I,,,. J. Heat Mass Transfir. Vol. 34. No. I, pp. 47-53. 1991 0017-9310191 P3.00+0.00 Printed in Great Britain Pergamon Press plc Heat transfer between a surface and a fluidized bed : consideration of pressure and temperature effects V. A. BORODULYA, YU. S. TEPLITSKY, I. I. MARKEVICH, A. F. HASSAN and T. P. YERYOMENKO Luikov Heat and Mass Transfer Institute, Minsk, 220728, U.S.S.R. zyxwvutsrqponmlkjihgfedc (Received 3 January 1989) Abstract-A two-zone model of heat transfer between a fluidized bed and an immersed surface (J. EHgng Phys. 56(S). 767-773 (1989)) is used to correctly take into account the effect of the fluidized gas pressure and of the surface and bed temperatures on the overall heat transfer coefficient considered as the sum of conductive (/I&, convective (h,,,,) and radiative (h,) components. The quantity hcand represents the effect of contact thermal conductivity of solid particles and also their convection near the heat transfer surface, h, takes account of the effect of the bed non-isothermicity near the surface on its effective emissivity. Based on the model used, correlations are obtained for computing the overall heat transfer coefficient. Comparison with the literature data shows that these correlations are valid over a wide range of experimental conditions:0.1~d~6.0mm;0.1~p~10.0MPa.293~T,~1713K;293~T,~1373K. INTRODUCTION IN RECENT times a considerable amount of attention has been given to investigations in the sphere of fluid- ized bed combustion and gasification of solid fuels. The new technology has certain advantages over tra- ditional techniques-a lower level of harmful emis- sions, a wider range of fuels being used, less cost of purification works, etc. The operating conditions of furnaces and reaction chambers of gas generators pri- marily involve high temperatures (1023-l 173 K) of the bed and also increased pressures of the fluidizing gas (up to 2.0 MPa). Under such conditions, heat transfer between a fluidized bed and a surface has a complex conductive-convective-radiative character. Its rate depends on a great number of factors and their correct representation involves great difficulties the elimination of which first of all requires the eluci- dation of the mechanism of heat transfer and then the development of rather adequate models of combined heat transfer. For the most part the models available at present are rather specialized and, as a rule, describe a very limited body of experimental data on con- ductive-convective heat transfer [l-5]. The inclusion of radiative heat transfer is aggravated by the fact that there is no substantiated technique for calculating the fluidized bed effective emissivity [5] which would take into account the non-isothermicity of the bed near the heat transfer surface. One of the most well-known empirical formulae for calculating h”“” is that of Baskakov and Panov [7] which predicts rather a strong dependence of the conductive component on pressure-the fact not confirmed experimentally [8]. Besides, this formula somewhat idealizes the effect of temperature T, on h,, fully ignoring the bed tem- perature (T,)-the fact which also lacks experimental confirmation [9]. In the present work attention is mostly paid to the functional dependence of the overall heat transfer coefficient on the governing parameters which reflects the effect of gas pressure and of the surface and bed temperatures on this coefficient and allows extremely wide generalizations of experimental data available in the literature. CONDUCTIVE-CONVECTIVE HEAT TRANSFER The analysis of the process of conductive- convective heat transfer is made with use of the two- zone model [lo] which presupposes the existence of an effective gas film at the heat transfer surface. Within the scope of this model [lo] the following simple expression was obtained for h,_, in terms of the gas film characteristics : h, = i;&. (1) The effective thermal conductivity and thickness of the film are defined as 1: = i,+O.O061p,c+ 1, = O.l4d(l-m)-2’3. The calculating formula for h,.,, i.e. (2) (3) N&X = 7.2(1-m)2’3+0.044RePr m (l -,)2’3 (4) which follows from equations (1) to (3), is used as the basis for obtaining the universal relations Nu,, and zyxwvut Nu;! . 47