M6 Heat Transfer from a Wall to Stagnant and Mechanically Agitated Beds
Granular and powdery products are often treated in contact equipment of various geometrical configurations (tray, paddle, drum, etc.). Heat transfer from the wall of the apparatus to the bed, or vice versa, is essential for this kind of processing and will, therefore, be discussed in the present chapter. Immersed surfaces such as the shaft of stirring devices may be used additionally to the apparatus wall for heating or cooling. Modelling of heat transfer will be presented in Sects. 2–5 on the basis of a model that considers the bed of particles as one continuous phase. This is usually called the penetration model. The heat exchanged between the wall and the bed may be used to just change bed temperature. Alternatively, a part of the supplied heat may be consumed for phase change or chemical reaction in the interior of the bed. These two cases will be distinguished, describing the former as heat transfer to beds without latent sinks (Sect. 2) and the latter as heat transfer to beds with latent heat sinks (Sect. 3). In case of merely heating or cooling, further distinction will be made between stagnant (static) and mechanically agitated beds (Sects. 2.1 and 2.2, respectively). Mechanical agitation can be provided by the rotation of the equipment (e.g., rotary drum) or by embedded, rotating stirrers. Modelling with heat sinks will be discussed for drying, distinguishing between drying in pure vapor atmosphere (vacuum contact drying, Sect. 3.1) and drying in the presence of inert gas (atmospheric contact drying, Sect. 3.2). Only mechanically agitated beds will be treated explicitly in Sect. 3. Parameters, which are necessary in order to conduct calculations with the penetration model, will be presented in Sect. 4. Extensions and some recent applications will be briefly outlined in Sect. 5, with reference to the relevant literature. Subsequently, a short introduction to emerging new modelling approaches that consider every particle of the bed individually (discrete models) will be given in Sect. 6. At the end, four examples that document and further illustrate calculations according to Sects. 2–4 will be provided.