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The present work investigates the magnetohydrodynamic (MHD) convective heat transport of hybrid nanofluids in a chamber with multiple heaters (such as hot microchips). The multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) and graphics processing unit (GPU) computing are used here. The present study is important due to its relevance to real-world applications, the use of advanced simulation techniques, the consideration of hybrid nanofluids, the inclusion of magnetohydrodynamics, and the identification of critical parameters influencing heat transfer. Thermally homogeneous blocks are set at the bottom of a rectangular enclosure filled with ethylene glycol Cu-Al2O3 hybrid nanofluids with temperature-dependent viscosity. The cold temperature of the enclosure's left and right walls and the bottom and top surfaces is kept at adiabatic conditions. The numerical outcomes for the various parameters Rayleigh number (1 0 4 ≤ Ra ≤ 1 0 6 ), volume fraction (0.00 ≤ ϕ ≤ 0.04), Hartmann number (0 ≤ Ha ≤ 60), and viscosity variation parameter (0 ≤ ε ∗ ≤ 5) are presented in terms of streamlines, isotherms, and the peripheral local and average Nusselt numbers for the heated chips. The results demonstrated that inside the chamber, the Rayleigh number (Ra), the Hartmann number (Ha), and the volume fraction of nanoparticles (ϕ) have the highest impact on the heat transfer rate for hybrid nanofluid. For increased Ha from 0 to 20, while ϕ = 0.0 and Ra = 1 0 6 , average Nusselt number decreased with 13.65%. For the same case, if the volume fraction was increased to ϕ = 0.04 , then the average Nusselt number decreased 14%. Finally, a sensitivity analysis was done to analyze the system's correctness and effectiveness to determine the significance of the specified parameters. [ABSTRACT FROM AUTHOR]

This article reports an investigation of the Soret and Dufour effects on the double-diffusive natural convection of A l 2 O 3 - H 2 O nanofluids in a U-shaped porous enclosure. Numerical problems were resolved using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). The indented part of the U-shape was cold, and the right and left walls were heated, while the bottom and upper walls were adiabatic. The experimental data-based temperature and nanoparticle size-dependent correlations for the A l 2 O 3 -water nanofluids are used here. The benchmark results thoroughly validate the graphics process unit (GPU) based in-house compute unified device architecture (CUDA) C/C++ code. Numeral simulations were performed for a variety of dimensionless variables, including the Rayleigh number, ( R a = 10 4 , 10 5 , 10 6 ), the Darcy number, ( D a = 10 − 2 , 10 − 3 , 10 − 4 ), the Soret number, ( S r = 0.0 , 0.1 , 0.2 ), the Dufour number, ( D f = 0.0 , 0.1 , 0.2 ), the buoyancy ratio, ( − 2 ≤ B r ≤ 2 ), the Lewis number, ( L e = 1 , 3 , 5 ), the volume fraction, ( 0 ≤ ϕ ≤ 0.04 ), and the porosity, ϵ = ( 0.2 − 0.8 ), and the Prandtl number, P r = 6.2 (water) is fixed to represent the base fluid. The numerical results are presented in terms of streamlines, isotherms, isoconcentrations, temperature, velocity, mean Nusselt number, mean Sherwood number, entropy generation, and statistical analysis using a response surface methodology (RSM). The investigation found that fluid mobility was enhanced as the R a number and buoyancy force increased. The isoconcentrations and isotherm density close to the heated wall increased when the buoyancy force shifted from a negative magnitude to a positive one. The local N u increased as the Rayleigh number increased but reduced as the volume fraction augmented. Furthermore, the mean N u ( N u ¯ ) decreased by 3.12 % and 6.81 % and the S h ¯ increased by 83.17 % and 117.91 % with rising Lewis number for ( R a = 10 5 and D a = 10 − 3 ) and ( R a = 10 6 and D a = 10 − 4 ), respectively. Finally, the B r and S r demonstrated positive sensitivity, and the R a and ϕ showed negative sensitivity only for higher values of ϕ based on the RSM. [ABSTRACT FROM AUTHOR]

This study aims to consider lattice Boltzmann method (LBM)–magnetohydrodynamics (MHD) data to develop equations to predict the average rate of heat transfer quantitatively. The present approach considers a 2D rectangular cavity with adiabatic side walls, and the bottom wall is heated while the top wall is kept cold. Rayleigh–Bénard (RB) convection was considered a heat-transfer phenomenon within the cavity. The Hartmann ( H a ) number, by varying the inclination angle (θ), was considered in developing the equations by considering the input parameters, namely, the Rayleigh ( R a ) numbers, Darcy ( D a ) numbers, and porosity (ϵ) of the cavity in different segments. Each segment considers a data-driven approach to calibrate the Levenberg–Marquardt (LM) algorithm, which is highly linked with the artificial neural network (ANN) machine learning method. Separate validations have been conducted in corresponding sections to showcase the accuracy of the equations. Overall, coefficients of determination ( R 2 ) were found to be within 0.85 to 0.99. The significant findings of this study present mathematical equations to predict the average Nusselt number ( N u ¯ ). The equations can be used to quantitatively predict the heat transfer without directly simulating LBM. In other words, the equations can be considered validations methods for any LBM-MHD model, which considers RB convection within the range of the parameters in each equation. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamical free convective heat transfer flow of non‐Newtonian power‐law fluids has been analyzed numerically. For numerical simulation, the multiple‐relaxation‐time (MRT) lattice Boltzmann method (LBM) has been employed based on graphics process unit (GPU) computing. The computational domain is a two‐dimensional square cavity with thermally adiabatic upper and base walls, uniformly heated left wall, and sinusoidal heat distribution on the right wall. There is no research on non‐Newtonian fluid using MRT‐LBM using this configuration. Hence it is a new study in this field and novel results have been achieved with the magnetic field effect and sinusoidal wall temperature. The numerical simulations are carried out for different vital parameters such as thermal Rayleigh number (Ra), Hartmann number (Ha), and power‐law index (n) to study the characteristics of heat transport along with the flow physics inside the square enclosure. The streamlines and isotherms elucidate the distribution of fluid flow and energy within the cavity. The energy transfer phenomena are interpreted as the local Nusselt number (Nu) distribution and the average Nusselt number (Nu¯) along the heated wall. Computational results show that the rate of energy transfer is attenuated due to the augmentation of the magnetic field. However, (Nu¯) exhibits direct correspondence with the Rayleigh number and an inverse relation with the power‐law index (n). The elevation of Hartmann number (Ha) results in the diminution of Nu and Nu¯ for pseudoplastic fluid (n<1) by 82.65% and 86.04%, respectively. Moreover, the temperature distribution (θ) of Ra=105 amplifies by 95.83% compared to Ra=104 as the fluid transitions from pseudoplastic to dilation behavior. For GPU computing, the NVIDIA CUDA C programming platform is used in the present study. [ABSTRACT FROM AUTHOR]

The magnetic field effect on natural convection flow of power-law (PL) non-Newtonian fluid has been studied numerically using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). A two-dimensional rectangular enclosure with differentially heated at two vertical sides has been considered for the computational domain. Numerical simulations have been conducted for different pertinent parameters such as Hartmann number, Ha = 0 − 2 0 , Rayleigh number, Ra = 1 0 4 − 1 0 6 , PL indices,  n = 0. 6 –1.4, Prandtl number, Pr = 6. 2 (water) , to study the flow physics and heat transfer phenomena inside the rectangular enclosure of aspect-ratio AR = 2. 0. Numerical results show that the heat transfer rate, quantified by the average Nusselt number, is attenuated with increasing the magnetic field, i.e. the Hartmann number (Ha). However, the average Nusselt number is increased by increasing the Rayleigh number, Ra and decreasing the PL index,  n. Besides, the generation of entropy for non-Newtonian fluid flow under the magnetic field effect has been investigated in this study. Results show that in the absence of a magnetic field, Ha = 0 , fluid friction and heat transfer irreversibilities, the total entropy generation decreases and increases with increasing n and Ra , respectively. In the presence of the magnetic field, Ha > 0 , the fluid friction irreversibility tends to decrease with increasing both the shear-thinning and shear thickening effect. It is noteworthy that strengthening the magnetic field leads to pulling down the total entropy generation and its corresponding components. All simulations have been performed on the Graphical Processing Unit (GPU) using NVIDIA CUDA and employing the High-Performance Computing (HPC) facility. [ABSTRACT FROM AUTHOR]

Lattice Boltzmann method is used to investigate the Rayleigh–Bénard convection of magnetohydrodynamic fluid flow inside a rectangular cavity filled by porous media. The Brinkman–Forchheimer model is considered in the simulation to formulate a porous medium mathematically, and the multi-distribution function model is considered to include the magnetic field effect with different inclination angles. The water is considered as the working fluid, which is electrically conducting. A comprehensive analysis of the impact of governing dimensionless parameters is performed by varying Rayleigh (Ra), Hartmann (Ha), and Darcy (Da) numbers, porosity (ϵ ), and inclination angles (ϕ ) of the applied magnetic field. Numerical results are evaluated in the form of streamlines, isotherms, and the rate of heat transfer in terms of the local and average Nusselt number as well as the entropy generation due to the irreversibility of the fluid friction, temperature gradient, and magnetic field effects. The results imply that increasing Ha and decreasing Da reduce the rate of heat transfer. The average Bejan number Be avg increases for increasing the Hartmann number. On the other hand, augmenting Ra and ϵ improves the heat transfer rate. It is also found that the change of the magnetic field inclination angle ϕ changes the rate of heat transfer and entropy generation. [ABSTRACT FROM AUTHOR]

This study is aimed to investigate the natural convection heat transfer from discrete heat sources (similar to heated microchips) using Bhatnagar‐Gross‐Krook lattice Boltzmann method via graphics process unit computing. The simulation is carried out separately for three and six heated blocks model for different Rayleigh numbers and fixed Prandtl number, Pr=0.71 (air). The uniformly heated blocks are placed at the bottom wall inside a rectangular enclosure. The enclosure is maintained by the cold temperature at its left and right walls. The top and bottom surface is maintained by adiabatic conditions apart from the regions where blocks are attached to the bottom wall. The numerical code is validated with the benchmark heat transfer problem of side‐heated square cavity as well as with an experimental study for one discrete heat source. The rate of heat transfer is presented in terms of the local Nusselt and average Nusselt number for each block. It is found that the heat transfer rate becomes maximized in the leftmost and rightmost blocks due to the adjacent cold walls. It is found that the number of blocks and their positions play a substantial role in determining their collective performance on the heat transfer rate. [ABSTRACT FROM AUTHOR]

In the present investigation the airflow and heat transfer for mixed convection have been simulated for a model general ward of hospital with six beds and partitions using the Lattice Boltzmann Method (LBM). Three different Reynolds numbers 100, 250, and 350 have been considered. Bounce-back condition has been applied at the wall. Results have been represented in three different case studies and the changes have been discussed in terms of streamlines and isotherms. Code validation has also been included before going through the simulation process and it shows good agreement with previously published papers when the comparison is made on average Nusselt number. Results show that the pattern of indoor airflow is varied in each and every case study due to the effect of mixed convection flow and placement of partition. In addition, the changes in average rate of heat transfer indicate that patients closer to inlet get the most air and feel better and if any patient does not need much air, he or she should be kept near the outlet to avoid temperature related complications. [ABSTRACT FROM AUTHOR]

A modified power-law (MPL) viscosity model of non-Newtonian fluid flow has been used for the multiple-relaxation-time (MRT) lattice Boltzmann methods (LBM) and then validated with the benchmark problems using the graphics process unit (GPU) parallel computing via Compute Unified Device Architecture (CUDA) C platform. The MPL model for characterizing the non-Newtonian behavior is an empirical correlation that considers the Newtonian behavior of a non-Newtonian fluid at a very low and high shear rate. A new time unit parameter (λ) governing the flow has been identified, and this parameter is the consequence of the induced length scale introduced by the power law. The MPL model is free from any singularities due to the very low or even zero shear-rate. The proposed MPL model was first validated for the benchmark study of the lid-driven cavity and channel flows. The model was then applied for shear-thinning and shear-thickening fluid flows through a backward-facing step with relatively low Reynolds numbers, R e = 100–400. In the case of shear-thinning fluids ( n = 0.5 ), laminar to transitional flow arises while R e ≥ 300 , and the large vortex breaks into several small vortices. The numerical results are presented regarding the velocity distribution, streamlines, and the lengths of the reattachment points. [ABSTRACT FROM AUTHOR]

The natural or free convection flow in an open cavity filled with ethylene glycol- Al 2 O 3 nanofluid has been integrated numerically using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) with the Graphics Process Unit (GPU) acceleration. The applications of this type of problem frequently appear in open-door ovens and refrigerators and in the cavities of central solar receptors. The ceiling and bottom walls of the cavity are thermally adiabatic. The right side of the cavity is fully opened while heat flux condition is imposed on its opposite wall. The thermal conductivity of the nanofluid varies with fluid temperature. Numerical simulations have been conducted for a fixed Prandtl number, Pr = 16.6 , with varying other controlling parameters, i.e., the Rayleigh number from Ra = 10 5 to 10 7 , and nanoparticle volume fraction from 0 to 5 %. The streamlines, isotherms, mid-line temperature and velocity distributions, and the rate of heat transfer regarding the Nusselt number have been presented in this article. The isolines and tabular form give the local and total entropy generation due to the fluid friction and temperature gradients. The tangential and normal velocity components grow dramatically as Ra increases; however, the temperature diminishes with Ra. Also, the locally distributed Nusselt number increases in magnitude with nanofluids' volume fraction and Rayleigh number. The total entropy enhances significantly for the augmentation of the nanoparticles volume fraction, and the entropy due to fluid friction dominates over the entropy generated by the temperature gradients. [ABSTRACT FROM AUTHOR]