Heat Transfer to Small Horizontal Cylinders Immersed in a Fluidized Bed

Heat transfer to horizontal cylinders immersed in fluidized beds has been extensively studied, but mainly in the context of heat transfer to boiler tubes in coal-fired beds. As a result, most correlations in the literature have been derived for cylinders of $25-50mm$ diameter in vigorously fluidizing beds. In recent years, fluidized bed heat treating furnaces fired by natural gas have become increasingly popular, particularly in the steel wire manufacturing industry. These fluidized beds typically operate at relatively low fluidizing rates $(G∕Gmf<5)$ and with small diameter wires $(1-6mm)$⁠. Nusselt number correlations developed based on boiler tube studies do not extrapolate down to these small size ranges and low fluidizing rates. In order to obtain reliable Nusselt number data for these size ranges, an experimental investigation has been undertaken using two heat treating fluidized beds; one a pilot-scale industrial unit and the other a lab-scale (⁠$300mm$ diameter) unit. Heat transfer measurements were obtained using resistively heated cylindrical samples ranging from 1.3 to $9.5mm$ in diameter at fluidizing rates ranging from approximately $0.5×Gmf$ (packed bed condition) to over $10×Gmf$ using aluminum oxide sand particles ranging from $dp=145-330μm$ (50–90 grit). It has been found that for all cylinder sizes tested, the Nusselt number reaches a maximum near $2×Gmf$⁠, then remains relatively steady $(±5-10%)$ to the maximum fluidizing rate tested, typically $8-12×Gmf$⁠. A correlation for maximum Nusselt number is developed.