We revised the treatment of interstellar dust in the KOSMA-tau PDR model code to achieve a consistent description of the dust-related physics in the code. The detailed knowledge of the dust properties is then used to compute the dust continuum emission together with the line emission of chemical species. We coupled the KOSMA-tau PDR code with the MCDRT (multi component dust radiative transfer) code to solve the frequency-dependent radiative transfer equations and the thermal balance equation in a dusty clump under the assumption of spherical symmetry, assuming thermal equilibrium in calculating the dust temperatures, neglecting non-equilibrium effects. We updated the calculation of the photoelectric heating and extended the parametrization range for the photoelectric heating toward high densities and UV fields. We revised the computation of the H2 formation on grain surfaces to include the Eley-Rideal effect, thus allowing for high-temperature H2 formation. We demonstrate how the different optical properties, temperatures, and heating and cooling capabilities of the grains influence the physical and chemical structure of a model cloud. The most influential modification is the treatment of H2 formation on grain surfaces that allows for chemisorption. This increases the total H2 formation significantly and the connected H2 formation heating provides a profound heating contribution in the outer layers of the model clumps. The contribution of PAH surfaces to the photoelectric heating and H2 formation provides a boost to the temperature of outer cloud layers, which is clearly traced by high-J CO lines. Increasing the fraction of small grains in the dust size distribution results in hotter gas in the outer cloud layers caused by more efficient heating and cooler cloud centers, which is in turn caused by the more efficient FUV extinction.
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