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Hydrogen bulk mobility plays an important role in determining a wide range of materials and electronic properties of hydrogenated amorphous silicon (a-Si:H). The existence of two types of hydrogen traps plays an important role in controlling hydrogen mobility in, and evolution of hydrogen from a-Si:H, however, theoretical and experimental literature values for the trap energetics vary considerably. We have developed a mean-field reaction-diffusion model which explicitly includes two trap states and realistic surface processes to model hydrogen evolution from a-Si:H. Modern numerical techniques were required to solve this challenging problem over the wide range of temperatures and concentrations encountered in typical hydrogen evolution experiments. The model is based on a number of experimentally established parameters. Comparison of our rigorous model with temperature programmed hydrogen evolution experiments provides a powerful method for characterizing the energetics, trap concentrations and diffusivity of hydrogen in a-Si:H.