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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]

A new method called simplified and highly stable thermal lattice Boltzmann method, which is based on the lattice Boltzmann framework, was used to simulate the hybrid nanofluid natural convection and heat transfer in a square enclosure with a heating obstacle at high Rayleigh numbers. Four fins protrude from the heating obstacle to affect the flow pattern and heat transfer performance. The effects of the Rayleigh number (106 ≤ Ra ≤ 109), nanoparticle volume fraction (0 ≤ ϕ ≤ 0.05), and length of the fin (0.1 ≤ h ≤ 0.3) on the flow pattern, temperature distribution, and heat transfer characteristics were illustrated and analyzed. To validate the present method, the benchmark simulation results were performed. Three kinds of flow patterns (steady symmetry, unsteady symmetry, and unsteady asymmetry) can be identified at various Rayleigh numbers. At different lengths of fins, the critical Rayleigh number of flow pattern transition (from steady symmetry to steady asymmetry and from steady asymmetry to unsteady asymmetry) is different. ϕ and h also significantly affect the flow pattern. At higher ϕ, the flow inside the enclosure is steadier and the effect of h on the flow pattern varies at different Ra. [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]

A combined immersed boundary–lattice Boltzmann approach is used to simulate the dynamics of the fluid–structure interaction of a hollow sealing strip under the action of pressure difference. Firstly, the multiple relaxation times LBM model, hyper-elastic material model and immersed boundary method were deduced. According to the strain characteristics of hyper-elastic materials and the specific situation of friction between the elastic boundary and solid boundary, the internal force and the external force on the immersed boundary were discussed and deduced, respectively. Then, a 2D calculation model of the actual hollow sealing strip system was established, during which technical problems such as the equivalent wall thickness of the sealing strip and the correction of the stiffness of the contact corner were solved. The reliability of the model was verified by comparing results of FEM simulation of quasi-static deformation. Following this, the simulation results of three typical cases of sealing strips were presented. The results show that when the sealing strip fails, there will be a strong coupling phenomenon between the flow field and the sealing strip, resulting in the oscillation of the flow field and the sealing strip at the same frequency. [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]

The lattice Boltzmann method is used to study natural convection of a CuO/water nanofluid in a hollow cavity. The hollow walls are fixed at a uniform temperature, and the effect of an applied magnetic field is examined. The Koo–Kleinstreuer–Li model, which accounts for nanoparticle's Brownian motion, is used to gain the nanofluid effective thermal conductivity and nanofluid viscosity. The mechanisms how the inclination angle of magnetic field, Hartmann number, Rayleigh number, hollow width and nanoparticle volume fraction affect the streamlines, isotherms and rate of heat transfer are also studied. The results show that the average Nusselt number is increased by incrementing the nanoparticle volume fraction, Ra, magnetic field inclination angle and hollow width, but decreased by the Ha. For L = 0.4, the value of Ra where the dominant mechanism of heat transfer is changed from conduction to convection is larger than 105. But for L = 0.48 or 0.56, the turning point of the dominant heat transfer mechanism is at Ra < 105. Besides, at L = 0.4 or 0.48, the average Nusselt numbers in hot walls are higher than those in cold wall, but the opposite trend is found at L = 0.56. [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]

Forced convection heat transfer of multi-wall carbon nanotubes–iron oxide nanoparticles/water hybrid nanofluid (MWCNT–Fe3O4/water hybrid nanofluid) inside a partially heated τ-shaped channel has been numerically investigated. The effect of magnetic field is taken into account. The governing equations are solved by the lattice Boltzmann method in the domain, and the results were compared with other numerical methods by an excellent agreement between them. The effects of parameters such as Hartmann number (0 ≤ Ha ≤ 60), volume fraction of nanoparticles (0 ≤ ϕ ≤ 0.003) and different location of two heaters on the fluid flow and heat transfer are studied. The results indicate that for all cases, the average Nusselt number of each heater increases as the volume fraction of nanoparticles increases. The heat transfer characteristics were significantly affected by the arrangement of the two heaters. The heaters located on the left half of the top wall is convection-dominant mechanism, and the conduction heat transfer is the primary mechanism when the heater is on the right half of the top wall. The average Nusselt number increases as Ha increases for the heater of dominating convection mechanism but decreases for the heater of dominating conduction mechanism. [ABSTRACT FROM AUTHOR]

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). [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]

A numerical investigation is carried out to analyze the flow patterns, drag and lift coefficients, and vortex shedding around a square cylinder using a control circular bar upstream and downstream. Lattice Boltzmann method (LBM) was used to investigate flow over a square cylinder controlled by upstream and downstream circular bar, which is the main novelty of this study. Compared with those available results in the literature, the code for flow over a single square cylinder proves valid. The Reynolds number (Re) based on the width of the square cylinder () and diameter of circular bar () are 100 for square cylinder, 30 and 50 for different circular bars. Numerical simulations are performed in the ranges of and , where and are the center-to-center distances between the bar and cylinder. Five distinct flow patterns are observed in the present study. It is found that the maximum percentage reduction in drag coefficient is 59.86% by upstream control bar, and the maximum percentage reduction in r.m.s. lift coefficient is 73.69% by downstream control bar. By varying the distance ratio for the downstream control bar, a critical value of distance ratio is found where there are two domain frequencies. [ABSTRACT FROM AUTHOR]

In this study, we present a numerical simulation of MWCNT-Fe 3 O 4 /water hybrid nanofluid forced convection heat transfer over the forward- and backward-facing steps channel having a baffle fixed on its top wall. A FORTRAN's homemade code based the lattice Boltzmann method (LBM) is used here. The effects of the Reynolds number (25 ≤ Re ≤ 100), the volume fraction of nanoparticles (0 ≤ ϕ ≤ 0.003), the position of baffle (3 ≤ X 2 ≤ 7), the length of baffle (0 ≤ h ≤ 1.5) and the geometry parameter (2 ≤ X 1 ≤ 4) on flow pattern and heat transfer characteristics are provided a deep insight. The results indicate that the average Nusselt number is an increasing function of Re and ϕ. The baffle has a significant effect on the flow pattern and heat transfer characteristics. When the length of the baffle increases, the recirculation region behind the backward-facing step shrinks. The average Nusselt number increases by increasing the length of the baffle or moving the baffle towards the backward-facing step. • Nanofluid forced convection over steps with a baffle was investigated. • Simulations have been performed via Lattice Boltzmann Method (LBM). • Effects of magnetic field on heat transfer are evaluated and examined. • When baffle length increases, the recirculation region downstream shrinks. • To increase Nu, the baffle should be moved towards the backward-facing step. • Increasing the baffle length leads to the rise of Nu. [ABSTRACT FROM AUTHOR]

The present work is investigated the heat management of thermogravitational convection inside a shell and tube heat exchanger filled with Fe 3 O 4 /water nanoliquid by lattice Boltzmann method (LBM). The seven internal pipes with hot or cold temperature insert in the I-shaped heat exchanger. The impacts of Rayleigh number (104-106), nanoparticles concentration (0–0.06), Hartmann number (0–60), magnetic field inclination angle (0- π /2) and the thermal arrangement of active pipes (Case 1–4) on the flow structure and energy transport characteristics are examined. The computational data are shown by streamlines, isothermal lines and the variations of the mean Nusselt number. It has been ascertained that the thermal arrangement of active pipes affects the velocity patterns and thermal transmission performance significantly. However, an increasing in the volume fraction of nano-size particles and Rayleigh number, the average Nusselt number raises regardless of the thermal arrangement. The rate of energy transport showed an opposite dependence with Hartmann number, but a direct relationship with the magnetic field inclination angle. The most suitable thermal arrangements for heat transfer rate of heated and cooled pipes are same at low magnitudes of the Rayleigh number, but different at high Rayleigh number. • Natural convection in a heat exchanger filled with nanofluid is studied. • There are seven active internal pipes with hot or cold temperature. • The governing equations are solved by the lattice Boltzmann method. • Thermal arrangement of active pipes affects the flow pattern and heat transfer. [ABSTRACT FROM AUTHOR]

In the present study, the Buongiorno's two-phase method was implemented to investigate the nanofluid heat transfer in a triangle solar collector with corrugated bottom wall. A novel hybrid Lattice Boltzmann method (LBM) with using Total Variation Diminishing (TVD) method was developed. The effects of important physical parameters such as Rayleigh number, volume fraction of nanoparticle and different types of corrugated walls on the fluid flow pattern, nanoparticles distribution and temperature fields are studied in details. Three cases were considered for the numerical simulation. It was found that the Case 2 has the largest heat transfer rate. Based on the obtained results, the center region (inside the enclosure) has nearly uniform particle distribution. However, the region near cold and hot wall have higher and lower nanoparticle concentration, respectively. With increasing nanofluid concentration (φ) while it is smaller than a critical value, the heat transfer enhancement's ratio increases. In addition, when solid volume fraction of nanofluid is larger than the critical value, the heat transfer efficiency will be decreased by increasing the φ. • A novel hybrid LBM-TVD method is used to simulate fluid flow and heat transfer. • The Buongiorno's two-phase method is implemented to study nanofluid. • Effect of corrugated walls on the heat transfer is significant. • Nanoparticles gather near the cold walls. [ABSTRACT FROM AUTHOR]

In this paper, the laminar forced convection heat transfer of nanofluid through a bent channel was numerically investigated. The lattice Boltzmann method was used for solving the governing equations in the domain. The effect of different parameters such as Reynolds number (50 ≤ Re ≤ 150), vertical passage ratio (2.0 ≤ M ≤ 4.0), and nanoparticle solid volume fractions (Φ = 0, 0.01, 0.03, 0.05) are analyzed in terms of streamlines, isotherms, and local Nusselt numbers. It was concluded from this study that the local and average Nusselt number increased with increasing nanoparticle volume fraction regardless of Re and M. Moreover, the effect of the nanofluid concentration on the increment of heat transfer was more remarkable at higher values of the Reynolds number. Simulations show that by increasing the Reynolds number or decreasing the vertical passage ratio, the local and average Nusselt number increases. [ABSTRACT FROM AUTHOR]