This paper deals with possible sources of convection arising from non-linear irreversible thermodynamic effects (non-Navier—Stokes fluid dynamics) and slip boundary conditions during typical processes of crystal growth from vapour phase. Attention is focused on the role played by thermal (Burnett) stresses and side-wall temperature creep in single component gases, but the extension and generalization to the more general case of binary mixtures is also indicated. A rigorous non-dimensional order of magnitude analysis is performed to compare these effects to the vapour transport mechanisms usually considered in vapour crystal growth fluid dynamics, e.g. buoyancy and Stefan-Nusselt flow; new characteristic velocities, lengths and corresponding non-dimensional numbers are introduced and discussed, and a priori conditions for the existence and characterization of all possible flow regimes are formulated. Then, a quantitative analysis of natural, thermal stress, and thermal creep convection is given by considering a simplified geometrical configuration, for which an analytical solution is derived.