Numerical Study of Single Phase/Two-Phase Models for Nanofluid Forced Convection and Pressure Drop in a Turbulence Pipe Flow

Document Type: Original Research Paper


1 Department of Mechanical Engineering, University of Bu Ali Sina, Hamedan, I. R.Iran

2 Department of Mechanical Engineering, Miandoab Branch, Islamic Azad University, Miandoab, I. R. Iran


In this paper, the problem of turbulent forced convection flow of water- alumina nanofluid in a uniformly heated pipe has been thoroughly investigated. In numerical study, single and two-phase models have been used. In single-phase modeling of nanofluid, thermal and flow properties of nanofluid have been considered to be dependent on temperature and volume fraction. Effects of volume fraction and Reynolds number (3000<Re<9000) on convective heat transfer coefficient and pressure drop were investigated for various axial locations of the tube. Numerical results have shown that the inclusion of nanoparticles into the base fluid produced a considerable augmentation of the heat transfer coefficient that increases with an increase of the volume fraction and Reynolds number. Moreover, the increase of volume fraction has no effects on the coefficient of friction, but it decreases with increasing Reynolds number. Comparison of numerical results with experiments shows that the results of single- phase analysis is near to the experimental results.


[1] Y. Yang: Characterizations and Convective Heat Transfer Performance of Nanofluids, Ph.D thesis, LehighUniversity, UMI Publisher, Ann Arbor (2011).

[2] Y. Xuan, Q. Li: Investigation on Convective Heat Transfer and Flow Features of Nanofluids, Journal of Heat Transfer 125 (2003) 151-155.

[3] W. Williams, J Bourgiorno, J Hu: Experimental Investigation of TurbulentConvective Heat Transfer andPressure Loss of Alumina/Water and Zirconia/WaterNanoparticle Colloids (Nanofluid) in Horizontal Tubes, Journal of Heat Transfer 130 (2008) 042412-042419.

[4] U. Rea, T. McKrell, L. Hu,  J. Buongiorno: Laminar convective heat transfer and viscous pressure loss of alumina–water and zirconia–water nanofluids, International Journal of Heat and Mass Transfer (2008) 2042-2048.

[5] S.M. Fotukian, M. Nasr Esfahany: Experimental study of turbulent convective heat transfer and pressure drop of dilute CuO/water nanofluid inside a circular tube, International Communications in Heat and Mass Transfer 37 (2010) 214–219.

[6] B. Pak, Y.I. Cho: Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particle, Experimental Heat Transfer 11(1998) 151–170.

[7] V. Bianco, O. Manca, S. Nardini: Numerical investigation on nanofluids turbulent convection heat transfer inside a circular tube, International Journal of Thermal Sciences, 50 (2011) 341-349.

[8] A. Behzadmehr, M. Saffar-Avval, N. Galanis: Prediction of turbulent forced convection of a nanofluid in a tube with uniform heat flux using a two phase approach, International Journal of Heat and Fluid Flow 28 (2007) 211–219.

[9] R. Lotfi, Y. Saboohi,  A.M. Rashidi: Numerical study of forced convective heat transfer of Nanofluids: Comparison of different approaches, International Communications in Heat and Mass Transfer 37 (2010) 74–78.

[10] W. Yu, D.  M. France, E.V. Timofeeva, D. Singh and J.L. Routbort: Convective Heat Transfer of Nanofluids in Turbulent Flow, Argonne NATIONAL LABORATORY, presented at: Carbon Nano Materials and Applications Workshop (2011).

[11] F. Vahidinia, M. Rahmdel: Turbulent mixed convection of a nanofluid in a horizontal circular tube with non-uniform wall heat flux using two-phase approach, Transport Phenomena in Nano and Micro Scales  3 (2015) 106-117.

[12] P. Hanafizadeh, M. Ashjaee, M. Goharkhah, K. Montazeri, M. Akram: The comparative study of single and two-phase models for magnetite nanofluid forced convection in a tube, International Communications in Heat and Mass Transfer 65 (2015) 58–70.

[13] S. Göktepe, K. Atalik, H. Erturk: Comparison of single and two-phase models for nanofluid convection at the entrance of a uniformly heated tube, International Journal of Thermal Sciences 80 (2014) 83-92.

[14] I. Behroyan, P. Ganesana, S. Heb, S. Sivasankaran: Turbulent forced convection of Cu–water nanofluid: CFD model comparison, International Communications in Heat and Mass Transfer 67 (2015) 163–172.

[15] M. Shehnehpour Borazjani, M. Bamdad, R. Hashemi: Numerical investigation on the single phase forced convection heat transfer characteristics of Al2o3 nanofluids in a double-tube counter flow heat exchanger,  International Journal of Basic Sciences and Applied Research 3 (2014)  266-273.

[16] R. Raj, N.S. Lakshman, Y. Mukkamala: Single phase flow heat transfer and pressure drop measurements in doubly enhanced tubes, International Journal of Thermal Sciences 88 (2015) 215-227.

[17] F. K. Suguimoto, R. A. Mazza: Experimental analysis of pressure gradients on a liquid-liquid two phase flow, IV Journeys in MultiphaseFlows (2015) 23-27.

[18] M. Akbari, N. Galanis, A. Behzadmehr: Comparative assessment of single and two-phase models for numerical studies of nanofluid turbulent forced convection, International Journal of Heat and Fluid Flow  37 (2012) 136–146.

[19] H.K. Versteeg , W. Malalaskera: An introduction to computational fluid dynamic, Longman Group Ltd (1995).

[20] M. Corcione: Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids, Energy Conversion and Management 52 (2011) 789–793.

[21] C.T. Nguyen, F. Desgranges, G. Roya, N. Galanis, T. Mare´ d, S. Boucher, H. Angue Mintsa: Temperature and particle-size dependent viscosity data for water-based nanofluids – Hysteresis phenomenon, International Journal of Heat and Fluid Flow 28 (2007) 1492–1506.

[22] F.P. Incorpra, D. Duit: An introduction to heat transfer.