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Nanofluid natural convection inside a cavity with a porous square obstacle in the presence of magnetic field is simulated by lattice Boltzmann method. The porous obstacle is adopted by Sierpinski carpets fractal pattern, and three kinds of temperature boundary conditions are set up on the hot walls. The combination of five topics including LBM, Sierpinski carpets, nanofluid, magnetic field and various temperature boundary conditions is the main novelty of the present paper. The effects of temperature boundary condition, configuration of Sierpinski carpets porous obstacle, Rayleigh number, nanoparticle volume fraction and Hartmann number on the flow pattern, temperature distribution and heat transfer characteristics are studied. The results show that the local and average Nusselt numbers are increasing functions of ϕ and Ra, but a decreasing function of Ha, regardless of the boundary conditions. The heat transfer enhancement by adding nanoparticles is more effective at low ϕ. The rate of heat transfer with different temperature boundary conditions is Case 3 ˃ Case 2 ˃ Case 1. At high Hartmann number, the obstacle configuration affects the rate of heat transfer very slightly. However, at low Hartmann number, the effect of obstacle configuration on the average Nusselt number should be considered. The effect of obstacle configuration on the rate heat transfer is also influenced by the temperature boundary conditions. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann method is utilized to investigate the mixed convection of a CuO/water nanofluid by magnetic field's effect in a lid-driven U-shaped enclosure filled with a baffle. The bottom wall's temperature is high. The Koo–Kleinstreuer–Li model, which considering the Brownian motion of nanoparticles, is adopted to obtain the thermophysical properties of the nanofluid. How the Hartmann number (Ha), Richardson number (Ri), Reynolds number (Re), and nanoparticle concentration (ϕ) affect streamlines, isotherms, and average Nusselt number (Nuave) is also examined. The results reveal that, at Re = 100 and for a large Ri, the nanofluid strategy degrades the Nu. The favorable effect of increasing the Re on the average Nu and adverse trends of the increment in the Ha on the heat transfer are the main highlights in this study. In addition, the increase in the Re more strongly affects the heat transfer rate at higher Ri. [ABSTRACT FROM AUTHOR]

Lattice Boltzmann method (LBM) was used to simulate two-dimensional MHD Al2O3/water nanofluid flow and heat transfer in an enclosure with a semicircular wall and a triangular heating obstacle. The effects of nanoparticle volume fraction (0 ≤ ϕ ≤ 0. 0 5), Rayleigh number (1 0 4 ≤ R a ≤ 1 0 6) , Hartmann number (0 ≤ H a ≤ 6 0) and heating obstacle position (Cases 1–7) on flow pattern, temperature distribution and rate of heat transfer were investigated. The results show that with the enhancing Rayleigh number, the increasing nanoparticle volume fraction and the reducing Hartmann number, an enhancement in the average Nusselt number and the heat transfer appeared. The effect of Ha on the average Nu increases by increasing the Ra. It can also be found that the action of changing the heating obstacle position on the convection heat transfer is more important than that on the conduction heat transfer. The higher obstacle position in Cases 6 and 7 leads to the small value of the average Nusselt number. Moreover, the effect of Ha on average Nu in Case 1 at R a = 1 0 6 is more significant than other cases because the flow pattern in Case 1 is changed as increasing Ha. [ABSTRACT FROM AUTHOR]

• The arrangement of heaters and coolers affects the temperature distribution. • The highest value of Nu loc occurs at the junction of the heater and the cooler. • The existent magnetic field suppresses the nanofluid convection. • By increasing the block side length, the Nu ave increases. • The heat transfer rate in Case 1 is most effective, followed by Case 3 and Case 2. A two-dimensional (2D) numerical simulation is presented to study the effect of magnetic field on Ag-MgO nanofluid forced convection and heat transfer in a channel with active heaters and coolers. A Fortran code according to Lattice Boltzmann method (LBM) is developed for this purpose. The effects of thermal arrangement (Case1, 2 and 3), block side length (0.3 ≤ h ≤ 0.5), Reynolds number (50 ≤ Re ≤ 100), Hartmann number (0 ≤ Ha ≤ 60) and volume fraction of nanoparticles (0 ≤ ϕ ≤ 0.02) on flow pattern and heat transfer characteristics are analyzed systematically. The obtained results showed that the highest value of local Nusselt number occurs at the junction of the heater and the cooler due to the high temperature gradient, followed by the sharp corner of heaters and coolers. Moreover, the heat transfer at the heater sharp corner is higher than that of the cooler sharp corner. The average Nusselt numbers indicated that the rate of heat transfer increases with increasing ϕ or decreasing Ha. Finally, the heat transfer rate in Case 1 is more than Case 3 and Case 2. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • MHD natural convection in a baffled U-shaped enclosure is studied. • KKL correlations are used to obtain nanofluid thermal conductivity and viscosity. • Governing equations have been solved by the lattice Boltzmann method. • Effects of Ra , Ha , ϕ and AR on the flow and heat transfer have been examined. Abstract In this study, nanofluid natural convection in a baffled U-shaped enclosure in the presence of a magnetic field is investigated. Lattice Boltzmann method (LBM) is used to study present problems. KKL (Koo-Kleinstreuer-Li) correlation is applied to calculate the effective thermal conductivity and viscosity of nanofluid. The effect of the Brownian motion on the effective thermal conductivity is considered in this correlation. The combination of the four topics (nanofluid, U-shaped enclosure, baffle, magnetic field) is the main novelty of the present study. Effect of Rayleigh number, Hartmann number, nanoparticle volume fraction and cavity aspect ratio on the flow field and heat transfer characteristics have been investigated. The results demonstrate that the average Nusselt number increases by increments of the Rayleigh number, nanoparticle solid volume fraction and aspect ratio. However, the rate of heat transfer is suppressed by the magnetic field. The effect of magnetic field on heat transfer is more significant at higher Rayleigh number and the effect of Ra on the average Nusselt number is more noteworthy at lower Ha. Besides, the effect of Rayleigh number on heat transfer enhancement becomes more significant at higher aspect ratio. [ABSTRACT FROM AUTHOR]