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 Al2O3, ZnO, CuO, and SiO2 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 SiO2-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. [
Haghshenas Fard et al. [
Namburu et al. [
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 Al2O3, ZnO, CuO, and SiO2. 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 | Al2O3 | CuO | SiO2 | ZnO |
---|---|---|---|---|---|
Density, |
998.2 | 3970 | 6500 | 2200 | 5600 |
Specific heat, |
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 (keff), effective dynamic viscosity, effective mass density (
The density of nanofluid,
The effective heat capacity at constant pressure of nanofluid,
The effective viscosity, (
By considering Brownian motion of nanoparticles in channel, the effective thermal conductivity can be obtained by using the mean empirical equations (
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
According to the proposed geometry, the cross section and length are 0.01 m2 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
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
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
Comparison between the computed data of Nusselt numbers and the data from two benchmarks at different concentrations for SiO2/water.
SiO2/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 Al2O3-water nanofluid at
Comparison between the computed data of Nusselt numbers and the data from four benchmarks at different concentrations for Al2O3-water.
Figure
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
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 SiO2-water are shown in Table
The comparison between prediction of Nusselt number and benchmarks at
SiO2/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 Al2O3-water nanofluid,
Comparison between the computed data of Nusselt numbers and the data from four benchmarks at different Re numbers for Al2O3-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 (Al2O3, CuO, SiO2, and ZnO), volume fraction of nanoparticles in the range of Among the investigated nanofluids SiO2 generates the highest Nusselt number followed by Al2O3, ZnO, CuO, and the pure water. Although SiO2 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/m2k)
Turbulent intensity
Initial turbulent intensity
Turbulence kinetic energy (m2/s2)
Thermal conductivity (W/m K)
Nusselt number (
Static pressure (N/m2)
Liquid Prandtl number
Heat flux (W/m2)
Reynolds number (
Temperature (K)
Fluctuating part of temperature (K)
Velocity (m/s)
Fluctuating part of velocity (m/s).
Dissipation rate of turbulence kinetic energy (m2/s3)
Dynamic viscosity (kg/m s)
Turbulent viscosity (kg/m s)
Density (kg/m3)
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.