A simplified analytical model of the coupled flow, heat, and mass transfer in the core region of a rectangular, low aspect ratio flow channel has been developed that can predict the magnitude of the flows and the convective transport resulting from small transverse steady and periodic accelerations typically associated with manned spacecraft. The effects of stabilizing and destabilizing axial gradients are determined for both steady and time dependent transverse accelerations. It is found that the time average of the heat and mass transport scales as the square of the Grashof number and is inversely proportional to the 7/2 power of the frequency. Furthermore, it is shown that the effects of multi-frequency disturbances are additive making it possible to integrate over a properly weighted power spectral density spectrum in order to obtain the net flow and transport. The relative transport from steady and periodic accelerations was estimated for the types of experiments germane to this model that are typically carried out in microgravity. It was also found that a stabilizing axial gradient has little effect on the flows and transport at higher frequencies, suggesting the possibility of testing the g-jitter predictions on the ground. Finally it is shown that the start-up transients can have profoundly different effects depending on the phase of the acceleration at the starting time.