Response surface method and finite element-based investigation of uniform/nonuniform hydromagnetic convection of nanofluids inside a quarter-circular enclosure

Abstract

Under the influence of magnetohydrodynamics (uniform, periodic, and inclined), the current research evaluates the two-dimensional unsteady dynamics of natural convection flow and heat transportation in the quarter-circular domain considering the Brownian motion of nanoparticles. The nonlinear partial differential equations (PDEs) solver finite element method (FEM) of the Galerkin type is used for the numerical simulation. In addition, the central composite design-based response surface methodology (RSM) is applied to analyze the optimization of the outcomes. To assess the models’ significance in learning the optimum thermal transport efficiency of nanofluids, an analysis of variance is performed. The impacts of several physical characteristics such as Rayleigh number, nanoparticles volume fraction, mean Nusselt number, Brownian effects, size, and shape of the nanoparticles, and magnetic effects (uniform, periodic, and inclined) are examined. The heat transfer rate is significantly influenced by the magnetic field’s period and inclined angle. As an illustration, the optimal heat transmission is noted at λ = 0.75 and γ = 0°. When Brownian effects are included, the heat transfer rate increases by 23.44% and it rises by 39.34% as nanoparticle size drops from 100 nm to 10 nm. Moreover, compared to spherical nano-sized particles, blade-shaped nano-sized particles can improve the transportation of heat by 9.56%. Furthermore, the optimization of the independent factors (Ra, Ha, ϕ, and d p) on the response function Nu (average) is demonstrated by the statistical RSM technique, and a novel correlation is proposed based on FEM numerical data. The optimal thermal transport (Nu av = 24.045) is found when Ra = 10, Ha = 0, ϕ = 0.05, and d p = 10 nm. The model’s average Nusselt number’s R 2-value of 0.9927 indicates that the results are effective.