CPU thermal management using nano-encapsulated phase change material: Numerical investigation of orientation and magnetic field effects on heat transfer and entropy generation

This study numerically investigates natural convection and entropy generation in an inclined square cavity for CPU thermal management. A heated CPU-shaped block with three horizontal fins is attached to the left wall. The cavity is filled with a water–NEPCM suspension. The NEPCM capsules consist of a polyurethane shell enclosing an n-nonadecane core, which absorbs and releases latent heat during solid–liquid transition. The governing equations include the magnetohydrodynamic (MHD) body force and are solved using the Galerkin finite element method. Six controlling parameters are examined: Rayleigh number ( 10³ ≤ Ra ≤ 10⁶ ), Hartmann number ( 0 ≤ Ha ≤ 75 ), NEPCM volume fraction ( 0 ≤ ϕ ≤ 0.035 ), Stefan number ( 0.25 ≤ Ste ≤ 0.75 ), dimensionless fusion temperature ( 0.1 ≤ θ f ≤ 0.9 ), and cavity inclination angle ( 0° ≤ γ ≤ 90° ). The analysis is conducted under an isothermal-heater idealization. All reported enhancements are therefore dimensionless parametric trends rather than absolute cooling metrics. Increasing Ra from 10³ to 10⁶ raises Nu av from ≈1.8 to ≈7.2. At Ra = 10⁶ , increasing ϕ from 0 to 0.035 enhances Nu av by ≈30%. A refined angular sweep locates the optimum inclination in the range γ ≈ 30°–35°, with a peak Nu av at γ = 35° that exceeds the horizontal case by ≈14% at Ra = 10⁵. The magnetic field acts as a passive damping mechanism: at Ha = 75, Nu av decreases by ≈35% and the total entropy generation S total decreases by ≈74%. Intermediate fusion temperatures ( θ f ≈ 0.4–0.5) maximize the engagement of the phase-change zone with the primary convective path. These findings provide parametric design guidance for passive NEPCM–MHD electronic-cooling configurations.