Nanoparticle Volume Fraction Parameter Research Articles

Viscous Flow Over a Permeable Stretching/Shrinking Surface in a Nanofluid: A Stability Analysis

This study deals with the boundary layer flow and heat transfer near the stagnation point on a permeable stretching/shrinking surface in a nanofluid. The nanoparticles considered in this study are copper and silver. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using an appropriate similarity transformation which then solved numerically to study the effect of solid volume fraction or nanoparticle volume fraction parameter Φ of the nanofluid. Multiple solutions are found for a certain range of shrinking and suction parameters, therefore, a stability analysis is performed to determine which solution is stable and physically realizable. The effects of the governing parameters on the skin friction coefficient, the local Nusselt number and the velocity and temperature profiles were presented and discussed. It was found that the nanoparticle volume fraction substantially affects the fluid flow and heat transfer characteristics.

Numerical study of melting effect with entropy generation minimization in flow of carbon nanotubes

Optimization of entropy generation in squeezing flow of carbon nanotubes is addressed. Nanoparticles consist of single- and multiple-walled carbon nanotubes. Heat transfer subject to melting effect is employed. Shooting technique along with the fifth-order Runge–Kutta algorithm (bvp4c) is employed for the simulation. Bejan number, entropy generation rate, velocity and temperature are studied. Nusselt number and skin friction are also discussed. Velocity intensifies for higher estimations of squeezing parameter, nanoparticle volume fraction and melting parameter, while it reduces the temperature of fluid. Nusselt number enhances with an increment in estimations of squeezing parameter, nanoparticle volume fraction and melting parameter. Rate of entropy production decays with higher nanoparticle volume fraction and squeezing parameter. Bejan number is an increasing function of squeezing parameter, while it decays with an increment in melting parameter and nanoparticle volume fraction. Furthermore, prominent behavior is shown by multiple-walled CNTs.

Entropy formation analysis of MHD boundary layer flow of nanofluid over a porous shrinking wall

In the current paper, we investigate the entropy analysis of MHD boundary layer flow of copper (Cu)-water based nanofluid along with the porous shrinking wall. Heat transfer analysis is also taken into account with the thermal radiation effects. The single phase nanofluid model is used for the analysis of the effective thermal conductivity. Mathematical modeling is performed to change the physical system into a set of mathematical equations which are further simplified by using suitable variables. Exact solutions for the velocity and temperature profiles are computed and interpreted for diverse physical of interest. It is depicted that by enhancing the magnitude of solid volume fraction and velocity slip parameter of nanoparticles the velocity profile is increased. The results indicate an increment in the Hartman number increases the temperature and thermal boundary layer thickness. It is observed that the entropy generation profile is enhanced by increasing the value of Brinkman number and Reynolds number. The irreversibility parameter is decreasing function of Brinkman number.

Overlapping Multi-Domain Spectral Method for Conjugate Problems of Conduction and MHD Free Convection Flow of Nanofluids over Flat Plates

An efficient overlapping multi-domain spectral method is used in the analysis of conjugate problems of heat conduction in solid walls coupled with laminar magnetohydrodynamic (MHD) free convective boundary layer flow of copper (Cu) water and silver (Ag) water nanofluids over vertical and horizontal flat plates. The combined effects of heat generation and thermal radiation on the flow has been analyzed by imposing a magnetic field along the direction of the flow to control the motion of electrically conducting fluid in nanoscale systems. We have assumed that the nanoparticle volume fraction at the wall may be actively controlled. The dimensionless flow equations are solved numerically using an overlapping multi-domain bivariate spectral quasilinearisation method. The effects of relevant parameters on the fluid properties are shown graphically and discussed in detail. Furthermore, the variations of the skin friction coefficient, surface temperature and the rate of heat transfer are shown in graphs and tables. The findings show that the surface temperature is enhanced due to the presence of nanoparticles in the base fluid and the inclusion of the thermal radiation, heat generation and transverse magnetic field in the system. An increase in the nanoparticle volume fraction, heat generation, thermal radiation, and magnetic field parameter enhances the nanofluid velocity and temperature while reducing the heat transfer rate. The results also indicate that the Ag–water nanofluid has higher skin friction and surface temperature than the Cu–water nanofluid, while the opposite behaviour is observed in the case of the rate of heat transfer. The computed numerical results are compared with previously published results and found to be in good agreement.

MHD Stagnation-point Flow over a Stretching/ Shrinking Sheet in Nanofluids

In this study, we investigated the problem of steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow over a linearly stretching/shrinking sheet in nanofluids. There are three types of metallic nanoparticles considered such as copper (Cu), alumina (Al2O3) and titania (TiO2) in the base fluid of water with the Prandtl number Pr = 6.2 to investigate the effect of the nanoparticles volume fraction parameter φ of the nanofluids. In this problem, the governing nonlinear partial differential equations are transformed into the nonlinear ordinary differential equations by using a similarity transformation and then solved numerically using the boundary value problems solver bvp4c in Matlab software. The influence of magnetic field parameter, M on the skin friction coefficient Cf, local Nusselt number Nu and the velocity and temperature profiles are presented graphically and discussed. The results show that the velocity and temperature are influenced by the magnetic field and nanoparticles volume fraction. The dual solutions exist for shrinking sheet case and the solutions are non-unique, different from a stretching sheet. The numerical values of and for M=0 are also computed, which show a favourable agreement with previous work.

A mathematical model for entropy generation in a Powell-Eyring nanofluid flow in a porous channel

The continuous generation of entropy leads to exergy destruction which reduces the performance of a physical system. Hence, entropy minimization becomes necessary. New applications of nanofluids due to their enhanced thermo-physical properties has spurred new studies into the heat transfer and entropy generation rate in nanofluids in the last decade. In this study, we investigate the heat transfer performance and entropy generation rate in a mixed convective flow of a hydromagnetic Aluminum oxide-water Powell-Eyring nanofluid flow through a vertical channel. The nanofluid dynamic viscosity adopted is based on experimental data. The combined effects of the magnetic field, nonlinear thermal radiation, viscous dissipation, suction/injection and convective cooling on the heat transfer and entropy generation were considered. The dimensionless equations describing the flow and energy balance were solved using an efficient iterative spectral local linearization method. The computational analysis of the rate of entropy generation in the channel for various flow parameters is presented. The result shows that increasing the nanoparticle volume fraction and thermal radiation parameter enhanced the temperature profiles, entropy generation and the Bejan number. The results from this study may help engineers in the optimization of thermal systems.

MHD oblique stagnation point flow of nanofluid over an oscillatory stretching/shrinking sheet: existence of dual solutions

An unsteady magnetohydrodynamic oblique stagnation point flow of an incompressible nanofluid towards a stretching/shrinking surface with the effect of mass suction on the oscillatory surface is analyzed. Water is considered as a base fluid while single wall carbon nanotubes are assumed as nanoparticles. The governing flow equations are transformed into a system of coupled nonlinear ordinary differential equations via suitable transformation. Dual solutions of these nonlinear coupled equations are obtained by utilizing the bvp4c package in MATLAB. It is also found that these solutions survive in a certain domain of controlling parameters. The physical influence of several controlling parameters like nanoparticle volume fraction parameter, Hartmann number, stretching/shrinking parameter and suction parameter on heat transfer characteristics and flow field are discussed in detail and are demonstrated through graphs. We find that dual solutions exist in both the stretching case and the shrinking case. Also, the lower solution branch shows singular behavior for the skin friction coefficient in the shrinking domain whereas the upper solution branch has smooth behavior in both the stretching and shrinking domains.

Numerical Analysis of Heat and Mass Transfer Flow of Nanofluid over a Moving Wedge Using Spectral Quasilinearization Method

In this paper the problem of unsteady two-dimensional heat and mass transfer flow of nanofluid past a moving wedge is considered. The effects of nanoparticle volume fraction, viscous dissipation, chemical reaction, and convective boundary conditions are studied. The physical problem is modeled using partial differential equations. Using suitable similarity variables, the governing equations and their related boundary conditions are transformed into dimensionless forms of a system of coupled nonlinear ordinary differential equations. The resulting systems of equations are then solved numerically using spectral quasilinearization method (SQLM). The results reveal that the skin friction coefficient increases with increasing the values of nanoparticle volume fraction, unsteadiness and permeability parameters. The local Nusselt number reduces with increasing the value of nanoparticle volume fraction, Prandtl number and Eckert number. The local Sherwood number enhances with greater the value of nanoparticle volume fraction, unsteadiness, pressure gradient and chemical reaction parameters. Moreover, the method is checked against the previously published results and a very good agreement have been obtained.

MHD Effects on Mixed Convective Nanofluid Flow with Viscous Dissipation in Surrounding Porous Medium

In existence of concerning magnetic field, heat together with mass transfer features on mixed convective copper-water nanofluid flow through inclined plate is investigated in surrounding porous medium together with viscous dissipation. A proper set of useful similarity transforms is considered as to transform the desired governing equations into a system as ordinary differential equations which are nonlinear. The transformed equations for nanofluid flow include interrelated boundary conditions which are resolved numerically applying Runge-Kutta integration process of sixth-order together with Nachtsheim and Swigert technique. The numerical consequences are compared together with literature which was published previously and acceptable comparisons are found. The influence of significant parameters like as magnetic parameter, angle for inclination, Eckert number, fluid suction parameter, nanoparticles volume fraction, Schmidt number and permeability parameter on concerning velocity, temperature along with concentration boundary layers remains examined and calculated. Numerical consequences are presented graphically. Moreover, the impact regarding these physical parameters for engineering significance in expressions of local skin friction coefficient in addition to local Nusselt together with Sherwood numbers is correspondingly examined.

Unsteady squeezing flow of magnetohydrodynamic carbon nanotube nanofluid in rotating channels with entropy generation and viscous dissipation

The most favorable gift of modern science is nanofluid. The nanofluid can able to move freely through micro channels with the spreading of nanoparticles. Due to improved convection between the base liquid surfaces and nanoparticles, the nano suspensions express high thermal conductivity. Also, the benefits of suspending nanoparticles in base fluids are increased heat capacity, surface area, effective thermal conductivity, collision, and interaction among particles. This research aim to study squeezing flow of carbon nanotubes based on water (H2O) in rotating channels. Entropy generation is evaluated and for this purpose, second law of thermodynamics is employed. The influences of thermal radiation, viscous dissipation, and applied magnetic field on nanofluid are taken into account. The flow of the nanofluid is considered in unsteady three dimensions. The transformed ordinary differential equations (ODEs) are solved by homotopy analysis method with the help of similarity variables. Results obtained for single and multi-wall carbon nanotubes are compared. Plots have been presented in order to examine how the velocities, temperature, and entropy profiles become affected by numerous physical parameters. Generally, the velocity profiles escalate when the upper plate of the channel moves toward the lower stretching one and reduces when the upper plate is moving away from the lower one. The velocity profile in y-direction escalates with the escalation in nanoparticle volume fraction and suction parameter while the rotation parameter bids dual behavior with the escalating values. The velocity profile in x-direction bids the oscillatory behavior with the enhancement in nanoparticle volume fraction, rotation parameter, and magnetic parameter. The physical properties of carbon nanotubes, thermo physical properties of carbon nanotubes and nanofluid of some base fluids, and thermal conductivity of carbon nanotubes with different volume fractions are shown through tables.

Numerical investigation of fractional-order unsteady natural convective radiating flow of nanofluid in a vertical channel

In the current article, we analyzed the unsteady natural convection with the help of fractional approach. Firstly, the unsteady natural convection radiating flow in an open ended vertical channel beside the magnetic effects. We assumed the channel is stationary with non-uniform temperature. Secondly, we utilized a fractional calculus approach for the constitutive relationship of a fluid model. The modeled problem is transformed into nondimensional form via viable non-dimensional variables. In order to investigate the numerical solutions of non-dimensional system of partial differential equations finite difference approach coupled with Crank Nicolson method is developed and successfully applied. The beauty of Crank Nicolson finite difference scheme is, this scheme is unconditionally stable. A very careful survey of literate witnesses that this scheme has never been reported in the literary for fluid problems. The physical changes are discussed with the help of graphics. The expression for both velocity field and temperature distribution has been made via said scheme. A comprehensive discussion about the influence of various related dimensionless parameters upon the flow properties disclosed our work. It is observed that velocity field decreases as enhancing the magnetic field effects. Heat transfer enhanced as enhancing the nanoparticle volume fraction parameter. Velocity field and heat transfer shows the dominant behavior for the case of Cu-based nanofluid as compare to Al2O3 based nanofluid. Comparative study also included to show the accuracy of the proposed finite difference scheme. It is to be highlighted that the proposed scheme is very efficient and well-matched to investigate the solutions of modeled problem and can be extended to diversify problems of physical nature.

MHD mixed convection of nanofluid due to an inner rotating cylinder in a 3D enclosure with a phase change material

PurposeThe purpose of this study is to numerically examine the mixed convection of CuO-water nanofluid due to a rotating inner hot circular cylinder in a 3D cubic enclosure with phase change material (PCM) attached to its vertical surface. Heat transfer and fluid flow characteristics were examined for various values of pertinent parameters.Design/methodology/approachFinite element method was used in the numerical simulation. Influence of various pertinent parameters such as Rayleigh number (between 10$^5$ and 10$^6$), Hartmann number (between 0 and 100), angular rotational speed of the cylinder (between −50 and 50), solid nanoparticle volume fraction (between 0 and 0.04) and PCM parameters (height-between 0.2H and 0.8H, thermal conductivity ratio- between 0.1 and 10) on the convective heat transfer characteristics are numerically studied.FindingsIt was observed that local heat transfer variations along the hot surface differ significantly for the cases with and without magnetic field where three distinct hot spots of peak Nusselt number are established when magnetic field is imposed. The average Nusselt number enhancement with the nanofluid at the highest particle volume fraction is 52.85 per cent at Hartmann number of 100, whereas its value is 39.76 per cent for the case in the absence of magnetic field. When the inner cylinder rotates, flow and thermal fields are affected within the cavity. The local heat transfer variations spread over the hot surface with cylinder rotation and 16.43 per cent of reduction in the average heat transfer is obtained with counter-clockwise rotation at 100 rad/sec. An enhancement in the PCM height and a reduction in the thermal conductivity of the PCM result in average heat transfer deterioration for the 3D cavity. The amount of the reduction is 43 per cent when the PCM height is increased from 0.2H to 0.8H, whereas 19.10 per cent enhancement in the heat transfer is achieved when thermal conductivity ratio (PCM) to the base fluid is increased from 0.1 to 10.Originality/valueSuch configurations can be designed for convection control, and in our case, various methods are available. Some of the investigated methods can be used in applications where magnetic field already exists. Convection control study in 3D cavity gives more realistic results as compared to 2D configurations, and results of the current investigation may be used for the design, optimization and flow control of many thermal applications involving magnetic field effects.

Flow and heat transfer analysis of carbon nanotubes-based Maxwell nanofluid flow driven by rotating stretchable disks with thermal radiation

A mathematical model is constructed to examine the impact of magnetic field and thermal radiation on flow and heat transfer analysis of carbon nanotubes-based nanofluids by taking base fluid as the water between two revolving stretchable disks with convective boundary conditions in the present investigation. The most extensively validated finite element technique is employed to solve the reduced nonlinear ordinary differential equations together with boundary conditions. Velocity and temperature distributions are calculated and are displayed through graphs for various values of pertinent parameters entered into the problem. Furthermore, the values of rates of change of velocity and temperature are examined in detail and are portrayed in tabular form. The values of skin friction coefficient at both upper and lower disks elevates in the boundary layer regime with rising values of Deborah number in both nanofluids, and this augmentation is higher in MWCNTs–water- than SWCNTs–water-based Maxwell nanofluid. Temperature of the fluid in both nanofluids deteriorates as the values of nanoparticle volume fraction parameter upsurge, and this deterioration in temperature distributions is higher in SWCNTs–water- than the MWCNTs–water-based Maxwell nanofluid.

Magnetic Field Effect on the Double Diffusive Natural Convection in Three-Dimensional Cavity Filled with Micropolar Nanofluid

This article presents a three-dimensional numerical investigation of heat and mass transfers and fluid flow in a cavity filled with an Al2O3/water micropolar fluid under uniform magnetic field. To solve the governing non-dimensional equations, Finite Volume Method (FVM) based on 3-D vorticity-vector potential formulation has been employed. The effects of various parameters such as buoyancy ratio (−2 ≤ N ≤ 0), Rayleigh number (103 ≤ Ra ≤ 105), Hartmann number (0≤ Ha≤ 60), nanoparticles volume fraction (0 ≤ φ ≤ 0.06) and micropolar material parameter (0≤ K≤ 5) on flow structure and on heat and mass transfers are presented. The results illustrate that for the micropolar nanofluid model, both heat and mass transfer rates and three-dimensional character of the flow are smaller when compared with the pure nanofluid model. It is also observed that increase and decrease in heat and mass transfer rates is experienced due to increase in Rayleigh number and Hartmann number, respectively. It is also noted that increase in vortex viscosity parameter reduces the average heat and mass transfer rates and is more evident when the magnetic field is imposed. Combined effects of magnetic field and nanoparticles volume fraction on heat and mass transfers are also explored.

Magnetohydrodynamic Boundary Layer Flow and Heat Transfer of Nanofluids Past a Bidirectional Exponential Permeable Stretching/Shrinking Sheet With Viscous Dissipation Effect

The problem of boundary layer flow and heat transfer of magnetohydrodynamic (MHD) nanofluids which consist of Fe3O4, Cu, Al2O3, and TiO2 nanoparticles and water as the base fluid past a bidirectional exponentially permeable stretching/shrinking sheet is studied numerically. The mathematical model of the nanofluid incorporates the effect of viscous dissipation in the energy equation. By employing a suitable similarity transformation, the conservative equations for mass, momentum, and energy are transformed into the ordinary differential equations. These equations are then numerically solved with the utilization of bvp4c function in matlab. The effects of the suction parameter, magnetic parameter, nanoparticle volume fraction parameter, Eckert number, Prandtl number, and temperature exponent parameter to the reduced skin friction coefficient as well as the local Nusselt number are graphically presented. Cu is found to be prominently good in the thermal conductivity. Nevertheless, higher concentration of nanoparticles leads to the deterioration of heat transfer rate. The present result negates the previous literature on thermal conductivity enhancement with the implementation of nanofluid. Stability analysis is conducted since dual solutions exist in this study, and conclusively, the first solution is found to be stable.

MHD boundary layer flow of SWCNT‐water and MWCNT‐water nanofluid over a vertical cone with heat generation/absorption

AbstractThe analysis is carried out to investigate the magneto hydro dynamics (MHD) boundary layer flow, heat and mass transfer characteristics of two carbon nanotubes, namely, single‐wall carbon nanotubes (SWCNTs) and multiwall carbon nanotubes (MWCNTs), with water as the base fluid by taking thermal radiation and chemical reaction into consideration. Suitable similarity conversions are employed to reduce nonlinear partial differential equations into the system of ordinary differential equations, and these equations together with boundary conditions are solved numerically using the finite element method. Velocity, temperature, and concentration distributions as well as skin friction coefficient, Nusselt number, and Sherwood number for diverse values of influencing parameters are examined in detail, and the results are displayed graphically and in tabular form. It is found that the rate of heat transfer is remarkably higher in water‐based MWCNTs than the SWCNTs as the value of the nanoparticle volume fraction parameter rises in the boundary layer regime.

MHD natural convection and entropy generation of ferrofluids in a cavity with a non-uniformly heated horizontal plate

Numerical analysis has been performed to study natural convection heat transfer combined with entropy generation of ferrofluid in a square cavity with a non-uniformly heated centered horizontal plate under the influence of inclined uniform magnetic field. The vertical borders of the enclosure are kept at constant low temperatures while the horizontal walls are adiabatic. The centrally located heated plate has a linear changed temperature along the plate. Basic equations formulated in dimensionless primitive variables have been solved by the finite difference method. The impacts of governing parameters such as Hartmann number (Ha = 0–100), magnetic field inclination angle (γ = 0°–90°), dimensionless temperature difference (Ω = 0.001–0.1), nanoparticles volume fraction (ϕ = 0.01–0.04) and plate non-uniformity parameter (λ = 0 and 1) on the flow structures, thermal transmission characteristics and entropy generation parameters have been investigated. Computational results have shown that a growth of the Hartmann number decreases the average Nusselt number and average entropy generation. In addition, it is observed that an inclusion of nanoparticles leads to the rise of the heat transfer rate and average entropy generation.

Mixed Convection Flow of Viscoelastic Nanofluid Past a Horizontal Circular Cylinder with Viscous Dissipation

The purpose of this study was to examine the effect of viscous dissipation on mixed convection flow of viscoelastic nanofluid past a horizontal circular cylinder. Carboxymethyl cellulose solution (CMC) is chosen as the base fluid and copper as a nanoparticle with the Prandtl number Pr = 6.2. The transformed boundary layer equations for momentum and temperature subject to the appropriate boundary conditions are solved numerically by using Keller-box method. The influenced of the dimensionless parameters such as Eckert number, mixed convection parameter, nanoparticles volume fraction and viscoelastic parameter on the flow and heat transfer characteristics is analyzed in detail and presented graphically. The results come out with the velocity profiles are increased while the temperature profiles are decreased by increasing the values of nanoparticles volume fraction and viscoelastic parameter, respectively. The graph shows that, increasing Eckert number the skin friction is also increases. The values of skin friction are increased by increasing mixed convection parameter, but the values of Nusselt number produce an opposite behavior. The present study has many applications especially in heat exchangers technology and oceanography. Therefore, in future, it is hoping to study the viscoelastic nanofluid flow past a different geometric such as sphere and cylindrical cone.

Heat transfer analysis of hydromagnetic water–graphene oxide nanofluid flow in the channel with asymmetric forced convection on walls

In this paper, heat transfer of hydromagnetic water–graphene oxide nanofluid flow in the channel with asymmetric forced convection on walls is analyzed. The basic partial differential equations include momentum and energy for this problem are reduced to the ordinary differential equations which are solved numerically by using finite element method (FEM) using FlexPDE software package. For validity, the results are compared with 4th order Runge–Kutta numerical solution. The effects of different physical parameters such as the nanoparticle volume fraction, the Magnet parameter, the Biot number and the Eckert number on the dimensionless velocity profile, the dimensionless temperature profile and the dimensionless gradient temperature profile are discussed. It was concluded that with increase in the nanoparticle volume fraction and Magnet parameter, the dimensionless velocity profiles of flow reduce. With rising of the Biot number, the dimensionless temperature decreases and dimensionless gradient temperature profile increases. Moreover, by increasing of the nanoparticle fraction volume, the dimensionless temperature profiles of flow is increased and the heat transfer coefficient enhanced. In addition, by increasing of the nanoparticle fraction volume, the convection on walls increases within the channel. Also, with increases of the Eckert number, the dimensionless temperature profile increases and the heat transfer rate on the channel walls is increased.

Stability Analysis of Mixed Convection Flow towards a Moving Thin Needle in Nanofluid

The problem of steady laminar mixed convection flow and heat transfer past a moving vertical thin needle in nanofluid for both assisting and opposing cases is analyzed in this paper. Three types of nanoparticles including copper, titania and alumina are taken into consideration. The nonlinear ordinary differential equations for momentum and energy have been transformed by adopting the similarity transformation in linear form. The problem is solved numerically using an implemented package called bvp4c in MATLAB software. The numerical computations are carried out for various parameters of interest, which consists of the velocity ratio parameter, mixed convection parameter, nanoparticle volume fraction parameter and the needle size. A stability analysis of the solution is performed showing that the upper branch solution is stable, while the lower branch solution is unstable. Validation of the present work is done by comparing the current results with those available in the existing literature and found to be in excellent agreement.