Nanofluid natural convection in trapezoidal annuli: Comparative effects of triangular, circular, and square inner walls

This work presents a novel numerical study on how inner-wall geometry influences natural convection in nanofluid-filled trapezoidal annular cavities, which has not been systematically addressed in previous studies. An Al2O3–water nanofluid is examined in three inner-wall configurations: square (Case 1), circular (Case 2), and triangular (Case 3). The governing equations, formulated under the Boussinesq approximation, are solved using the Galerkin finite element method and validated against established benchmark data. The numerical simulations were conducted for nanoparticle volume fractions in the range of ϕ=0.00–0.1, the characteristic length L=0.02–0.07m, and particle diameters of dp=1–60nm. These ranges were selected to represent typical conditions encountered in nanofluid-based natural convection systems. The results reveal that the circular wall enhances peak velocity, whereas the triangular wall provides more uniform velocity fields, higher average velocity magnitude, and consistently larger Nusselt numbers compared to the square and circular cases. In addition, the triangular geometry ensures more homogeneous temperature and concentration distributions, which is advantageous for stable thermal performance. The study also identifies optimal nanoparticle loading for enhanced convection, while showing that particle sizes beyond ∼60nm lead to suppressed transport phenomena. Aspect ratio and wall shape strongly influence skin-friction behavior, highlighting geometry as a key design parameter. Over time, velocity magnitude, Nusselt number, temperature, and nanoparticle concentration initially exhibit transient fluctuations before reaching steady-state, with Case 3 (triangular inner wall configuration) stabilizing fastest in velocity and concentration and achieving the highest heat transfer efficiency. These findings provide physically grounded design guidelines for engineering compact and efficient nanofluid-based thermal management systems.