Lattice Boltzmann study of multi-walled carbon nanotube (MWCNT)- Fe 3 O 4 /water hybrid nanofluids natural convection heat transfer in a P- shaped cavity equipped by hot obstacle Amin Matori 1 • Rasul Mohebbi 2 • Zahra Hashemi 1 • Yuan Ma 3,4 Received: 13 August 2018 / Accepted: 23 October 2018 Ó Akade ´miai Kiado ´, Budapest, Hungary 2018 Abstract In the present paper, the effect of nanofluid and the hot obstacle in a P-shaped cavity is investigated. Lattice Boltzmann method is used to simulate the fluid flow and heat transfer. The effects of the parameters such as the nanoparticle solid volume fraction, the Rayleigh number, aspect ratio of cavity and hot obstacle position on the flow pattern and heat transfer parameters are studied. The numerical results are compared with previous results for validation, and a good agreement obtained. It is found that the average Nusselt number is increased by increasing the nanoparticle solid volume fraction, the Rayleigh number and the aspect ratio of cavity. Moreover, the effect of Rayleigh number on the average Nusselt number at high Rayleigh numbers (10 5 – 10 6 ) is more pronounced than that at low Rayleigh numbers (10 3 –10 4 ) due to the different heat transfer mechanisms. The position of the hot obstacle affects the heat transfer significantly. When the hot obstacle is located on the center, the heat transfer is more effective. Keywords P-Shaped cavity Á Natural convection heat transfer Á LBM Á Hot obstacle Á MWCNT-Fe 3 O 4 /water hybrid nanofluids List of symbols a Height of obstacle AR Cavity obstruction ratio b Length height of obstacle c s Speed of sound in lattice scale e i Discrete lattice velocity in direction F Force term f Density distribution function f eq Equilibrium density distribution function g Gravity g eq Equilibrium energy distribution function H Height of the cavity k Thermal conductivity L Width of the cavity M The number of lattices in the y-direction Ma Mach number Nu Nusselt number P Non-dimensional pressure Pr Prandtl number Ra Rayleigh number S x Positions of the heater from upper side of cavity T Temperature U Non-dimensional velocity V Components W Length of the cavity Greek symbols h Non-dimensional temperature x i Weight function in direction i / Volume fraction s m Relaxation time for flow s g Relaxation time for flow a Thermal diffusivity m Viscosity & Rasul Mohebbi rasul_mohebbi@du.ac.ir 1 Department of Mechanical Engineering, Bushehr Branch, Islamic Azad University, Bushehr, Iran 2 School of Engineering, Damghan University, P.O. Box: 3671641167, Damghan, Iran 3 Shanghai Automotive Wind Tunnel Center, Tongji University, No. 4800, Cao’an Road, Shanghai 201804, China 4 Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, No. 4800, Cao’an Road, Shanghai 201804, China 123 Journal of Thermal Analysis and Calorimetry https://doi.org/10.1007/s10973-018-7881-8