Heat switches are widely used in cryogenic systems, playing an important role in controlling thermodynamic cycles and accelerating the cooling of cryogenic components. Among them, the convective heat switch, normally made from two identical tubes, realizes the on/off state by the presence/absence of a natural convective gas loop, which can be used to shorten the cooling time of cryogenic systems. In order to further understand the heat transfer mechanism of the passive convective heat switch, three-dimensional steady-state models of twin-tube and triple-tube configurations are established in this paper. The simulations of the twin-tube heat switch with different hot-end heat loads and different charge pressures are conducted and compared with the experimental results. The influence of the asymmetry of two tubes on thermal conductance is analyzed. Meanwhile, the simulation and comparison of twin-tube and triple-tube convective heat switches with equal void volume are carried out. It is found that the convective heat transfer performance of the twin-tube heat switch is slightly better than the triple-tube configuration, and when the cold-end temperature is 4 K and the hot end is applied 0.3 W heat load, the hot-end temperature is stable at 11.57 K, leading to a thermal conductance of 39.4 mW/K.