Analysis of variance of nanofluid heat transfer data for forced convection in horizontal spirally coiled tubes

1. Introduction

Due to enhanced heat transfer characteristics, the curved tubes have been extensively used in industrial applications such as refrigeration, geothermal heating/cooling, air conditioning, etc. According to these wide ranges of curved tube applications, the heat transfer enhancement has been emphasized by many researchers [1-6].They tried to find new ways to enhance the heat transfer rate and thermal performance of the curved tubes and especially the spirally coiled tubes. One of the newest methods to increase the heat transfer rate is to use the nanofluids [7]. Mirzaei and Dehghan [7] showed that adding of only few vol. % of nanoparticles has the potential to increase the heat transfer rate up to 20%. They showed that this enhancement in the thermal performance of microchannels is more evident by the temperature-dependent property approach. Jamal-Abad et al. [8] extensively analyzed the use of nanoparticles added to the working fluid (water) to increase the heat transfer rate and thermal performance of a spirally coiled tube. Jamal-Abad et al. [9] recently interpreted experimental measurements of the shear rate response versus time for some nanofluids based on the non-Newtonian model of Power-Law. They showed that the best model to express the shear rate vs. time response of nanofluids is the non-Newtonian model. In addition, they found that adding of few vol.% of nanoparticles may decrease the kinematic viscosity of the working fluid which is durable in decreasing the pressure drop through heat exchangers.

The aim of the present experimental investigation is to study of heat transfer rate of nanofluids in spirally coiled tubes. In this study, nanofluids consisting of Aluminium and Copper nanoparticles were prepared in water. The forced convective heat transfer inside a spirally coiled tube was investigated at different concentrations of nanoparticles and operating temperatures in the laminar flow regime. The Nanofluids were used as the working fluid under the constant wall temperature boundary condition. The experimental results for the two types of nanofluids were analyzed based on the analysis of variance (ANOVA) method.

1. 2.  Experimental procedure

The schematic diagram of the experimental set-up is shown in Fig. 1. The Relevant dimensions of the spirally coiled tube and thermo-physical properties of Al and Cu nanoparticles are given in Tables 1 and 2. Details of the set-up were introduced in Ref. [8] and consequently, any duplicate information offering is avoided.

3. Nanofluid preparation

To protect nanoparticles from oxidation, the nanofluids were prepared by the one-step method using Al and Cu nanoparticles. For more information regarding to the advantages and disadvantages of one and two-step methods, one can refer to Refs. [8, 10].

4. Data processing

The heat transfer characteristics of fluids are defined in terms of the convective heat transfer coefficient and the Nusselt number [11]:

where  is the mass flow rate of the fluid, k is the fluid thermal conductivity, C_p is the effective specific heat of the fluid and L represented tube length. ,  and  are the averaged wall temperature, the outlet and inlet temperatures of the fluid, respectively.

The thermophysical properties of nanofluid were calculated at the bulk temperature of the nanofluid by the following equations [12, 13]:

Where  is the specific heat of the nanofluid,  is the volume concentration,  is the viscosity of the nanofluid and  is the effective density of nanofluid. The Subscripts b, s, and nf refer respectively to the base fluid, the nanoparticles, and the nanofluid. The properties of the nanofluid shown in the above equations are evaluated from water and nanoparticles at the bulk temperature.

5. Results and discussion

5.1 Validation

To evaluate the accuracy of the measurements, experimental system was tested with distilled water before measuring the convective heat transfer of nanofluids. The results were compared with the predictions of the following Kubair and Kuloor equation for laminar flows under the constant wall temperature boundary condition [14]:

where a is the diameter of tube and represents the average radius. The experimental setup was validated by comparing the theoretical and experimental results of pure water. As shown in Fig. 2, a good agreement exists between the experimental data and theoretical results.

5.2 The thermal conductivity of nanofluids

Figure 3 indicates the thermal conductivity enhancement of Al-water and Cu- water nanofluids. The Results show that nanofluids have noticeably higher thermal conductivities than the pure base-fluid. For example, the thermal conductivity enhancement rises from a low amounts of 1.12 at 0.55 vol. % to a peak of 1.26 at 2.23 vol. %at 45 ⁰C for the Cu-water nanofluid. With increasing temperature, the viscosity of the base fluid is decreased and the Brownian motion of nanoparticles is increased and consequently, the thermal conductivity increases. The slope of the thermal conductivity versus the volume fraction can be divided into two linear regimes. At lower concentrations, the slope was greater than mentioned higher concentrations. The Linear trend which is observed in this work has also been observed in the literature [15-18].

Figure 4 illustrates comparison between thermal conductivity of nanofluid ratio to the base fluid for different concentrations at 45 °C. Cu-water nanofluids have more enhancements in the effective thermal conductivity than those of Al-water nanofluids. For example, at the 0.55 and 1.12 vol.%, the effective thermal conductivity of Cu-water nanofluid increases respectively 12% and 26% whereas, the thermal conductivity of Al-water nanofluid increases respectively about 11% and 22%.

5.3 Convective heat transfer of nanofluid

Figure 5 demonstrates the Nu number for nanofluids versus Gz number for different concentrations at wall temperature 30 ^oC. It can be clearly seen that Nu enhances for both type of the nanofluids with a higher enhancement for the Cu-water nanofluid compared to the Al-water nanofluid at 2.23%.In a flow through a spiral coil, the centrifugal force strongly influences the Nu number. The Flow through a spiral, where in the radius of curvature varies continuously, results in a continuously variable centrifugal force .So, an increase in the Nusselt number can be seen for spirally coiled tubes. The secondary flow causes these oscillations by exposing the tube wall alternatively to the hot and cold fluids. There are similar results for 35 and 40 ^oC which can be seen in figures 6 and 7. For example, at wall temperature 35 ^oC and at the Gz number of about 28, the Nu number  rises from 23 for Al-water with 2.23 vol. % to 27 for Cu-water at the same concentration. This trend can be seen for other concentrations in this situation.

The Nu number ratio (Nu_nf/Nu_f) for a specific concentration (0.55 vol %.) is illustrated in Figure 8. As expected, the Nusselt ratio increases with increasing the Gz number. This is due to the Nusselt number depends directly on the rat of mass

flow. In fact, there are significant fluctuations for the Nusselt number and there is no exact increasing trend when temperature rises because of the centrifugal force has a significant effect on the secondary flow. This secondary flow has significant effect on the fluid flow mixing, so it   numerous fluctuations in the Nusselt number. These fluctuations once again reflect the effects of the secondary flow on the Nusselt number for both nanofluids at different temperatures. Also, the Nusselt number ratios of Al-water nanofluid are only slightly lower than mentioned Cu-water nanofluids. The Nu number of the Al-water nanofluid at 30, 35 and 40^oC are about 10%, 6%, and 2% higher than those of pure water. The enhancement of the Nu number for Cu-water nanofluid at 30 ^oC exceeds 15%, while for 35 and 40^oC are 6% and 5% respectively. This shows that, as the temperature increases, the Nu_f increases more than Nu_nf. Figures 9 and 10 illustrate this fact for Al-water nanofluid and Cu-water nanofluid at 1.12 and 2.23 vol. %, respectively.

5.4 Analysis of variance

Among the controllable factors, nanofluid type (A), concentration (B), temperature (C) and Gz number (D) were selected because they can affect

the Nu number. The Variable factor levels are shown in tables 3.

The residual plot of Nusselt number is shown figure 11distributed evenly around the zero-line without showing any evident pattern. This satisfies the constant variance assumption. If the data are not evenly distributed around the mean, an extra term should be added to the model.

To reiterate the interpretation of ANOVA results, a calculated F-value that is greater than F_crit for a stated level of confidence (typically 90%) means that the difference being tested is statistically significant at that level. As an alternative to using the F-values, the p-value can be used to indicate the degree of confidence we have that there is a significant difference between means.

The aim of the analysis of variance (ANOVA) is to determine their percentage of effective parameters on the Nu number. The results of ANOVA analysis are shown in Table 4. The F_0.1,1,47 was 251.15 for a significant level  of 0.1 (or 90% confidence level). From Table 4, it is clear that the

F-values of factor B, factor C, and factor D are greater than F_0.05,1,47= 251.15. Factor A was not a significant parameter effective on the Nu number.

5.5 Correlations for the Nusselt number

In general, the Nusselt number of nanofluids may be related to the parameters as follows:

By considering the above-mentioned statement, the Nusselt number based on the experimental results of nanofluids in the spiral coil has been correlated by the following equation by using the least squares regression analysis:

Equation 9 fits the experimental data within ±10% error as shown in figure 12 and the correlation is valid for laminar flow with GZ < 2300, and for Al-water and Cu-water nanofluid concentrations less than 2.23 vol. %.

6. Conclusions

The Experimental investigations on the convective heat transfer and the thermal conductivity of Al-water and Cu-water nanofluids were carried out in the laminar regime inside a spiral coil with constant wall temperature. Nanofluids were prepared by one-step method and they were found very stable. The Results showed that adding of nanoparticles to the base fluid increases its thermal conductivity. The Effects of the nanofluid concentrations, Gz number and the constant wall temperature on the Nusselt number were investigated. The Nusselt number increases by increasing both the Gz number and the concentration. However, there are significant

fluctuations due to the secondary flow. An ANOVA analysis showed that the Gz number, temperature, and concentration are the parameters which affect the Nu number significantly.

References

[1]     Naphon P, Wongwises S. An experimental study the in-tube convective heat transfer coefficients in aspiral-coil heat exchanger. IntCommun Heat Mass Transfer 29, (2002) 797–809.

[2]     J.C. Ho, N.E. Wijeysundera, S. Rajasekar, T.T. Chandratilleke,Performance of a compact spiral coil heat exchange, Heat RecoverySystem nas CHP 15, (1995) 457–468.

[3]      S. Rahul, S.K Gupta, P.M.V Subbarao, An experimental study for estimating heat transfer coefficient from coiled tube surfaces in cross-flow of air, Proceeding of the third ISHMT-ASME heat and mass transfer conference and Fourth National heat and mass transfer conference, India, December (1997) 381-385.

[4]     M.K. Khan, R. Kumar, P.K. Sahoo, An experimental studyof the flow of R-134a inside an adiabatic spirally coiledcapillary tube, International Journal of Refrigeration (2008); doi:10.1016/j.ijrefrig. 2008.01.008  

[5]     C.E Kalbe and J.D. Seader, Fully developed viscous-flow heat transfer in curved circular tubes with uniform wall temperature, AIChe Journal, 20, (1974) 340-346.

[6]     M.K. Mittal, R. Kumar, A. Gupta, Numerical analysis of adiabatic flow of refrigerantthrough a spiral capillary tube, International Journal of Thermal Sciences 48, (2009) 1348-1354

[7]     M. Mirzaei, M. Dehghan, Investigation of flow and heat transfer of nanofluid in microchannel with variable property approach, Heat Mass Transfer 49 (2013) 1803-1811.

[8]     M. T. Jamal-Abad, A. H. Zamzamian, M. Dehghan, Experimental studies on the heat transfer and pressure drop characteristics of Cu-water and Al-water nanofluids in a spiral coil, Experimental Thermal and Fluid Science 47 (2013) 206-212.

[9]     M.T. Jamal-Abad, M. Dehghan, S. Saedodin, M.S. Valipour, A. Zamzamian, An Experimental investigation of rheological characteristics of non-Newtonian nanofluids, J. Heat Mass Trans. Res. 1 (2014) 17-23.

[10]  Yu, W., France, D. M., Routbort, J. L., Choi, S. U. S., Review and Comparison of Nanofluid Thermal Conductivity and Heat Transfer Enhancements. Heat Transfer Engineering. 29(5) (2008) 432-460.

[11]  M. Dehghan, M. Daneshipour, M.S. Valipour, R. Rafee, S. Saedodin, Enhancing heat transfer in microchannel heat sinks using converging flow passages, Energy Conversion and Management 92 (2015) 244-250.

[12]  Milad Tajik Jamal-Abad,A. Zamzamian,E. Imani, M. Mansour, Experimental Study of the Performance of a Flat-Plate Collector Using Cu–Water Nanofluid, Journal of Thermophysics and Heat Transfer 27(4) (2013) 756-760.

[13]  A. Zamzamiana, M.T Jamal-Abad, Factor  Effect  Estimation  in  the  Convective  Heat  Transfer  Coefficient  Enhancement of Al2O3 /EG Nanofluid  in a Double-pipe Heat Exchanger, IJE TRANSACTIONS B: Application   Vol. 26 (8), (2013) 837-844.

[14]  V. Kubair and N. R. Kuloor, Heat transfer to Newtonian fluids in spiral coils at constant tube walltemperature in laminar flow, Indian J. Technol., Vol. 3, (1965) 144 -146.

[15]  Das, S.K., N. Putra, P. Thiesen, and W. Roetzel, Temperature dependence of thermal conductivity enhancement for nanofluids. Journal of Heat Transfer- Transactions of the Asme, 125(4), (2003) 567-574.

[16]  Xie, H.Q., J.C. Wang, T.G. Xi, Y. Liu, F. Ai, and Q.R. Wu, Thermal conductivity enhancement of suspensions containing nanosized alumina particles. Journal of Applied Physics, 91(7), (2002) 4568-4572.

[17]  Eastman, J.A., U.S. Choi, S. Li, L.J. Thompson, and S. Lee, Enhanced thermal conductivity through the development of nanofluids. Materials Research Society Symposium Proceedings, 457(Nanophase and Nanocomposite Materials II), (1997) 3-11.

[18]  Lee, S., S.U.S. Choi, S. Li, and J.A. Eastman, Measuring thermal conductivity of fluids containing oxide nanoparticles. Journal of Heat Transfer-Transactions of the Asme, 121(2), (1999) 280-289.