FEM simulation and optimization for thermal performance of a hybrid magneto-nanofluid in an inclined free convective energy system

In heat exchangers, solar collectors, and geophysical transport, the temperature difference is significant, so the linear form of the density-temperature approximation (the Boussinesq approximation) is inadequate to describe actual density variations. Thus, the current study took into account the effect of nonlinear buoyancy on the thermal performance of a homogeneous nanofluid with hybrid nanoparticles in a free convective inclined energy system. In addition, response surface methodology with central composite design (RSM-CCD) is implemented to build a quadratic model based on three factors and levels (Ha, α, ϕ). To perform thermal evaluation, the experimental correlations are utilized with dimensionless controlling parameters such as Rayleigh number (Ra = 103 to 106), Hartmann number (Ha = 0 to 50), nanoparticle volume fraction (ϕ = 0 to 0.02) and angle of inclination (α = 0 to π) using Galerkin finite element method (GFEM) with a refined mesh (degree of freedoms (DOFs) = 208977, domain elements = 25636 and boundary elements = 858) for grid independent results. According to RSM-CCD, the Hartmann number has a significant impact on the thermal behavior of energy system. Also, the maximum average Nusselt number (Nur = 5.4938) is achieved with the optimal combination of key parameters i.e., Ha=36.707, α=0.5236 and ϕ=0.001.