Pergamon h,r .I Ha,/ Muss Trans/ ~r. Vol 3X. No 9. pp. 1675-1681, 199 Copynghf II> 1995 Elsewer Science Ltd Printed m Great Bntain. All rlghls reserved 0017 9310195 $9.50+0.00 0017-9310(94)00284-3 A mathematical model for the prediction of heat transfer from finned surfaces in a circulating fluidized bed P. K. NAG, M. NAWSHER ALIt and P. BASU$ Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur-721302. India (Received29 January 1994 and in,% al,form 10 August 1994) Abstract-A mathematical model has been developed to predict heat transfer coefficients on projected finned surfaces in a circulating fluidized bed (CFB). To validate the model, experiments were conducted in a 100 mm i.d., 5.15 m high CFB unit, in which heat transfer coefficients were measured for fins having rectangular and pin shapes. Experiments covered a range of superficial velocity from 5.6 to 11.4 m SS’, bed temperature from 66.5 to 91.5”C and for 3 IO pm sand particles. Heat transfer coefficients predicted from the model have been compared with those experimentally obtained and a good agreement is observed. INTRODUCTION The mechanism of heat transfer in a circulating fluid- ized bed (CFB) is complex because of the dependence of bed behaviour on a large number of variables. The process of heat exchange between the system and the heat transfer surface is closely related to the process of heat transfer between the fluidized solids and the fluidizing gas, the rate of mixing of particles in the bed, and the geometry of the fluidized bed. The fluid- ized bed represents a complex interaction of gas and solid. In addition, the radial variation of bed density complicates the development of a fundamental model for the prediction of heat transfer at the wall, especially when fins are attached to the inner surface of the bed. Finned tubes are widely used in heat exchangers. In a CFB boiler, the heat absorption by each wall tube may be considerably increased if additional heating surfaces can be provided by welding vertical fins to each tube. Tung et ul. [ 11, Li et al. [2] and many others have observed a dilute core of solids accompanied by a dense wall region in a CFB. So, the heat transfer coefficient along the fin surface varies as the fin extends from the wall towards the centre of the bed. To the best of the authors’ knowledge no model for the pre- diction of heat transfer for the finned surface in a CFB has yet been published in the literature. In the present paper an analytical model has been proposed for pre- dicting heat transfer in a circulating fluidized bed with finned surface. It has been validated by conducting experiments in a CFB facility developed for the inves- tigation. This being the first attempt, the analysis is f On leave from Bangladesh Institute of Technology, Khulna, Bangladesh. 1 Technical University of Nova Scotia, Halifax, Canada B3J 2X4. limited to temperatures where radiation is negligible. Radiation will be considered later in the model when experimental data from high temperature beds will be used for its validation. MODEL Assuming that a cluster of particles from the bulk of the bed moves to the heated finned surface. receives heat from the wall, and then moves away from the surface, and neglecting radiation, the temperature dis- tribution along the fin (Fig. 1) is given by the following differential equation [6] : d’T Ph, pzz dx2 &T-T,). Let x be the axial coordinate with its origin at the tip so that (x/L& = 0 and (x/L& = 1 and the fin lies in the region 0 < x/L < 1. It is assumed that the fin is sufficiently long so as to neglect the tip loss, but being long it will be subjected to radial distribution of suspension density in the fast bed. Glicksman [3] and Basu [4] observed that, for small beds (< 15 cm diameter), the heat transfer coefficient varies approximately with the square root of cross-section average suspension density. In the present analysis, however, it has been assumed that h, = kf&, where k’ is an experimentally determined constant and p1 is the local suspension density varying linearly along the fin length so that PI = PI1 + 2 (Pw -Pill PW+Ph and p =p 2 ’ which on substitution in equation (1) gives d2T pk’ 1’2 -=- dx’ k.4 Ph+ g(Pw--P) 1 (T- Th). (2) 1675