Numerical investigation of MHD effects on nanofluid heat transfer in a baffled U-shaped enclosure using lattice Boltzmann method Yuan Ma 1,2 • Rasul Mohebbi 3 • M. M. Rashidi 4 • O. Manca 5 • Zhigang Yang 1,2 Received: 5 June 2018 / Accepted: 28 June 2018 Ó Akade ´miai Kiado ´, Budapest, Hungary 2018 Abstract Lattice Boltzmann method (LBM) was carried out to investigate the effects of magnetic field and nanofluid on the natural convection heat transfer in a baffled U-shaped enclosure. The combination of different specifications of the baffle, LBM, nanofluid and magnetic field is the main innovation in the present study. In order to consider the effect of Brownian motion on the thermal conductivity, Koo–Kleinstreuer–Li model is used to define thermal conductivity and viscosity of nanofluid. Effects of Rayleigh number, Hartmann number, nanoparticle volume fraction, height and position of the baffle on the fluid flow and heat transfer characteristics have been examined. It was found that raising the Rayleigh number and nanoparticle solid volume fraction leads to increase the average Nusselt number irrespective of the position of the hot obstacle. However, the heat transfer rate is suppressed by the magnetic field. The heat transfer enhancement by introducing nanofluid decreases as increasing Rayleigh number, but it increases as increasing the Hartmann number. Moreover, the maximum heat transfer rate was observed when the enclosure equipped with a baffle with (s, h) = (0.2, 0.3) or (0.4, 0.3). Keywords Magnetic field  Nanofluid  Natural convection  Baffle  LBM  U-shaped  Enclosure List of symbols s Position of the baffle h Length of the baffle e i Discrete lattice velocity in direction f Density distribution function f eq Equilibrium density distribution function Ha Hartmann number Nu Nusselt number U, V Nondimensional velocity components Pr Prandtl number H Height of the enclosure W Weight of the enclosure c s Speed of sound in Lattice scale g Energy distribution function g eq Equilibrium energy distribution function k B Boltzmann constant T Fluid temperature k Thermal conductivity Greek symbols x i Weight function in direction i / Volume fraction s c Relaxation time for temperature a Thermal diffusivity q Density s v Relaxation time for flow b Thermal expansion coefficient l Dynamic viscosity Subscripts loc Local s Solid particles nf Nanofluid c Cold ave Average & O. Manca oronzio.manca@unicampania.it 1 Shanghai Automotive Wind Tunnel Center, Tongji University, No. 4800, Cao’an Road, Shanghai 201804, China 2 Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, No. 4800, Cao’an Road, Shanghai 201804, China 3 School of Engineering, Damghan University, P.O. Box: 3671641167, Damghan, Iran 4 Department of Civil Engineering, School of Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK 5 Dipartimento di Ingegneria, Universita ` degli Studi della Campania ‘‘Luigi Vanvitelli’’, 81031 Aversa, (CE), Italy 123 Journal of Thermal Analysis and Calorimetry https://doi.org/10.1007/s10973-018-7518-y