The thermal treatment of the powdered materials (solids) in fluid-bed apparatus is widely used in various branches of industry. The bed is fluidized by filtration of a gaseous heat carrier through the layer of solids. The height of the layer of solids should be sufficient to secure the evenly distribution of the heat carrier and to prevent it from the outburst in one or several locations and stagnation of the rest of the layer. The extra height of the layer of solids increases the hydraulics resistance and leads to additional energy losses. However, the advantage of such apparatus makes them very attractive. Unfortunately, such kind of apparatus and processes cannot be used for the thermal treatment of the fine particles due to their adhesiveness. To overcome this hurdle, the vibration motion is applied. The fluidized bed may be obtained by means of vibration with or without filtration heat carrier through the layer of solids. In this paper, the fluid dynamics equation for the vibration of the bed of the particulates without force air filtration through the layer is solved by numerical method. The results concur with the experimental data that on the whole shows the alternation of pressure and vacuum between the particulates layer and the vibrating plate. This phenomenon has an influence on the quality of the mixing process of particulates. A set of differential equations describing heat and mass transfer in a batch and continuous modes of operations is presented and solved for variable temperature of the vibrating heating surface.
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