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Thermal characteristics of turbulent nanofluid flow in a rectangular pipe have been investigated numerically. The continuity, momentum, and energy equations were solved by means of a finite volume method (FVM). The symmetrical rectangular channel is heated at the top and bottom at a constant heat flux while the sides walls are insulated. Four different types of nanoparticles Al_{2}O_{3}, ZnO, CuO, and SiO_{2} at different volume fractions of nanofluids in the range of 1% to 5% are considered in the present investigation. In this paper, effect of different Reynolds numbers in the range of 5000 < Re < 25000 on heat transfer characteristics of nanofluids flowing through the channel is investigated. The numerical results indicate that SiO_{2}-water has the highest Nusselt number compared to other nanofluids while it has the lowest heat transfer coefficient due to low thermal conductivity. The Nusselt number increases with the increase of the Reynolds number and the volume fraction of nanoparticles. The results of simulation show a good agreement with the existing experimental correlations.

Since nanofluids have shown the capability of transmitting heat more than the conventional fluids, researchers are interested in thermal conductivity which could be useful in many applications including air conditioning and refrigeration. Thus much research has been focusing on this area. Kulkarni et al. [_{2}-water nanofluids [

Haghshenas Fard et al. [_{2}O_{3}-water nanofluid in a horizontal tube under heating at the top half surface of a copper tube was investigated numerically by Allahyari et al. [_{2}O_{3}-water nanofluid flow in an annular tube by simulation. In general the higher nanoparticle volume fraction is added to base fluid, and the more convective heat transfer coefficient is resulted.

Namburu et al. [_{2}O_{3}-water nanofluid flowing through a horizontal curved pipe with particles size of about 28 nm. The effect of the buoyancy force, centrifugal force, and nanoparticles concentration are assessed in this study. The result illustrated that increases of the nanoparticle volume fraction enhanced the Nusselt number even though its impact on the skin friction coefficient was not remarkable. The turbulent flow of nanofluids with different volume fractions of nanoparticles flowing through a two-dimensional duct under constant heat flux condition was simulated by Rostamani et al. [_{2}O_{3}/water nanofluid inside a circular tube experimentally and found that increasing the volume fraction of nanoparticles in the range of less than 0.2% provides no significant influence on heat transfer enhancement.

In this paper, an effective single-phase model was applied to study the turbulent forced convection flow of a nanofluid in a uniformly heated rectangular tube. The influence of particles volume fraction and Reynolds number is also studied for each type of particles.

It is very important to set the governing equations (momentum, continuity, and energy) to complete the CFD analysis of the rectangular channel. The phenomenon under consideration is governed by the steady two-dimensional form of the continuity, the time-averaged incompressible Navier-Stokes equation, and energy equation. In the certain tensor systems these equations can be written as

continuity equation:

momentum equation:

energy equation:

The standard

In order to conduct numerical simulation for nanofluids, the effective thermophysical properties of nanofluids must be determined first. In this study, the nanoparticles being used are Al_{2}O_{3}, ZnO, CuO, and SiO_{2}. Thermophysical properties of base fluid and the nanoparticles which are used in the present work are reported in Table

Thermophysical properties of the base fluid and the nanoparticles used in this study [

Property | Pure water | Al_{2}O_{3} |
CuO | SiO_{2} |
ZnO |
---|---|---|---|---|---|

Density, |
998.2 | 3970 | 6500 | 2200 | 5600 |

Specific heat, _{p} |
4182 | 765 | 535.6 | 703 | 495.2 |

Thermal conductivity, |
0.6 | 40 | 20 | 1.2 | 13 |

Dynamic viscosity, |
0.001003 | — | — | — | — |

Generally the required properties for numerical simulations are effective thermal conductivity (k_{eff}), effective dynamic viscosity, effective mass density (

The density of nanofluid,

The effective heat capacity at constant pressure of nanofluid,

The effective viscosity, (^{23} moL^{−1}, and

By considering Brownian motion of nanoparticles in channel, the effective thermal conductivity can be obtained by using the mean empirical equations (^{−23} J/k.

The modified

A rectangular pipe with constant heat flux at the wall is considered in this study. The effects of various types of nanofluids are investigated under different volume fractions (1–5%) and Reynolds number in the range of 5000 to 25000. Fluid at the entrance has been considered as a constant temperature of 300 K and uniform axial velocity.

In the present study of heat transfer to turbulent nanofluids in a rectangular duct, the standard ^{−5} for all parameters.

According to the proposed geometry, the cross section and length are 0.01 m^{2} and 2 m respectively. The geometry is simplified to 2-dimenssional planner structure and only half of the pipe is considered for simulation as the upper and lower parts are symmetrical.

The boundary conditions and grid layout for this study are specified for the computational domain as shown in Figures ^{2}) and the bottom wall is symmetry to the top wall. The left side is subjected to velocity inlet and the right side is subjected to pressure outlet.

Schematic diagram of the rectangular channel.

Mesh layout of present geometry, axisymmetric about

Several different grid distributions have been tested to ensure that the calculated results (Nu numbers) are grid independent (Figure

Comparison of the Nusselt number for water with different grids.

Equations (

Maïga et al. [

Pak and Cho [

Dittus and Boelter [

Bejan [

Gnielinski [

According to Figure

The selected residual value is 10^{−5} for less computational effort. Since the less residual value might influence the accuracy of the results, the residual sensitivity test has been done to assess the effect of this value. According to Figure ^{−5} shows no significant deviation from those with 10^{−6} and 10^{−8} residual values.

Residual sensitivity test for water.

To justify the computational model, evaluated numerical results are compared with the calculated data from some empirical correlations. Figure

Comparison of Nusselt number from computed values and benchmarks for water.

The effect of volume concentrations of different types of nanoparticles on the Nusselt number is presented in Figure _{2}-water nanofluid shows the most enhancement of Nusselt number, while the other nanoparticles (Al_{2}O_{3}, ZnO, and CuO) have little variation of Nusselt numbers at all the volume fractions. It should be noted that the Gnielinski formula is more accurate than Dittus and Boelter correlation, so the discrepancies between simulated results and Gnielinski equation are presented in Table

Comparison between the computed data of Nusselt numbers and the data from two benchmarks at different concentrations for SiO_{2}/water.

SiO_{2}/water, Re = 15000 | ||||
---|---|---|---|---|

Concentration | Nu (simulation) | Nu (Dittus-Boelter) | Nu (Gnielinski) | Discrepancy between simulation and Gnielinski |

1% | 134.71 | 112.83 | 117.97 | 12.43% |

2% | 138.26 | 116.61 | 121.76 | 11.93% |

3% | 142.64 | 121.42 | 126.55 | 11.28% |

4% | 149.27 | 127.47 | 132.50 | 11.23% |

5% | 157.19 | 135.32 | 140.13 | 10.85% |

Effect of volume concentrations of different nanoparticles on Nusselt number.

In addition to this, for more comprehensive comparison, the simulation results for Al_{2}O_{3}-water nanofluid at

Comparison between the computed data of Nusselt numbers and the data from four benchmarks at different concentrations for Al_{2}O_{3}-water.

Figure _{2} has the maximum Nusselt number while it shows the least heat transfer coefficient due to the lowest thermal conductivity. In this case Al_{2}O_{3} shows the maximum heat transfer coefficient while CuO and ZnO are after it with a slight difference.

Effect of volume concentrations of nanoparticles on heat transfer coefficient.

The effective thermophysical properties of the different nanofluids are used at a constant volume fraction of 3% but at different inlet velocities or Reynolds numbers varied from 5000 to 25000.

Figures _{2}-water has the highest Nusselt number but it shows the least heat transfer coefficient. Slopes of the graphs in Figures

Nusselt number of different types of water based nanofluids at different Reynolds numbers.

Heat transfer coefficient of different types of water based nanofluids at different Reynolds numbers.

Moreover, discrepancies between simulated results and Gnielinski correlation for SiO_{2}-water are shown in Table ^{4} [

The comparison between prediction of Nusselt number and benchmarks at _{2 }nanoparticles.

SiO_{2}/water (3%) | ||||
---|---|---|---|---|

Re | Nu (Simulation) | Nu (Dittus-Boelter) | Nu (Gnielinski) | Discrepancy between simulation and Gnielinski |

5000 | 59.25 | 50.41 | 44.16 | 25.47% |

10000 | 102.18 | 87.78 | 87.31 | 14.55% |

15000 | 142.64 | 121.41 | 126.55 | 11.28% |

20000 | 181.69 | 152.83 | 163.65 | 9.93% |

25000 | 219.86 | 182.70 | 199.32 | 9.34% |

In addition to this, for more comprehensive comparison, the simulation results of Al_{2}O_{3}-water nanofluid,

Comparison between the computed data of Nusselt numbers and the data from four benchmarks at different Re numbers for Al_{2}O_{3}-water 3% nanofluid.

Numerical simulation of turbulent forced convection heat transfer in a rectangular heated pipe was performed in the present study. The emphasis was given on the heat transfer enhancement resulting from various parameters which include different types of nanofluids (Al_{2}O_{3}, CuO, SiO_{2}, and ZnO), volume fraction of nanoparticles in the range of

Among the investigated nanofluids SiO_{2} generates the highest Nusselt number followed by Al_{2}O_{3}, ZnO, CuO, and the pure water.

Although SiO_{2} has the highest Nusselt number, it has the least heat transfer coefficient because of the lowest thermal conductivity among the tested nanofluids.

The Nusselt number increases gradually with the increase of the volume fraction of nanoparticles and Reynolds number.

Effect of Reynolds number is more dominant than concentration effect of nanoparticles on heat transfer to nanofluids.

The advent of computational fluid dynamic software (Fluent) could provide fair and agreeable result from experimental correlations as noticed in the present research.

Specific heat capacity at constant pressure (J/kg·K)

Hydraulic diameter (m)

Nanoparticle diameter (m)

Heat transfer coefficient based on mean temperature (W/m^{2}k)

Turbulent intensity

Initial turbulent intensity

Turbulence kinetic energy (m^{2}/s^{2})

Thermal conductivity (W/m K)

Nusselt number (

Static pressure (N/m^{2})

Liquid Prandtl number

Heat flux (W/m^{2})

Reynolds number (

Temperature (K)

Fluctuating part of temperature (K)

Velocity (m/s)

Fluctuating part of velocity (m/s).

Dissipation rate of turbulence kinetic energy (m^{2}/s^{3})

Dynamic viscosity (kg/m s)

Turbulent viscosity (kg/m s)

Density (kg/m^{3})

Kinematic viscosity

Particle volume fraction.

Effective

Fluid

Particle phase

Solid

Wall

Axial direction

Mean

Initial.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors gratefully acknowledge High Impact Research Grant UM.C/HIR/MOHE/ENG/45 and the UMRG Fund RP012D-13AET, University of Malaya, Malaysia, for support to conduct this research work.

_{2}O

_{3}/water nanofluid inside a circular tube

_{2}O

_{3}nanoparticle suspension