Parametric study of MHD mixed convection heat transfer in a trapezoidal cavity with NEPCM suspension and rotating star-shaped heat source

• This study examines thermal performance of NEPCM in a chamber with a hot rotating star-shaped body. • Higher Re and Da increase Nu, while higher Ha decreases Nu. • Adding 8% NEPCM raises heat transfer by ~1.5% without affecting flow dynamics. • Higher Re and Da boost average Nu by up to 47% and 23%; 8% NEPCM adds ~2% due to viscosity. A comprehensive numerical investigation of two-dimensional, steady, laminar magneto–hydrodynamic (MHD) mixed convection in a trapezoidal cavity filled with a nano-encapsulated phase–change material (NEPCM) suspension is presented. A star‑shaped heat source located at the cavity centre rotates with a constant angular velocity, while a uniform transverse magnetic field acts on the flow. The physical model couples the energy equation with a temperature–dependent effective specific heat formulation to represent the phase transition of NEPCM particles. The dimensionless governing equations are solved using a Galerkin weighted residual finite‑element method. Detailed parametric studies are carried out for Reynolds number Re = 10–1000, Darcy number Da = 10 −6 –10 −2 , Hartmann number Ha = 0–100 and NEPCM volume fraction φ = 0–0.08. Grid independence and code verification against benchmark solutions are demonstrated. Results reveal that increasing Re and Da enhances the average Nusselt number by up to 47 % and 23 %, respectively, whereas an 8 % NEPCM loading yields a modest ≈2 % enhancement due to increased slurry viscosity. Lorentz forces progressively damp convective rolls, reducing heat transfer at Ha > 40. The unique combination of a rotating internal heater, complex cavity geometry, and phase‑change suspension provides new insights for the design of compact thermal energy‑storage and electronics‑cooling devices.