Numerical Investigation on Natural Convection Heat Transfer of Spherical Cactus-like Bodies Based on Constructal Theory

In both nature and engineering, there are many structures similar to spherical cacti with ribs. In this study, we investigated numerically the laminar natural convection heat transfer characteristics of spherical cactus-like bodies. An analytical framework was established based on constructal theory, and the maximum temperature as well as the temperature distribution factor were obtained via numerical simulations. The results show that for a fixed total volume and rib volume ratio (ω = 17%), there exists an optimal rib number nopt = 34 at which the maximum temperature Tmax reaches its minimum value of 58.97 °C, 5.45 °C lower than that of the smooth sphere. The body with a lower maximum temperature also features a larger low-temperature region. Under specified conditions, as the Rayleigh number increases from 105 to 107, nopt increases from 24 to 42; as the thermal conductivity increases from 0.12 to 3 W/(m·K), nopt rises from 24 to 36; conversely, a larger rib volume ratio (ω = 30%) reduces nopt accordingly. Compared with the single-scale rib structure, the adoption of a two-scale rib design or ellipsoidal designs further improves the heat transfer performance, with the temperature distribution factor indicating a larger low-temperature region. The results of this study can provide a reference for the thermal design of cactus-like engineering devices and offer a heat transfer perspective for understanding the heat dissipation mechanism of cactus-type plants in nature.