Heat Transfer to Submerged Surfaces

Similar behavior has been reported by other researchers for both vertical and horizontal tubes, though the magnitude of the heat transfer coefficients change with operating conditions, (Mickley and Trilling, 1949 Vreedenberg, 1960 Botterill and Desai, 1972 Ozkaynak and Chen, 1980). 

In contrast to the strong effect of gas properties, it has been found that the thermal properties of the solid particles have relatively small effect on the heat transfer coefficient in bubbling fluidized beds. This appears to be counter-intuitive since much of the thermal transport process at the submerged heat transfer surface is presumed to be associated with contact between solid particles and the heat transfer surface. Nevertheless, experimental measurements such as those of Ziegler et al. (1964) indicate that the heat transfer coefficient was essentially independent of particle thermal conductivity and varied only mildly with particle heat capacity. These investigators measured heat transfer coefficients in bubbling fluidized beds of different metallic particles which had essentially the same solid density but varied in thermal conductivity by a factor of nine and in heat capacity by a factor of two. 

Temperature of the fluidized bed is another parameter that could influence the heat transfer coefficient. Increasing bed temperature affects not only the physical properties of the gas and solid phases, but also increases radiative heat transfer. Yoshida et al. (1974) obtained measurements up to 1100°C for bubbling beds of aluminum oxide particles with 180 pm diameter. Their results, shown in Fig. 6, indicate an increase of over 100% in the heat transfer coefficient as the bed temperature increased from 500 to 1000°C. Very similar results were reported by Ozkaynak et al. (1983) who obtained measurements for bubbling beds of sand particles (dp = 1030 pm) at temperatures up to 800°C. 

The first type of model considers the heat transfer surface to be contacted alternately by gas bubbles and packets of closely packed particles. This leads to a surface renewal process whereby heat transfer occurs primarily by transient conduction between the heat transfer surface and the particle packets during their time of residence at the surface. Mickley and Fairbanks (1955) provided the first analysis of this renewal mechanism. Treating the particle packet as a pseudo-homogeneous medium with solid volume fraction, e, and thermal conductivity (kpa), they solved the transient conduction equation to obtain the following expression for the average heat transfer coefficient due to particle packets, 

Assuming that this packet renewal mechanism accounts for all the heat transfer associated with the particle phase, h can be equated to hd in Eq. (3). 

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