the Brownian motion parameter increased, the local skin friction decreased while the local Nusselt number and local Sherwood number increased. However, they both decreased as the thermophoresis parameter increased. The approach used in optimizing the transient boundary layer heat transfer of nanofluid problems. The use of nanoparticles improve the heat transfer performance of the base fluids having poor thermophysical properties which are not able to meet the cooling rate of modern engineering equipments.