ELSEVIER Powder Technology 98 (1998) 13-20 The influence of particle thermal time constants on convection coefficients in bubbling fluidized beds Robert C. Brown *, Scott P. Overmann Department of Mechanical Enl¢ineering, Iowa State University, 2025 H.M. Black, Ames, IA 50011, USA Received 22 April 1997; received in revised form 12 November 1997; accepted 4 December 1997 Abstract The goal of this study is to determine the effect of particle thermal time constants on fluidized bed convection coefficients and explain this behavior in terms of mechanistic models of particle convection. Heat transfer coefficients from a vertically oriented, cylindrical heat transleJ probe were measured in beds of steel or bismuth particles fluidized in either nitrogen or carbon dioxide. Nusselt numbers were measured as functions of superficial velocities in the fluidized beds, corrected for voidage, consistent with either single-particle or packet theories of heat transfer in fluidized beds, and plotted against the dimensionless velocity ratio. The results of this study suggest that residence times of particles or packets do not increase regularly with increasing superficial velocity, but may increase rather abruptly above the minimum fluidization velocity and then become relatively constant. © 1998 Elsevier Science S.A. All rights reserved. K,'vwords: Thermal time constants: Convection coefficients: Bubbling beds: Fluidized beds 1. Introduction The rate of heat transfer in gas fluidized beds of small particles is generally agreed to depend on the heat capacity of the particulate material ! ! ]. However, this dependence is difficult to establish experimentally because specific heats of most particulate material commonly employed in fluidized beds do not differ much from one another. Knowledge of this dependence, though, would be useful in testing various the- oretical models of particle convective heat transfer in fluidi- zed beds, such as the packet 12 ! and particle 13 ] theories of heat transfer. Experiments were performed in our laboratory with bis- muth and steel particles fluidized in nitrogen and carbon diox- ide. The densities of steel and bismuth differ by only 20%, while their specific heats differ by a factor of four, which make them ideal for determining the effect of heat capacity. However, several other properties are also important in deter- mining heat transfer in fluidized beds, including gas thermal conductivity, particle size and density, and residence time of particles at heat transfer surfaces. Some particle properties are not easily controlled in heat transfer experiments. For this reason, the thermal time constant, a fundamental parameter * Corresponding author. Tel.: + I 515 294 7934: Fax: + ! 515 294 3091; E-mail: rcbrown@iastate.edu 0032-5910/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PI! S003 2-5910 ( 97 ) 03407-4 in all mechanistic models of heat transfer, is used as a proxy for heat capacity in this study, it can be easily calculated from well-known physical and thermal properties of the particles. On the other hand, the residence time of particles at heat transfer surfaces, another important fundamental parameter, is not easily measured or accounted for in experiments. Accordingly, experimental conditions were chosen such that hydrodynamic similitude existed between beds of the two kinds of particles. Under conditions of hydrodynamic simil- itude, particles in the two beds are assumed to have the same residence times 141. 2. Background Most currently accepted models for heat transfer in flui- dized beds of small particles can be classified as packet mod- els or single-particle models. The basis of all packet models is the Mickley-Fairbanks 121 model, which assumes that packets of particles are swept to a heat transfer surface where the packet as a whole absorbs heat until it is swept away under the action of bubbles. Heat transfer between a packet and the heat transfer surface is described by the relationship [ (I] 6m k,, r, Nuo= ~ (l-~,,,t) - (I) 7r ~'r