A review of two different, one-dimensional models of the vapor transport within the thermal diffusion cloud chamber (TDCC) is presented. In one case the assumption is made that there are no convective fluxes within the chamber and that heat and mass transport occur by diffusion only. Although in this model there are no restrictions on the transport of the two components within the chamber, the assumption of no velocities within the chamber results in an incorrect flux boundary condition for the background, carrier gas. The second model is based on the typical, stagnant background gas assumption and the equations of this model closely follow those of the classical Stefan tube problem in which there is transport of a volatile species through a noncondensible, carrier gas. Unfortunately, this model of the TDCC also suffers from the same inconsistencies as noted by several researchers for the Stefan tube. When the convective contributions to the flux are low in the stagnant background gas model, the two models give reasonably close results. For more convective situations, the supersaturation results can differ by more than 50%. One interesting feature of the zero velocity model is that it predicts a change in the supersaturation profile with pressure, whereas no pressure dependence is predicted with the stagnant background gas model. Unfortunately, the direction of this pressure change is opposite to that seen in experimental observations.