depth is increased by a factor of about 4. Since gas mixing implies a high coefficient a t the entrance and low coefficient in the upper regions, increasing the bed depth should tend to lower the average coefficient. At the low Reynolds numbers, the heat transfer coefficients are still a factor of about 20 less than for single spheres and there is no apparent reason for this if gas mixing is good. Some experimenters have measured temperature gradients in the lower portions of fluidized beds (7-4). Statements to the effect that the gas mixing is improved in fluidized beds of small length-diameter ratio are sometimes based on tracer gas experiments in which the action of the tracer material is not completely understood. For example, the tracer material could be adsorbed and desorbed later in other parts of the bed by the particles themselves, indicating good gas mixing where it really might not exist. From these considerations and our experiment, we believe that an exponential temperature rise determined by a constant heat transfer coefficient is much closer to the actual temperature profile than a step function change. The temperature profile is almost surely not precisely exponential (or the heat transfer coefficient constant) because the Reynolds number, gas velocity, etc., change as the gas is heated. Perhaps one would expect instead that the Nusselt number should remain constant and determine the temperature profile. I n any case, a small deviation from an exponential temperature rise would have to be determined by another experiment. Some readers have also inquired about the “magnetic gun” effect possible when conductors are placed in alternating nonuniform magnetic fields. I n our experiment it was estimated to be less than 1/20 of the force of gravity. The effect is minimized by using particles with a high electrical resistivity and low magnetic permeability and keeping the magnetic field as uniform as possible.
440
l&EC FUNDAMENTALS
A point which seems to be underemphasized is that, because of the counter flow exchanger effect of the moving particles and the large surface area, the fluidized bed is an excellent heat exchanger even though the heat transfer coefficients are low.
literature Cited
(1) Heertjes, P. M., McKibbins, S. W., Chem. Eng. Sci. 5 , 161 (1956). (2)’ Ketternring, K. N., Manderfield, E. L., Smith, J. M., Chem. Eng. Progr. 46, 139 (1950).
(3) Richardson, J. F., Ayers, P., Trans. Inst. Chem. Engrs. (London) 37, 314 (1959). (4) Walton, J. S., Olson, R. L., Levenspiel, Octave, Ind. Eng. Chem. 44,1474 (1952). Allan C. Juveland John E. Dougherty Herman P. Deinken Los Alamos Scientific Laboratory Los Alamos, N . M .
Correction
DIFFUSIONAL EFFECTS I N GAS-SOLID REACTIONS I n this article by John Shen and J. M. Smith [IND.ENG. CHEM.FUNDAMENTALS 4, 293 (1965)], there is an error on page 295 in Equation 27. T h e equation should read
