Numerical simulation of laminar forced convection heat transfer of Al 2 O 3 ewater nanofluid in a pipe with return bend Jongwook Choi a, * , 1 , Yuwen Zhang b a School of Mechanical and Aerospace Engineering, Sunchon National University, Jeonnam 540-742, Korea b Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA article info Article history: Received 23 April 2011 Received in revised form 27 December 2011 Accepted 30 December 2011 Available online 17 January 2012 Keywords: Correlation equation Finite element method Heat transfer enhancement Nanofluid Return bend abstract Laminar forced convection heat transfer of the Al 2 O 3 ewater nanofluid in a pipe with a return bend is analyzed by using a finite element method. The results show that the average Nusselt number increases with increasing Reynolds number and Prandtl number, and the increment of specific heat in the nanofluid contributes to the heat transfer enhancement. The average Nusselt number in the return bend appears higher than that in the inlet and outlet pipes due to the secondary flows. However, the pressure drop in the pipe largely increases with the increment of nanoparticle volume concentration. The empirical correlations for the average Nusselt numbers are obtained as functions of the Dean number and the Prandtl number. Ó 2012 Elsevier Masson SAS. All rights reserved. 1. Introduction Various industries in many countries have made great efforts to reduce the greenhouse emissions that cause global warming. To achieve this, the active endeavor to increase the energy efficiency has been made in industrial settings. The methods to improve the efficiency of heat exchangers can also be one of these many efforts. In this connection, many researchers have been interested in the geometry of the heat exchanger to get higher thermal efficiency [1e3]. Meanwhile, other research groups have been trying to enhance the heat transfer in pipe systems by using nanofluids. The concept of the nanofluids started from the fact that the thermal conductivity of the fluid containing suspended nanoparticles is improved more than that of the conventional heat transfer fluid [4]. Before the nanoparticles appeared, the researches on the fluid and heat transfer problems had been carried out with millimeter- or micrometer-sized particles [5e7]. These particles were not put to practical use because they may have brought about poor suspen- sion stability, channel clogging, system abrasion and so on. However, the fluids including nanometer-sized particles do not have those serious problems and the measured thermal conduc- tivity of the nanofluid is anomalously greater than the theoretical prediction [8]. The nanofluid technology has been studied and developed by many research groups worldwide [9,10]. Effects of particle volume concentration, particle material, particle size, particle shape, base fluid material, temperature, additive, and acidity on heat transfer enhancement were investigated experimentally by multiple research groups. Although the heat transfer data were partially inconclusive or conflicting, the heat transfer enhancement appeared in the range of 15e40% [11]. Straight pipes have been mainly utilized in the experimental or numerical studies on the convective heat transfer enhancement using nanofluids. Pak and Cho [12] experimentally investigated the turbulent friction and the heat transfer behaviors of the nanofluids such as gAl 2 O 3 ewater and TiO 2 ewater in a circular tube at the Reynolds numbers of 10 4 e10 5 . The measured viscosities at the volume concentration of 10% were approximately 200 times greater for the gAl 2 O 3 ewater and 3 times greater for the TiO 2 ewater than for the pure water. Also, the Nusselt number of the nanofluids increased with the augmentation of the volume concentration as well as the Reynolds number. However, the results showed that the convective heat transfer coefficient of the nano- fluids was smaller than that of the pure water under the condition of same average velocity. * Corresponding author. Tel.: þ82 61 750 3826; fax: þ82 61 750 3820. E-mail addresses: choijw99@scnu.ac.kr (J. Choi), zhangyu@missouri.edu (Y. Zhang). 1 Presently visiting professor at Department of Mechanical and Aerospace Engi- neering, University of Missouri, Columbia, MO 65211, USA. Tel.: þ1 573 268 3961; fax:þ1 573 884 5090. Contents lists available at SciVerse ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts 1290-0729/$ e see front matter Ó 2012 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2011.12.017 International Journal of Thermal Sciences 55 (2012) 90e102