MRT-LB simulation and response surface analysis of natural convection of non-Newtonian ferrofluid in an enclosure with non-uniformly heated radiator through GPU computing

Abstract

The multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) has been applied to numerically analyze the natural convection of non-Newtonian ferrofluid in an enclosure with a horizontal plate or radiator that is not uniformly heated. The left and right walls of the enclosure are cold (Tc), while the bottom and upper walls are assumed to be adiabatic. Simulations using numerical models are run for a variety of dimensionless variables, including Rayleigh numbers (Ra=104,105,106), Hartmann numbers (Ha=0,20,40,60,80), power-law index (n=0.6,0.8,1.0,1.2,1.4), magnetic field inclination angles (γ=0,π/4,π/2,3π/4), and the maximum ferroparticle volume fractions is 6% (ϕ=0.06). The numerical results are reported in the form of isotherms, streamlines, velocity, temperature, mean Nusselt number, and entropy production. The study found that the Nu¯ rises with the increment of the Rayleigh number but decreases with the enhancement of the Ha, n, and ϕ. The temperature declines rapidly when the magnetic field inclination angle values increase to γ=90°, then gains temperature. The velocity and temperature both increase as the ϕ increases. For increasing the power-law index, the Nu¯ grows by 1.6% in the case of Ra=104 but falls by 14.56% and 54.87% when Ra=105 and Ra=106, respectively. The entropy profile is discussed in detail. The Be number is more significant than 0.5 for various n at Ra=104 and 105, suggesting that entropy formation is primarily due to heat gradients. Response surface methodology (RSM) also describes the numerical results with variable Ra numbers (104, 105, 106), n=0.6,1.0,1.4), angles (γ=0,π/2,3π/4), Ha=40 and ϕ=0.06. Finally, the residual plots, 2D and 3D plots are described. All the simulations are conducted by the GPU (Graphics Processing Unit) computing with the NVIDIA CUDA C/C++ platform.