The aim is to determine the role and influence of the hypothesis concerning both dynamics and radiative transfer in models of winds and mass loss of evolved stars, when the radiative force on dust grains plays a major role in the structuration of the circumstellar envelope of the star. The flow is described successively using two models coupling the grains-gas dynamics in a self-consistent way with radiative transfer for two different approaches of the dynamics: the Momentum Coupling Hypothesis and the Full Problem. Complete radiative transfer including multiple scattering, absorption and thermal emission is taken into account. The medium is not necessarily optically thin. In all cases, numerical iterations couple dynamics with transfer. This study emphasizes the importance of the drift velocity between the grains and the gas and the inertia of dust together with hydrodynamics and transfer coupling.