Natural Convection of MHD Double Diffusive Nanoencapsulated Phase Change Material (NEPCM) in the Annulus Between Concentric Horizontal Circular and Square Cylinders

The investigation focuses on the natural convection of magnetohydrodynamic (MHD) double-diffusive nanoencapsulated phase change material (NEPCM) in an annulus composed of square and concentric horizontal circular cylinders. The right, upper, and bottom walls of the outer square cylinder are cooled, while the inner circular cylinder is heated. The NEPCM particles are driven by natural convection inside the cavity. The PCM cores absorb some of the surrounding heat in the hot zone as latent heat, which they then release when they solidify in the cold zone. The PCM cores also experience a phase transition from solid to liquid. It is demonstrated that partial differential equations govern the conservation of mass, velocity, and heat in NEPCM suspensions. After the governing equations are transformed into nondimensional forms, the finite element method is used to solve them. Among the significant parameters that have been numerically simulated are the Rayleigh number, (10⁴, 10⁵, and 10⁶), the Hartmann number, 0 ≤ Ha ≤ 50, the Stefan number, 0.15 ≤ Ste ≤ 0.7, the fusion temperature, 0.1 ≤ θ_f ≤ 0.9, the volume fraction, 0.0 ≤ ϕ ≤ 0.05, the Lewis number, 1 ≤ Le ≤ 5, the aspect ratio, 0.1 ≤ AR ≤ 0.25, and the buoyancy ratio, −2 ≤ Br ≤ 2. To verify the accuracy of the simulations, the results go through a grid check and a validation test. The findings indicate that the (Formula presented.) and (Formula presented.) increase with Br. On the other hand, when ϕ increases, (Formula presented.) increases and (Formula presented.) decreases. As Ra rises, so do the local Nu and Sh. When AR rises from 0.10 to 0.25 at Ra = 10⁶ and Le = 5, the (Formula presented.) and (Formula presented.) decrease by 34.15% and 34.05%, respectively.