Please cite this article in press as: Mosayebidorcheh, S., et al. Analysis of turbulent MHD Couette nanofluid flow and heat transfer using hybrid DTM–FDM. Particuology (2014), http://dx.doi.org/10.1016/j.partic.2014.07.004 ARTICLE IN PRESS G Model PARTIC-726; No. of Pages 8 Particuology xxx (2014) xxx–xxx Contents lists available at ScienceDirect Particuology jo ur nal home page: www.elsevier.com/locate/partic Analysis of turbulent MHD Couette nanofluid flow and heat transfer using hybrid DTM–FDM S. Mosayebidorcheh a,∗ , M. Sheikholeslami b , M. Hatami c , D.D. Ganji b a Young Researchers and Elite Club, Najafabad Branch, Islamic Azad University, Najafabad, Iran b Department of Mechanical Engineering, Babol University of Technology, Babol, Iran c Esfarayen University of Technology, Engineering and Technical College, Mechanical Engineering Department, Esfarayen, North Khorasan, Iran a r t i c l e i n f o Article history: Received 8 June 2014 Received in revised form 21 July 2014 Accepted 27 July 2014 Keywords: Turbulent Hall effect Hybrid DTM–FDM Nanofluid MHD Couette flow a b s t r a c t Unsteady turbulent nanofluid flow and heat transfer in the presence of a magnetic field is studied by considering the Hall effect. The zero-equation turbulence model is used to simulate turbulent flow. The modeling results obtained by applying the hybrid differential transformation method–finite difference method (DTM–FDM) to solve this problem confirm its viability. An analytical procedure is used for various values of active parameters. Results indicate that the Nusselt number over the lower plate depends linearly on nanoparticle volume fraction, Hall parameter, Reynolds number, and turbulent Eckert number whereas it is inversely proportional on the Hartmann number and the turbulent parameter. © 2014 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved. Introduction Algebraic turbulence models or zero-equation turbulence mod- els are models that do not require the solutions of any additional equations, and are calculated directly from the flow variables. As a consequence, zero-equation models may not be able to properly account for history effects on the turbulence, such as convection and diffusion of turbulent energy. These models are often too simple for use in general situations, but can be quite useful for simpler flow geometries or in start-up situations (e.g., the initial phases of a computation in which a more complicated model may have difficulties). This method has several advantages such as ease of implementation, fast calculation times, and good predictions for simple flows where experimental correlations for the mixing length exist (Biswas & Eswaran, 2002). The differential transformation method (DTM) was introduced by Zhou (1986) to solve some problems analytically. A hybrid numerical technique that combines the DTM and finite differ- ence method (FDM) is used in many studies (Gkdo˘ gan, Merdan, & Yildirim, 2012; Odibat, Bertelle, Aziz-Alaoui, & Duchamp, 2010; ∗ Corresponding author. Tel.: +98 9358855140. E-mail addresses: sobhanmosayebi@yahoo.com (S. Mosayebidorcheh), mohsen.sheikholeslami@yahoo.com (M. Sheikholeslami), m.Hatami2010@gmail.com (M. Hatami), ddg davood@yahoo.com (D.D. Ganji). Rashidi, Chamkh, & Keimanesh, 2011). It is a suitable and efficient method for solving the time-dependent problem in heat and mass transfer subjects. For instance, Peng and Chen (2011) investigated an annular fin with temperature-dependent thermal conductiv- ity using this hybrid-DTM; also Chu and Lo (2007) developed the hybrid differential transformation-finite difference method to ana- lyze nonlinear transient heat conduction problems. Motivated by the above-mentioned work, the main objective of our study is to introduce the hybrid-DTM as a highly accurate and efficient method for the unsteady magnetohydrodynamic (MHD) Couette fluid flow between two parallel plates. Outcomes reveal that the hybrid- DTM as an explicit method can overcome all nonlinearity terms of the problem without needing linearization. Peng and Chen (2011) showed that the convective heat transfer plays a dominant role in the heat dissipation under convection-radiation conditions. Nanofluids are produced by dispersing the nanometer-scale solid particles into base liquids of low thermal conductivity such as water, ethylene glycol, and oils. The term “nanofluid” was first coined by Choi (1995) to describe this new class of fluids. The presence of nanoparticles in the fluids noticeably increases their effective thermal conductivity and consequently enhances their heat transfer characteristics. Nanofluids as a pas- sive method for enhancement heat transfer became popular in the last decade (Domairry & Hatami, 2014; Hatami & Ganji, 2014; Hatami, Sheikholeslami, & Ganji, 2014a, Hatami, Sheikholeslami, & Ganji, 2014b; Sheikholeslami & Ganji, 2013, Sheikholeslami & http://dx.doi.org/10.1016/j.partic.2014.07.004 1674-2001/© 2014 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.