Multiple-Relaxation-Time Lattice Boltzmann Simulation of Soret and Dufour Effects on the Thermosolutal Natural Convection of a Nanofluid in a U-Shaped Porous Enclosure

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.