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tokens: however, is insufficient for the pressure gradient to change sign. The top panel of Figure 6 shows the mdot1e-7 case with parameters as in Table 2 , but N 2 = 3 and N 3 = 170. It shows that the active zone inside the rounded-off rim is in its final size. After the active zone has reached a certain size small temperature deviations start to occur and travel through it. These small deviations manifest in the depiction as walls where the dust is present. Since the simulation does not include latent heat it is not possible to decide whether these small deviations have to occur or not, but they were consistently found for every parameter set that produced a dust-free zone. The surface density in Figure 7 mirrors the cavity that is also present in Figure 6 . The dust density falls to g cm −2 in the dust-free zone. To further analyze the equilibrium in the dust-free zone an alternative sublimation formula is in progress. Figure 7. Comparison of gas (solid line) and dust (dotted line) surface density for model mdot1e-7 . The optical depth at constant radiusfor near-infrared radiation in Figure 8 suggests that the dust-free zone forms after a large enough depth in the θ direction is reached because diffusion of radiation energy is no longer sufficient to cool the disk. Figure 8. Vertical optical depth in NIR for model mdot1e-7 . 5. Discussion This work represents an early stage in developing a self-consistent model of the inner rim of protoplanetary disks. In this section some important limitations of the model will be discussed. The simplifications introduced in Flock et al. ( 2016 ), such as a uniform dust-to-gas ratio in the shadowed region and a non-frequency-dependent gas opacity are also applied in this work. A more elaborate sublimation formula is needed in the future, especially with respect to the dust-free cavity inside the disk. A detailed implementation of gas line radiation transfer would go beyond the scope of this work. Further, the value of α was chosen to be constant throughout the box. However, the strength of the turbulence is expected to be influenced by the temperature and could be lower in MRI inactive regions (Lesur et al. 2014 ; Turner et al. 2014 ; Simon et al. 2015 ). A temperature-dependent α will be explored in further work. The temperature deviations and dust walls described at the end of Section 4.3 will have to be further scrutinized in combination with the modeling of the dust-to-gas ratio. Small differences in the temperature can lead to significant changes in the dust-to-gas ratio around the sublimation temperature. This is therefore a delicate problem that needs to be explored tentatively and might necessitate the inclusion of further effects like dust diffusion, latent heat, and temperature-dependent viscosity. 6. Conclusions and Outlook This paper presents a 2D model for protoplanetary disks that consistently includes viscous heating and thermal conduction. The model expands previous works (Flock et al. 2016 )