Total and Radiative Heat Transfer to an Immersed Surface in a Gas-Fluidized Bed A high-temperature heat transfer probe capable of measuring both the total and radiative heat transfer coefficients between an immersed surface and the bed has been designed, fabricated, and tested. Mea- surements zyxwvutsrqp of these coefficients in beds of 559 and 751 pm sand par- ticles at temperatures up to 1,175 K have been made using this probe. A thermal analysis of the probe is developed in order to ensure a reliable interpretation of the measured quantities. The dependence of the total and radiative heat transfer coefficients on such parameters as bed tem- perature, fluidizing air velocity, and mean bed particle size are investi- gated. The various models proposed to describe high-temperature heat transfer are evaluated from this perspective. The models capable of best simulating the heat transfer process with relative ease of computa- tion are identified and evaluated using data generated in the study. Introduction zyxwvutsrqp The presence of radiation as a mode of heat transfer in high- temperature gas-fluidized beds, along with particle and gas con- vection, leads to an enhancement of the overall heat transfer rate between the bed and an immersed surface, as compared to that in beds at low and moderate temperatures. This necessi- tates the development of reliable mechanistic models and simple correlations capable of adequately describing the heat transfer characteristics of the bed at elevated temperatures. High-tem- perature heat transfer is significantly more difficult to describe since the convective (particle and gas) and radiative modes occur simultaneously and in parallel, and the inclusion of the two processes in a single step becomes difficult due to the nonlin- ear dependence of radiation on temperature. Due to the indus- trial interest in fluidized-bed technology, efforts have been made from time to time to measure the total heat transfer coeffi- cient at high temperatures. Various experimental techniques have been used to obtain the value of the total heat transfer coef- ficient h,, and the radiative heat transfer coefficient zyxwvutsr h, as a function of bed and surface temperatures, particle size, and fluidizing velocity. These efforts are examined here, and are uti- lized in developing a high-temperature heat transfer probe for the simultaneous measurement of zyxwvutsrqp h, and h,,. The results obtained with this probe up to a maximum tem- zyxwvut Correspondence concerning this paper should be addressed to zyxwvutsrqpo S. C. Saxena. Ajay Mathur is with theTata Energy Research Institute, New Delhi, India, Ajay Mathur, S. C. Saxena Department of Chemical Engineering University of Illinois Chicago, IL 60680 perature of 1,175 K for both heat transfer coefficients in fluid- ized beds of silica sands of average diameters of 559 and 751 pm are reported as a function of fluidizing velocity. The results are examined in the light of the data available in the literature, and also on the basis of the theoretical models. This has enabled the estimation of the relative adequacies of different theoretical models and also helped in resolving some of the existing contro- versies concerning the parametric dependence of the radiative heat transfer coefficient on different parameters. Heat Transfer Fluxes and Coefficients at High Temperatures The heat transfer process at high temperatures in gas-fluid- ized beds consists of particle convection, gas convection, and radiation. The total heat zyxw flux from the bed to an immersed sur- face at a lower temperature zyxw is given by: here, and AIChE Journal 1124 July 1987 Vol. 33, No. 7