Context. Cometary dust particles are subjected to various forces after being lifted off the nucleus. These forces define the dynamics of dust, trajectories, alignment, and fragmentation, which, in turn, have a significant effect on the particle distribution in the coma. Aims. We develop a numerical thermophysical model that is applicable to icy cometary dust to study the forces attributed to the sublimation of ice. Methods. We extended the recently introduced synoptic model for ice-free dust

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... ticles to ice-containing dust. We introduced an additional source term to the energy balance equation accounting for the heat of sublimation and condensation. We use the direct simulation Monte Carlo approach with the dusty gas model to solve the mass balance equation and the energy balance equation simultaneously. Results. The numerical tests show that the proposed method can be applied for dust particles covering the size range from tens of microns to centimetres with a moderate computational cost. We predict that for an assumed ice volume fraction of 0.05, particles with a radius, r 1 mm, at 1.35 AU, may disintegrate into mm-sized fragments due to internal pressure build-up. Particles with r < 1 cm lose their ice content within minutes. Hence, we expect that only particles with r > 1 cm may demonstrate sustained sublimation and the resulting outgassing forces.