El Bachir Lahmer

This study presents a three‐dimensional numerical analysis of natural convection in a U‐shaped cavity filled with a copper–water (Cu–water) nanofluid under the influence of an external magnetic field. A hybrid numerical approach is adopted, in which the multiple‐relaxation‐time lattice Boltzmann method is used to simulate the fluid flow, while the finite difference method is employed to solve the energy equation. The effects of the Rayleigh number ( Ra ), the nanoparticle volume fraction ( ϕ ), and the Hartmann number ( Ha ) on heat transfer are systematically investigated. The results show that increasing the Rayleigh number from 10 ³ to 10 ⁶ enhances the average Nusselt number by up to 595.7%, illustrating the transition from conduction‐ to convection‐dominated heat‐transfer regime. The addition of copper nanoparticles further improves the thermal performance. For a nanoparticle volume fraction of ϕ = 0.1, the average Nusselt number increases by up to 35.94% compared with pure water. In contrast, the application of a magnetic field suppresses fluid motion through the Lorentz force. For Ha = 300 and Ra = 10 ⁶ , the average Nusselt number decreases by up to 80.06%, leading to a gradual return to a conduction‐dominated regime. These findings provide a better understanding of the combined effects of buoyancy, nanoparticle addition, and magnetic field strength on heat transfer in U‐shaped cavities, offering useful guidance for the design and optimization of thermal systems involving magnetohydrodynamic nanofluid flows.

This study focuses on numerically investigating thermal behavior within a differentially heated cavity filled with nanofluid with and without obstacles. Numerical comparison with previous studies proves the consistency and efficacy of the lattice Boltzmann method associated with a single relaxation time and its possibility of studying the nanofluid and heat transfer with high accuracy. Key parameters, including nanoparticle type and concentration, Rayleigh number, fluid basis, and obstacle position and dimension, were examined to identify optimal conditions for enhancing heat transfer quality. Principal findings indicated that increasing the Rayleigh number boosts buoyancy forces and alters vortex structure, improving the heat transfer efficiency across all nanofluid configurations. Moreover, nanoparticles with higher thermal conductivity, particularly Cu nanoparticles, exhibit slight improvements in heat transfer quality compared to Al2O3 nanoparticles, while higher nanoparticle concentrations generally lead to enhanced heat transfer effectiveness. Water-Cu nanofluids also demonstrate superior heat transfer performance over ethylene glycol-Cu nanofluids. Furthermore, the presence of obstacles at cavity extremities hampers overall heat transfer, whereas those positioned centrally augment heat exchange rates. This research offers valuable insights into optimizing convective heat transfer in nanofluid-filled cavities crucial for various engineering applications.

This study explores the impact of the magnetic field on heat transfer and entropy generation in a simulated electronic device using magnetohydrodynamic principles through a three-dimensional hybrid Runge–Kutta and lattice Boltzmann method. By varying Rayleigh number (Ra) from 103 to 106 and Hartmann number (Ha) between 0 and 100, the research evaluated the influence of these parameters on the average Nusselt number (⟨Nu⟩), heat exchange ratio (R), and entropy generation within a confined cavity. The results demonstrated that higher Ra values, particularly for Ra ≥105, significantly enhance convective heat transfer, as reflected by an increase in ⟨Nu⟩. However, introducing a magnetic field (Ha = 50, 100) diminishes this effect by damping fluid motion, resulting in a reduction of ⟨Nu⟩. The heat exchange ratio increases with Ra, reaching a peak value of 0.93 for Ha = 100 and Ra = 105, indicating improved heat dissipation under the magnetic influence. In terms of entropy generation, at low Ra (Ra = 103), thermal conduction is the predominant heat transfer mechanism, with entropy primarily generated due to thermal effects. As Ra increases to 106, the system shifted toward a convection-dominated regime, where entropy generated by viscous effects becomes more significant. Under stronger magnetic fields, particularly at Ha = 100, magnetic entropy generation emerges as a dominant factor, further increasing energy dissipation. These results suggested that magnetic fields can be strategically applied to optimize thermal management in electronic devices by controlling both heat transfer and entropy generation. The effectiveness of this approach, however, is highly dependent on the specific flow conditions and the strength of the applied magnetic field.

The present article provides a three‐dimensional numerical investigation of thermal convection and entropy generation. The lattice Boltzmann method, coupled with the finite difference approach, is applied to perform numerical simulations. The validation of these numerical approaches for thermal convection simulation and entropy calculation is performed by comparing our numerical results with those in the published literature for the case of benchmark problems. The physical geometry studied in this paper concerns a hot obstacle having the shape of a plus sign (+) placed in the center of a cubic enclosure. This cube is filled with air of a Prandtl number of 0.71 and characterized by two cold vertical walls. The heat exchange between the fluid and the hot body is studied as a function of the Rayleigh number (). The performed simulations show that the heat transfer rate can be increased by about 429% by switching from to . The entropy generation due to fluid friction, heat transfer, and total entropy are also calculated and discussed. For an irreversibility coefficient , the analysis of the results showed that for low values of the Rayleigh number (), the entropy production due to temperature gradients predominates over that produced by viscous effects. In the cases of and , entropy generation is due to both fluid friction and heat transfer. However, when the Rayleigh number becomes large (), entropy generation due to viscosity predominates over entropy production related to heat exchange. These results have important implications for the optimization and design of heat transfer systems in various industrial applications.

This research reports a numerical analysis of the enhancement of heat transfer on a backward-facing step in a rectangular channel containing inclined partitions

Numerical study of various physical phenomena in three dimensions has become a necessity to better understand the physical process than in two dimensions. Thus, in this paper, the code is elaborated to be adapted to the simulation of heat transfer in three dimensions. The numerical simulations are performed using a hybrid method. This method is based on the lattice Boltzmann approach for the computation of velocities, and on the finite difference technique for the calculation of temperature. The used numerical code is validated by examining the free convection in a cubic enclosure filled with air. Then, the analysis of the heat exchange between two cold vertical walls and a heated block located at the center of a cubic cavity is considered. The performed simulations showed that for a small value of the Rayleigh number (Ra=10³ for example), the fluid exchanges its heat almost equally with all hot surfaces of the obstacle. However, for large values of Ra (Ra≥10⁴), the numerical results found showed that the heat exchange rate is greater on the bottom face compared to the other faces of the obstacle.

The objective of this research is to study the fluid flow control allowing the reduction of aerodynamic drag around a square cylinder using two parallel partitions placed downstream of the cylinder using the lattice Boltzmann method with multiple relaxation times (MRT-LBM). In contrast to several existing investigations in the literature that study either the effect of position or the effect of length of a single horizontal or vertical plate, this work presents a numerical study on the effect of Reynolds number (Re), horizontal position (g), vertical position (a), and length (Lp) of the two control partitions. Therefore, this work will be considered as an assembly of several results presented in a single work. Indeed, the Reynolds numbers are selected from 20 to 300, the gap spacing (0 ≤ g ≤ 13), the vertical positions (0 ≤ a ≤ 0.8d), and the lengths of partitions (1d ≤ Lp ≤ 5d). To identify the different changes appearing in the flow and forces, we have conducted in this study a detailed analysis of velocity contours, lift and drag coefficients, and the root-mean-square value of the lift coefficient. The obtained results revealed three different flow regimes as the gap spacing was varied. Namely, the extended body regime for 0 ≤ g ≤ 3.9, the attachment flow regime for 4 ≤ g ≤ 5.5, and the completely developed flow regime for 6 ≤ g ≤ 13. A maximal percentage reduction in drag coefficient equal to 12.5%, is given at the critical gap spacing (gcr = 3.9). Also, at the length of the critical partition (Lpcr = 3d), a Cd reduction percentage of 12.95% was found in comparison with the case without control. Moreover, the position of the optimal partition was found to be equal to 0.8d i.e. one is placed on the top edge of the square cylinder and the second one is placed on the bottom edge. The maximum value of the lift coefficient is reached for a plate length Lp = 2d when the plates are placed at a distance g = 4. On the other hand, this coefficient has almost the same mean value for all spacings between the two plates. Similarly, the root means the square value of the lift coefficient (Clrms) admits zero values for low Reynolds numbers and then increases slightly until it reaches its maximum for Re = 300.