U = superficial velocity, ft./sec. fi
Equation 1 is applicable to horizontal slug flow but gives low values at low U a / U ~ ratios, as shown by Figure 1. This may occur because of significant backmixing of the liquid in vertical upward flow. Average absolute deviation between experimental and calculated values is 12% for the air-water data and 18% for the air-ethylene glycol data. Nomenclature
C
D h k
L
R
= = = =
specific heat, B.t.u./lb. inside tube diameter, ft. heat transfer coefficient, B.t.u./(hr.)(sq. ft.)(OF.) thermal conductivity, B.t.u./(hr.)(sq. ft.)(OF./ft.) = length, ft. = holdup fraction
= viscosity, lb./(hr.)(ft.)
SUBSCRIPTS G = gas L = liquid T P = two-phase W = wall surface at i.d. literature Cited
(1) Hughmark, G. A., A . I. Ch. E. J. 11,937 (1965). (2) Hughmark, G.A,, Chem. Eng. Progr. 58,62 (April 1962). (3) Zbbid., 59, 54 (July 1963). (4) Hughmark, G. A.,Chem. Eng. Sci. 20,1007 (1965). (5) Hughmark, G. A., IND.ENG.CHEM.FUNDAMENTALS 2, 315 ( 1 963). (6) Kudirka, A. A., Grosh, R. J., McFadden, P. W., Zbid., 4, 339 (1965).
G. A . Hughmark Ethyl Corp. Baton Rouge, La.
PARTICLE-TO-GAS HEAT TRANSFER I N FLUIDIZED BEDS SIR: The paper of .Juveland, Deinken, and Dougherty (7) is an interesting and valuable study. The authors have devised a way to measure solid temperatures, thus eliminating a factor which cast doubt on some earlier studies. In one particular, :however, I question the conclusions. The heat balance from which coefficients are calculated seems to assume plug flow of the gas. I would rather expect that this small length-diameter ratio fluidized bed would more nearly approach complete mixing. If this should be true, the mean temperature (differenceswould be much less and the
coefficients much higher. I wonder if the authors would care to comment on this point.
SIR: We are glad to comment on the point brought up by Oliver. The assumption used in our paper for defining the heat transfer coefficient was that at a given height in the bed there is a well-defined average gas temperature whose variation with bed height is determined by a constant heat transfer coefficient. I n our experiment the heat transfer coefficient so defined decreased about 30% for the largest particles when the static bed depth w,as increased a factor of about 4. For the smallest particles, it decreased about a factor of 2 when the static bed depth increased a factor of 2. This tends to indicate, but does not prove, that the heat transfer coefficient is indeed not constant, but decreases with height in a given bed. We do not take this as a very strong indication, however, because changes in other characteristics of the bed with static bed depth make the interpretation of this effect difficult. I n the conclusion of our paper it was described how gas bypassing, which would be expected to occur when particle size is small compared to boundary layer thickness, could explain, qualitatively, variation of the heat transfer coefficient with static bed depth without violating the assumption of constant coefficient within a given bed. I t should also be remembered that if gas
mixing is important, it would influence the heat transfer coefficients as defined in our paper. I t should increase them, especially if the mixing penetrates the boundary layers. However, the coefficients are small, and gas bypassing arguments consider gas elements passing generally upward through the bed as receiving different amounts of heat. Complete gas mixing would tend to preclude these types of arguments for low heat transfer coefficients. If one assumes complete gas mixing, a natural assumption might be that the gas temperature is constant throughout the bed. This is conceptually difficult, since it implies that the heat transfer coefficient is infinite at the bed entrance, and zero in the upper parts of the bed. However, an average heat transfer could be defined, as implied by Oliver, by using the difference between the bed temperature and exit gas temperature as the mean temperature difference. This leads to average coefficients which are from about 3 to 10 times higher. Two observed effects are hard to understand from the standpoint of complete gas mixing: For the large particles, instead of decreasing these average transfer coefficients increase by a factor of about 3 as the bed
literature Cited
(1) Juveland, A. C., Deinken, H. P., Dougherty, J. E., IND.END. CHEM.FUNDAMENTALS 3,329 (1964). Earl D. Oliver Colony Development Co., Agent 7600 Sherman St. Denver, Colo.
VOL. 5
NO. 3
AUGUST 1966
439
