The thermal fluidynamic behaviour of a variety of fluids filling either vertical cylinders or vertical annuli under external conditions giving rise to natural convective motions has been thoroughly investigated, both experimentally and numerically, because of the several possible engineering applications that can be well approximated and described by these kinds of configurations. This study aims at investing through a numerical analysis the mixed convection arising inside cavities formed between two horizontal adiabatic disks and two isothermally and differentially heated vertical cylindrical walls, one of which is rotating. Previous studies reported and discussed the role played by both the Rayleigh number the Reynolds number for the case of the rotation of either the inner or the external wall and for a specified geometry of the cavity. The focus of the present study is to analyse the role played by the aspect ratio, A=H/(Re-Ri), for the case of rotating inner cylinder. It is reported that this role is particular relevant with respect to the flow structures established within the cavity and, as a consequence, also with respect to the Nusselt number.