Physica A 509 (2018) 729–745 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Develop the lattice Boltzmann method to simulate the slip velocity and temperature domain of buoyancy forces of FMWCNT nanoparticles in water through a micro flow imposed to the specified heat flux Arash Karimipour a , Annunziata D’Orazio b , Marjan Goodarzi c ,∗ a Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran b Dipartimento di Ingegneria Astronautica, Elettrica ed Energetica, Sapienza Università di Roma, Via Eudossiana 18, Roma 00184, Italy c Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam highlights • Develop LBM ability to simulate effects of buoyancy forces. • Water/FMWCNT slip velocity through a micro flow. • Simulation of specified heat flux along microchannel by LBM. article info Article history: Received 22 February 2018 Received in revised form 20 May 2018 Available online 21 June 2018 Keywords: Lattice Boltzmann Micro flow Specified heat flux Carbon nanotubes abstract Lattice Boltzmann method ability is improved to simulate the mixed convection of Water / FMWCNT nanofluid inside a two dimensional microchannel. The influences of gravity on hydrodynamic and thermal domains are studied while the microchannel walls are imposed by a constant thermal heat flux at three different case studies as no-gravity, Ri = 1 and Ri = 10. The flow Reynolds number is chosen as one and the liquid micro flow conditions are involved by B = 0.005, B = 0.01 and B = 0.02. The mass fraction of carbon nanotubes in water are selected as φ = 0, φ = 0.1% and φ = 0.2%. Double population distribution func- tions of ‘‘f’’ and ‘‘g’’ are used in lattice Boltzmann method. To the best of author’s knowledge, there is no article concerned the way of heat flux boundary condition simulation by LBM considering the buoyancy forces effects on nanofluid slip velocity. Generate a rotational cell due to gravity in entrance region which leads to observe the negative slip velocity phenomenon can be presented as the several interesting achievements of this work. © 2018 Elsevier B.V. All rights reserved. 1. Introduction Micro devices, which are concerned fluid flow and heat transfer in micro and nano scales level (MEMS & NEMS), have different applications in nowadays industries which lead to report a large number of studies about them. It should be noticed to different specifications of macro flows in comparison with micro and nano ones. The different level of a micro and a nano flow is presented by dimensionless Kudsen number which is shown by Kn = λ/D H where λ represents the molecular mean ∗ Corresponding author. E-mail address: marjan.goodarzi@tdt.edu.vn (M. Goodarzi). https://doi.org/10.1016/j.physa.2018.06.031 0378-4371/© 2018 Elsevier B.V. All rights reserved.