Heat transfer in liquid-fluidized beds

Abstract

There exist two pertinent heat transfer modes in a fluidized bed: one—convective heat transfer between points of the bed, caused by particles' mixing; and the other—surface heat transfer between particles and fluid. The two modes produce an effective heat conduction, or diffusion, in the fluidized bed. In order to predict the temperatures in the fluidized bed, the knowledge of the effective thermal diffusivity is necessary. The achieved objectives of the present research are: (a) theoretical explanation of the heat transfer; (b) experimental determination of the said diffusivity. The work is divided into two main parts, experimental and theoretical. In the experimental part, the effective thermal diffusivity values are obtained by means of a fluidized bed test apparatus. The obtained values fit the semi-empirical correlation developed later in our theoretical analysis κ eff v f = C · ρ sc s ρ fc f · Re ∗0.25 Pr 0.75 where Re ∗ is a Reynolds number based on the particle's diameter and the root mean square fluctuation velocity defined by equation (√u′ 2) = 1.21 (gd) 0.5 (1−ε) 0.33 · (1 − ρ f ρ s) 0.5 . C is a proportionality factor. By plotting the test data it is found that C = 5320. The test data fit the above equation with a standard deviation ± 34 per cent. In the theoretical part of work, an analysis of the heat transfer caused by particle mixing is performed by means of the theory of stochastic processes. It is shown that with certain simplifying assumptions the heat transfer process becomes a Wiener process. From the theory of Wiener processes it is found that the effective thermal diffusivity of fluidized bed is a function of the mean kinetic energy of particle and the heat-transfer coefficient. To complete the analysis, the expressions of the mean kinetic energy of particle and the heat transfer coefficient are developed. Both expressions in conjunction with the theory of Wiener processes produce the semi-empirical correlation shown above.