Numerical study of convective heat transfer with nanofluids in turbulent flow using a Lagrangian-Eulerian approach Nishant Kumar a , B.P. Puranik b,⇑ a ISRO Propulsion Complex, Mahendragiri, Thirunelveli Dist., Tamil Nadu 627133, India b Indian Institute of Technology, Bombay, Powai, Mumbai 400076, India article info Article history: Received 22 March 2016 Revised 5 August 2016 Accepted 5 August 2016 Available online xxxx Keywords: Nanofluids Lagrangian–Eulerian approach Discrete Phase Model Single phase model abstract In the present study, numerical simulations of forced convection heat transfer with Water-Al 2 O 3 , Water- TiO 2 and Water-Cu nanofluids in fully developed turbulent flow in a tube of circular cross-section under constant surface heat flux condition are performed, using a Lagrangian-Eulerian approach. The nanopar- ticles movement is tracked using the Lagrangian approach while the governing equations for the base fluid are solved using the Eulerian approach. The simulation results are compared with the predictions from the experimental correlations generated for corresponding conditions. Numerical results are also compared with the single phase model that treats the nanofluid as an equivalent single phase fluid with enhanced thermophysical properties. The comparison seems to indicate that the Lagrangian-Eulerian approach is a more accurate model for simulating forced convection heat transfer with dilute nanofluids with the particle volume concentration less than 0.5%, while for higher particle volume concentrations the single phase model appears to be more accurate. Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction A stable suspension of nanoparticles in a liquid (called the ‘‘base fluid”) is known as a ‘‘nanofluid”. In general, nanoparticles of a higher thermal conductivity material are mixed in small propor- tions for the purpose of enhancing heat transfer characteristics of the base fluid. A number of different approaches have been pro- posed to model the nanofluid, which can then be used for the numerical simulation of heat transfer using a nanofluid. Amongst these approaches, the ‘‘single phase model” has been extensively used for numerical prediction of heat transfer performance of a nanofluid [1–9]. In this approach, the nanofluid is assumed to be an equivalent single phase fluid with enhanced thermophysical properties that are obtained from either experimental results or from various theoretical estimation models. Often, conducting experiments to obtain thermophysical properties of nanofluid at particular composition and temperature is cumbersome, while the theoretical estimation models have their own inaccuracies. Recently, Kumar and Puranik [9] have investigated the accuracy of the single phase approach using generalized models for the var- ious thermophysical quantities of interest for various water based nanofluids. A few researchers [3,6,7] have compared predictions from the single phase model with those from the more involved two phase models of nanofluids, and concluded that a ‘‘multiphase mixture model” is better than the single phase model, although the results obtained by Akbari et al. [8] are in contradiction with this conclusion. In the multiphase mixture model, the nanofluid is con- sidered as a single fluid with two phases. The mixture model allows the phases to move at different velocities by using the con- cept of slip and drift velocities [10]. In this model, the dynamic vis- cosity of each phase is required. Behzadmehr et al. [3] have used Miller and Gidaspow [11] solid viscosity model to calculate the vis- cosity of solid nanoparticles. The commercial Computational Fluid Dynamics (CFD) software Ansys-Fluent Ò 14.5, in its documentation [12], has a model for calculating the solid viscosity. However, such models introduce uncertainty and the contribution in the overall dynamic viscosity due to the solid phase cannot be accurately eval- uated for each composition of the nanofluid. In the Lagrangian-Eulerian approach of modeling a nanofluid, the nanoparticles are tracked using the Lagrangian approach, while the governing equations for the base fluid are solved using the Eulerian approach. The advantage of the Lagrangian-Eulerian approach is that accurate inputs for the thermophysical properties of the base fluid and the nanoparticle material can be given sepa- rately, unlike in the single phase model where the enhanced ther- mophysical properties need to be specified either through experimental data or various estimation models. The Lagrangian- http://dx.doi.org/10.1016/j.applthermaleng.2016.08.038 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: puranik@iitb.ac.in (B.P. Puranik). Applied Thermal Engineering xxx (2016) xxx–xxx Contents lists available at ScienceDirect Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng Please cite this article in press as: N. Kumar, B.P. Puranik, Numerical study of convective heat transfer with nanofluids in turbulent flow using a Lagrangian- Eulerian approach, Appl. Therm. Eng. (2016), http://dx.doi.org/10.1016/j.applthermaleng.2016.08.038