The operation parameters of a special heat exchange scraped-surface apparatus ware studied and mathematically described in the article. The feature of the apparatus was the use of perforated cleaning devices in order to increase the turbulence of a product. The developed device can be used in the dairy, meat, and fat and oil industry to cool cream, animal fats, margarine emulsions, cooking fats, and other viscous food products. The increase in the productivity of the apparatus was achieved as a result of the more intensive mixing of the cleaned wall layers with the bulk of the cooled product due to the presence of cylindrical holes in the slats with a diameter of at least 
 0.05–0.1 of the diameter of the working cylinder. As a result of processing experimental data on heat exchange taking into account energy dissipation, a calculated criterial heat exchange equation for the nonisothermal motion of products and their different flows – laminar and transient – was obtained explicitly. In addition, the article considers the effect of starting modes on the operation of apparatus with mixing devices. These data can make it possible to take into account the possible deviations of parameters caused by nonsteady operating modes. On the basis of the data obtained, we have proposed assumptions about the degree of impact of viscosity and inertia in the considered range of parameters on a starting mode. The results of the study are relevant since they allow us to intensify the thermal processes in this type of common apparatus by 10–12%.
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