The equations describing Compton scattering in an optically thick fluid flow are derived under the diffusion approximation. The relative importance of the bulk and random motions of the scattering electrons is discussed. In a converging fluid flow of speed u, bulk acceleration of photons dominates thermal Comptonization when u ≳ |(12 kT_ e/m_ e)1/2|.
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Blandford et al. (1981) studied this question.