In thermal diffusion cloud chambers (TDCCs), a decrease of nucleation rate with increasing total pressure was observed repeatedly, both near atmospheric pressures and at elevated pressures. Because this pressure effect was observed almost only using TDCCs, there have been some concerns inside the nucleation community whether it is not an experimental artifact. One questionable point in this context is that, to calculate the profiles of temperature and saturation ratio in TDCCs it is assumed that if the chamber is sufficiently "flat", a 1-d model can be used for the description of the transport processes in the central part of the chamber. The major concern in this context is that the heated chamber wall may cause a buoyancy driven convection that can propagate toward the center of the chamber and cause a slow motion of the gas mixture. To investigate this effect, a 2-d model of coupled mass, heat, and momentum transport in TDCCs has been developed. In the paper this model is described, and its predictive force is shown in comparison with a state-of-the-art 1-d model and with experimental data from the system n-propanol-He. Furthermore, results concerning the effects of wall heating, total chamber pressure, carrier gas, and chamber geometry on nucleation rates are presented. The influence of wall heating, on the nucleation rate was found to be significant when transport processes inside TDCC are dominated by buoyant convection. Using the 2-d model made it possible to partly (but not completely) explain the pressure effect observed in TDDCs. It was also shown that including the process of thermal diffusion in the model may have a significant influence on the resulting profiles of nucleation rate. It was confirmed that the choice of the carrier gas in the chamber can strongly influence stability of chamber operation. With respect to the optimal chamber geometry it was shown that TDCCs should have a diameter as small and a diameter-to-height ratio as large as possible to minimize the 2-d effects. All in all, it was proven that application of 1-d models to describe the heat and mass transfer in TDCC may lead to an erroneous determination of temperature, saturation ratio, and nucleation rate profiles.