Within the context of finite-time thermodynamics (FTTs) some models of convective atmospheric cells have been proposed to calculate the efficiency of the conversion of solar energy into wind energy and also for calculating the surface temperature of the planets of the solar system. One of these models is the Gordon and Zarmi (GZ) model, which consists in taking the sun-earth-wind system as a FTT-cyclic heat engine where the heat input is solar radiation, the working fluid is the earth's atmosphere and the energy in the winds is the work produced. The cold reservoir to which the engine rejects heat is the 3 K surrounding universe. In the present work we apply the GZ-model to investigate some features of the convective zone of the sun by means of a possible structure of successive convective cells along the well-established convective region of the sun. That is, from 0.714 𝑅 𝑆 up to 𝑅 𝑆 being 𝑅 𝑆 the radius of the sun. Besides, we estimate the number of cells of the model, the possible size of the cells, their thermal efficiency, and also their average power output. Our calculations were made by means of two FTT regimes of performance: the maximum power regime and the maximum ecological function regime. Our results are in reasonable agreement with others reported in the literature.