Values Of Nanoparticle Volume Fraction Research Articles

Three-dimensional rotating flow of carbon nanotubes with Darcy-Forchheimer porous medium.

Here we are concerned with the Darcy-Forchheimer three-dimensional flow of carbon nanotubes in a rotating frame. Flow is generated by stretching of the surface. Xue model is adopted for nanofluid transport mechanism. Results for single wall carbon nanotubes (SWCNTs) and multi wall carbon nanotubes are achieved and compared. Flow saturating porous space obeys Darcy-Forchheimer expression. Boundary layer approximations are invoked to simplify governing partial differential system. Optimal homotopy analysis method (OHAM) is utilized for solutions of governing model. The optimal values of auxiliary parameters are computed. Plots have been displayed in order to analyze how the velocities and temperature fields get affected by various flow parameters. Skin-friction coefficients and local Nusselt number are presented through numerical data for both SWCNTs and MWCNTs. Moreover the skin-friction coefficients and local Nusselt number are enhanced for larger values of nanoparticles volume fraction.

On Darcy-Forchheimer flow of carbon nanotubes due to a rotating disk

The present communication deals with the Darcy-Forchheimer flow of water based carbon nanotubes (CNTs) due to a rotating disk. Results for single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) have been obtained and compared. Flow in porous medium is described by utilizing Darcy-Forchheimer model. Suitable transformations lead to strong nonlinear differential system. Optimal homotopy analysis method (OHAM) is employed for solution development of governing system. The optimal values of auxiliary parameters are obtained. Plots have been displayed in order to analyze how the velocity and temperature fields are affected by various pertinent variables. Further the skin friction coefficients and local Nusselt number have been graphically examined for both SWCNTs and MWCNTs. Our findings reveal that the skin friction coefficients and local Nusselt number are enhanced for larger values of nanoparticles volume fraction.

Computational modeling for homogeneous-heterogeneous reactions in three-dimensional flow of carbon nanotubes

Here homogeneous-heterogeneous reactions in three-dimensional flow of water based nanofluid saturating a porous medium is modeled. A bidirectional nonlinearly stretching surface has been employed to generate the flow. The characteristics of nanofluid are explored using CNTs (single and multi walled carbon nanotubes). Equal diffusion coefficients are considered for both reactants and auto catalyst. The conversion of partial differential equation equations (PDEs) to ordinary differential equations (ODEs) is done via appropriate transformations. Optimal homotopy approach is implemented for solution of governing problem. The optimal solution relations of velocities and concentration are explored through plots by using several values of physical parameters. The coefficients of skin friction are examined through graphs. Our results indicate that the skin friction coefficients are enhanced for larger values of nanoparticle volume fraction.

Bio-mathematical analysis for the peristaltic flow of single wall carbon nanotubes under the impact of variable viscosity and wall properties

ObjectiveThe main objective of this paper is to study the Bio-mathematical analysis for the peristaltic flow of single wall carbon nanotubes under the impact of variable viscosity and wall properties. Design/approachThe right and the left walls of the curved channel possess sinusoidal wave that is travelling along the outer boundary. The features of the peristaltic motion are determined by using long wavelength and low Reynolds number approximation. Exact solutions are determined for the axial velocity and for the temperature profile. FindingsGraphical results have been presented for velocity profile, temperature and stream function for various physical parameters of interest. Symmetry of the curved channel is disturbed for smaller values of the curvature parameter. It is found that the altitude of the velocity profile increases for larger values of variable viscosity parameter for both the cases (pure blood as well as single wall carbon nanotubes). It is detected that velocity profile increases with increasing values of rigidity parameter. It is due to the fact that an increase in rigidity parameter decreases tension in the walls of the blood vessels which speeds up the blood flow for pure blood as well as single wall carbon nanotubes. Increase in Grashof number decreases the fluid velocity. This is due to the reason that viscous forces play a prominent role that's why increase in Grashof number decreases the velocity profile. It is also found that temperature drops for increasing values of nanoparticle volume fraction. Basically, higher thermal conductivity of the nanoparticles plays a key role for quick heat dissipation, and this justifies the use of the single wall carbon nanotubes in different situations as a coolant. ConclusionsExact solutions are calculated for the temperature and the velocity profile. Symmetry of the curved channel is destroyed due to the curvedness for velocity, temperature and contour plots. Addition of single wall carbon nanotubes shows a decrease in fluid temperature. Trapping phenomena show that the size of the trapped bolus is smaller for pure blood case as compared to the single wall carbon nanotubes.

Water-carbon nanofluid flow with variable heat flux by a thin needle

The objective of this article is to investigate the stagnation point flow with variable heat flux. Flow is caused by a linear stretched surface. The velocity and thermal fields of this study strongly depend upon the shape and the needle size. Water-carbon nanofluid in presence of thin needle is considered. Non-linear ordinary differential equations are obtained by using suitable transformation through fundamental laws of mass, momentum and energy. ND Solve shooting technique is used for solving differential equations numerically. The effects of physical parameters on velocity and temperature profiles are pointed out. It is observed that velocity profile enhances for larger values of nanoparticles volume fraction.

Fluid flow and heat transfer of non-Newtonian nanofluid in a microtube considering slip velocity and temperature jump boundary conditions

Forced convection of non-Newtonian nanofluid, aqueous solution of carboxymethyl cellulose (CMC)–Aluminum oxide through a microtube is studied numerically. The length and diameter of tube are L=5 mm and D=0.2 mm, respectively which means the length is long enough compared to the diameter. The effects of different values of nanoparticles volume fraction, slip coefficient and Reynolds number are investigated on the slip velocity and temperature jump boundary conditions. Moreover the suitable validations are presented to confirm the achieved results accuracy. The results are shown as the dimensionless velocity and temperature profiles; however the profiles of local and averaged Nusselt number are also provided. It is seen that more volume fraction and slip coefficient correspond to higher Nusselt number especially at larger amounts of Re.

Analysis of Entropy Generation in Mixed Convective Peristaltic Flow of Nanofluid

This article examines entropy generation in the peristaltic transport of nanofluid in a channel with flexible walls. Single walled carbon nanotubes (SWCNT) and multiple walled carbon nanotubes (MWCNT) with water as base fluid are utilized in this study. Mixed convection is also considered in the present analysis. Viscous dissipation effect is present. Moreover, slip conditions are encountered for both velocity and temperature at the boundaries. Analysis is prepared in the presence of long wavelength and small Reynolds number assumptions. Two phase model for nanofluids are employed. Nonlinear system of equations for small Grashof number is solved. Velocity and temperature are examined for different parameters via graphs. Streamlines are also constructed to analyze the trapping. Results show that axial velocity and temperature of the nanofluid decrease when we enhance the nanoparticle volume fraction. Moreover, the wall elastance parameter shows increase in axial velocity and temperature, whereas decrease in both quantities is noticed for damping coefficient. Decrease is notified in Entropy generation and Bejan number for increasing values of nanoparticle volume fraction.

Numerical simulation of water based magnetite nanoparticles between two parallel disks

Present study examines the fully developed squeezing flow of water functionalized magnetite nanoparticles between two parallel disks. For strongly magnetite fluid (water) three different types of nanoparticles having better thermal conductivity: Magnetite (Fe3O4), Cobalt ferrite (CoFe2O4) and Mn–Zn ferrite (Mn–ZnFe2O4) are incorporated within the base fluid (water). Systems of equations containing the nanoparticle volume fraction are rehabilitating in the form of partial differential equations using cylindrical coordinate system. Resulting mathematical model is rehabilitated in the form of ordinary differential equations with the help of compatible similarity transformation. Results are analyzed for velocity, temperature, reduced skin friction and reduced Nusselt number with variation of different emerging parameters and determine the superb thermal conductivity among mentioned nanoparticles. Comparison among each mixture of ferrofluid has been plotted as response to differences in reduced skin friction and reduced Nusselt number distributions. Dominating effects are analyzed for squeezing parameter and it is found that water based-magnetite (Fe3O4) gives the highest reduced skin friction and reduced Nusselt number as compared to the rest of the mixtures. Isotherms are also plotted against various values of nanoparticle volume fraction to analyze the temperature distribution within the whole domain of squeezing channel.

Entropy generation analysis of a nanofluid flow in MHD porous microchannel with hydrodynamic slip and thermal radiation

Combined effects of hydrodynamic slip, magnetic field, suction/injection, thermal radiation, nanoparticle volume fraction and convective boundary conditions on the heat transfer and global entropy generation in a viscous electrically conducting nanofluid flow through a microchannel with permeable plates are studied. Analytical solutions of the momentum and the energy equations are obtained in closed form. Particularly, considering the radiative term, joule heating and viscous dissipation in the energy equation, the temperature field of the nanofluid is derived analytically. Influences of pertinent parameters on global entropy generation are discussed in detail and depicted graphically. Analysis of our results indicates that entropy generation minimization can be achieved by appropriate combination of the geometrical and physical parameters of the system. It is possible to determine optimum values of radiation parameter, nanoparticle volume fraction, Hartmann and Biot numbers which lead to a minimum global entropy generation rate. The Nusselt number is also calculated and explored for different conditions. Optimum values of nanoparticle volume fraction and magnetic field strength that maximize heat transfer are derived.

Influences of slip and Cu-blood nanofluid in a physiological study of cilia

ObjectiveThe objective of this paper is to study the influences of slip and Cu-blood nanofluid in a physiological study of cilia. Design/methodology/approachThe right wall and the left wall possess metachronal wave that is traveling along the outer boundary of the channel. The features of ciliary structures are determined by the dominance of viscous effects over inertial effects using the long wavelength approximation. The flow possessions for the viscous nano fluid are solved as a function of the cilia and metachronal wave velocity. Mathematica numerical simulation is used to calculate pressure rise. Exact solutions are calculated for the temperature and for the velocity profile. FindingsNumerical integration has been implemented to get the expression of pressure rise. Graphical results have been offered for pressure rise, temperature and stream function for various physical parameters of interest. Symmetry of the curved channel is recovered for larger values of the curvature parameter. It is found from the graphs of the pressure rise that reflux case occurs for increasing values of curvature and velocity slip parameter. It is also found that temperature decreases for increasing values of nanoparticle volume fraction. Basically, higher thermal conductivity of the nanoparticles plays a key role for quick heat dissipation, and this justifies the use of the copper nanoparticles in different situations as a coolant. ConclusionsVelocity graph near the right wall of the channel decreases when we add nanoparticles into our base fluid, whereas an opposite behavior is depicted near the left wall due to ciliated tips. Pressure gradient increases for increasing values of Gr (Grashof number), L (velocity slip parameter) ϕ (nanoparticle volume fraction) and k (curvature parameter). Pressure rise shows increasing behavior for the increasing values of ε, Gr and ϕ throughout the region. Shear stress graphs show the increasing behavior for increasing values of curvature parameter and volume fraction of the nanoparticle. Temperature profile decreases when we add nanoparticles into our base fluid. Temperature profile also increases with an increase in thermal slip parameter γ and heat absorption parameter. It is observed that the number of trapped bolus increases when we increase the value of the cilia length parameter.

Influences of an effective Prandtl number model on nano boundary layer flow of γ Al2O3–H2O and γ Al2O3–C2H6O2 over a vertical stretching sheet

Nanoparticles provide potentials in augmenting the performance of convective heat transfer in the boundary layer flow region. Prandtl number plays a vital role in controlling the momentum and thermal boundary layers. In view of this, the influences of an effective Prandtl number model which is derived from experimental data (Pop et al., 2007) on the nano boundary layer, steady, two-dimensional and laminar flow of an incompressible γ Al2O3–H2O and γ Al2O3–C2H6O2 nanofluids over a vertical stretching sheet are investigated for the first time in the present article. The models which are used for viscosity and thermal conductivity also derived from experimental data (Maiga et al., 2004a; Maiga et al., 2005). The second law of thermodynamics also analysed for the present problem. The transformed governing nonlinear boundary layer equations are solved numerically using fourth order Runge–Kutta method with shooting technique and analytical solutions are presented for a special case. The numerical results obtained for the temperature profile, skin friction coefficient and reduced Nusselt number are presented through plots for two different cases such as with and without effective Prandtl number. It is found that the increasing values of nanoparticle volume fraction of γ Al2O3 nanoparticles decrease the temperature of the nanofluids in the presence of effective Prandtl number and increase in the absence of effective Prandtl number. The entropy generation number is higher for ethylene glycol based nanofluids compared to water based nanofluids.

Single wall carbon nanotube (SWCNT) examination on blood flow through a multiple stenosed artery with variable nanofluid viscosity

The present theoretical model deals with the analysis of variable viscosity and thermal conductivity of a single wall carbon nanotube within the considered base fluid flowing through multiple stenosed arteries. A mathematical model is presented for the mild stenosis case and then solved by using symmetry boundary conditions to determine the exact solution of temperature, axial velocity and pressure gradient. The main hemodynamics due to multiple stenosis is also computed under the influence of a SWCNT. Numerical simulations are presented for the SWCNT with different values of nanoparticles volume fraction. The behavior of fluid flow for blood based SWCNT is discussed through graphs and streamlines.

Slip-Flow and Heat Transfer of a Non-Newtonian Nanofluid in a Microtube

The slip-flow and heat transfer of a non-Newtonian nanofluid in a microtube is theoretically studied. The power-law rheology is adopted to describe the non-Newtonian characteristics of the flow, in which the fluid consistency coefficient and the flow behavior index depend on the nanoparticle volume fraction. The velocity profile, volumetric flow rate and local Nusselt number are calculated for different values of nanoparticle volume fraction and slip length. The results show that the influence of nanoparticle volume fraction on the flow of the nanofluid depends on the pressure gradient, which is quite different from that of the Newtonian nanofluid. Increase of the nanoparticle volume fraction has the effect to impede the flow at a small pressure gradient, but it changes to facilitate the flow when the pressure gradient is large enough. This remarkable phenomenon is observed when the tube radius shrinks to micrometer scale. On the other hand, we find that increase of the slip length always results in larger flow rate of the nanofluid. Furthermore, the heat transfer rate of the nanofluid in the microtube can be enhanced due to the non-Newtonian rheology and slip boundary effects. The thermally fully developed heat transfer rate under constant wall temperature and constant heat flux boundary conditions is also compared.

Study on the thermal behavior and cooling performance of a nanofluid-cooled microchannel heat sink

This paper presents an analysis of the heat transfer characteristics and cooling performance of a microchannel heat sink with water– γAl 2O 3 nanofluids having different nanoparticle volume fraction. In view of the small dimensions of the microstructures, the microchannel heat sink is modeled as a fluid-saturated porous medium for problem solving. The Forchheimer–Brinkman–extended Darcy equation is used to describe the fluid flow and the two-equation model with thermal dispersion is utilized for heat transfer. Typical results for the temperature distributions of the fluid phase and the channel wall are presented for various values of nanoparticle volume fraction and the inertial force parameter. It is found that the temperature distribution of the channel wall is practically not sensitive to the inertial effect, while the fluid temperature distribution and the total thermal resistance change significantly due to the inertial force effect. In general, the effect of fluid inertia is to reduce the total thermal resistance and the temperature difference between the channel wall and the fluid phase. The total thermal resistances obtained from the present model with inertial effect match well with the existing experimental results, whereas the thermal resistance is overestimated as the inertial effect is neglected.