The apparatus, in which fluidization of the particulates is obtained by filtration of the gas in the upward direction through the layer of the particulates, is widely used in the industry for various types of processes. This gas serves as source of fluidized agent and the heat transfer carrier. In particular, the fluidized bed creates a favorable condition to carry out numerous heterogeneous processes. In spite of a significant advantage of this hydrodynamics regime, there are some drawbacks. The fluidization occurs only when sufficient filtration velocity of gases is achieved. In some cases when there is a significant difference in particulate sizes, this condition is not acceptable, and for a layer of fine particulates, such type of fluidization cannot be obtained at all. In the latter case, a combination of vibration and filtration of very small amount of gas through the layer is used, and the heat transfer to the solids occurs by conduction from the heating surface. In this paper, a set of differential equations for the heat and mass transfer are formulate and solved for variable and constant temperature of the heating surface. As a result, a relationship of the solid temperatures as a function of time is established. An experimental research also was performed. A comparison of the experimental research data and theoretical analysis shows that the deviation does not exceed 10%. The experimental research also shows that the main influence on the intensity of the mass transfer process has the amplitude of vibration and to the lesser extent the effects of frequency of vibration.

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