Convective transport in a nanofluid-filled annulus with an eccentric hypocycloid within a square disk

Considering varying cusp numbers, we investigate the time-dependent, incompressible natural convective flow of an iron oxide-water nanofluid within an annulus formed between a square and a concentric hypocycloid. The vertical walls of the annulus are treated as relatively colder walls, while the bottom wall of the square disk and the inner hypocycloid wall act as heat sources. The outer upper wall of the square is considered adiabatic. We transform the dimensional, nonlinear, and strongly coupled fundamental equations of nanofluids in Cartesian coordinates into non-dimensional equations. We utilize the Galerkin finite element method to solve the governing equations. This study comprehensively explores the flow and heat transfer of nanofluids, considering the essential parameters relevant to the problem. The results highlight a remarkable observation, as the ferric oxide-water nanofluid exhibits significantly enhanced heat transfer compared to the conventional fluid. The precise positioning of the hypocycloid in the cusp configuration represents a critical phenomenon that substantially improves the flow and heat transfer rates of the nanofluid. The three cusped hypocycloids positioned on the inner wall of the annulus perpendicular to the horizontal axis result in a nanofluid flow configuration and heat transfer that surpasses other configurations and cusp numbers studied in the analysis. Notably, heat transfer exhibits a discernible increase with an increase in the nanoparticle volume fraction (maximum 3vol%), while it declines with an increase in the nanoparticle diameter. The intricate relationship between the nanoparticle diameter, volume fraction, cusp number, and hypocycloid configuration substantially influences the friction factor and particle-surface interactions. As the number of cusps on the inner surface increases, the velocity magnitude, Nusselt number, and concentration profiles near the boundary layer decrease, while the fluctuations of the middle annulus indicate the combined influence of nanoparticle dispersion and the formation of the annulus boundary layer due to the orientation of hypocycloidal cusps. Furthermore, an increase in the particle diameter and the sharpness of the corners of the hypocycloid lead to a proportional increase in the nanofluid flow resistance within the annulus.