Enhanced thermal management with NE-PCM–water in a fan-shaped sinusoidal enclosure under linear side-wall heating

Improving thermal management through suspensions of Nano-Encapsulated Phase Change Materials (NE-PCM) in conventional fluids is essential for optimizing thermal system performance, as it influences flow behavior and thermal distributions in complex-shaped enclosures, which are crucial for enhancing system efficiency. In this context, the present article investigates the flow and thermal behavior of NE-PCM–H2O inside a closed enclosure, where all walls are sinusoidally designed to resemble a fan-like structure. The enclosure features varying undulation configurations, with the bottom wall heated, the top wall cooled, and the side walls exhibiting a linearly varying temperature. The NE-PCM consists of an n-nonadecane core encapsulated in a polyurethane shell, suspended in water. Experimental-based correlations for effective viscosity and thermal conductivity, as functions of suspension volume fraction, are employed to model the governing equations, which are then non-dimensionalized and solved using the Galerkin Finite Element Method. The impact of the Rayleigh number (103≤Ra*≤5×104) and the non-dimensional fusion temperature (0.1≤θf*≤0.9) on heat transfer is explored in the enclosure with varying undulations (0.3≤A*≤0.4), focusing on streamlines, isotherms, heat capacity ratio, and Nusselt numbers. Increasing the Rayleigh number from 103 to 5×104enhances the Nusselt number by 34.35%, 17.54%, and 5.98% for A⁎ = 0.3, 0.35, and 0.4, respectively. Additionally, increasing A* from 0.3 to 0.4 raises the Nusselt number by 37.45%, 37.06%, and 8.43% for Ra* = 103, 104, and 5×104, highlighting the significant influence of both parameters on heat transfer. A sensitivity analysis of the fusion temperature parameter further reveals that the highest average Nusselt number is attained at θf*=0.6, with enhanced heat-transfer performance occurring within the range 0.5≤ θf*≤0.7 for enclosures with higher undulation.