A. NONPROXIMITY AGITATORS
Despite the great range of possibilities in geometry [see Eq. (1)], in types of impellers (see Fig. 1 in Chapter 3) and in disposition of heat transfer surfaces, the relatively small a m o u n t of published information provides correlations for most of the more c o m m o n systems a n d at least an indication of the cor-relation forms for the other systems. This is in large measure the case because of the limited or negligible influence of all geometric parameters except D, the impeller size. The c o m m o n surface dispositions are only jackets and coils, for both of which there is information. M o s t of the d a t a available are for
324 Vincent W. Uhl
paddles and turbines of pitched-blade and disk flat-blade types. There is little data for propellers. Actually the other impeller types are not important for heat transfer systems. Some of the gaps in our information which appear t o require filling are listed below:
a. M o r e heat transfer studies for systems with propellers, including some investigation of the effect of a draft tube.
b . M o r e test work t o ascertain effect of the impeller position on hj and hc. The optimum position would obviously vary with impeller type.
c. Studies to determine for what viscosity the nonproximity impellers become ineffective for heat transfer.
d. M o r e information on the improvement in heat transfer resulting from the use of baffles in jacketed vessels.
e. Investigation of different coil arrangements, including concentric helical coils.
f. Information which would permit prediction of the vortexing stage which induces gassing.
g. Heat transfer rates by free convection only to jackets and coils.
h. The optimum system design for c o m m o n services. These designs would involve cost factors.
B. PROXIMITY AGITATORS
Except for the anchor and the Votator there is little published information for the variety of proximity designs. Based on an analysis of available data, neither empirical correlations (Fig. 12) nor the penetration theory model are satisfactory for prediction of heat transfer rates. There appear to be no published data for materials having viscosities greater than 100 poises, n o interpretation of the effect of non-Newtonian fluid behavior, and only very limited information is provided for granular solids and operations such as melting and crystallization. Although there is a considerable body of such d a t a in the files of equipment manufacturers, very little of it appears to be cor-related. Since such data if released will be generally incomplete and at best piecemeal, the real hope of more information appears to lie with the universi-ties. When more data become available, it would appear that they might be correlated by a semiempirical modification of the penetration theory model to take into account the effect of flow rate, degree of mixing, and non-Newtonian character of the fluid. This is a large order.
5. Mechanically Aided Heat Transfer 325 List of Symbols
Β baffle width (radially), ft.
c specific heat, B.t.u./lb.-°F
C for nonproximity agitators, the distance from center of impeller to vessel bottom, see Fig. 1 ; for proximity agitators, the clearance between the outer edge of the agitator blade and the vessel wall, see Fig. 7; ft.
d outside diameter of tube in immersed coil, ft.
dt inside diameter of tube in immersed coil, ft.
dg gap between individual turns of the coil, ft.
D impeller diameter, ft.
Dc diameter of coil at tube center, ft.
/ function of
g acceleration due to gravity, ft./sec.2 gc conversion factor, ft.-lb./sec.Mb. (force)
h coefficient of heat transfer, vessel liquid, B.t.u./hr.-sq. ft.-°F.
hc coefficient of heat transfer, vessel liquid to coil wall, B.t.u./hr.-sq.
ft.-°F.
hj coefficient of heat transfer, vessel liquid to jacket wall, B.t.u./hr.-sq.
ft.-°F.
h0 coefficient of heat transfer, heat transfer medium, B.t.u./hr.-sq. ft.-°F.
h0c coefficient of heat transfer, heat transfer medium to coil wall, B.t.u./
hr.-sq. ft.-°F.
h0j coefficient of heat transfer, heat transfer medium to jacket wall, B.t.u./hr.-sq. ft.-°F.
hs coefficient of heat transfer which includes all resistances for jacket or coil side. (It includes film coefficient for heating or cooling medium, fouling and metal wall.) B.t.u./hr.-sq. ft.-°F.
k thermal conductivity, B.t.u./hr.-sq. ft.-°F./ft.
Κ, Κ', Κ", Κ'" constants
/ length of horizontal side of square tank, ft.
L length of Votator units, sum of length of units if operated in series [Eq. (14)], ft.
Lc over-all height of helical coil, ft.
nb number of baffles, Eq. (1); number of vertical tube baffle-type coils [See Fig. 6(b)], Eq. (11)
ttj number of blades in impeller Ν impeller rotational speed, r.p.s.
N' impeller rotational speed, r.p.m.
Ρ power input, ft.-lb. (force)/sec.
Rm coil or jacket wall resistance to heat transfer, 1 B.t.u./hr.-sq. ft.-°F.
Rf resistance to heat transfer due to fouling of both sides of heat transfer surface, 1
B.t.u./hr.-sq. ft.-°F.
t time interval between two successive scraping actions, hr.
Τ vessel diameter, ft.
U over-all coefficient of heat transfer, based on vessel (inside) surface, B.t.u./hr.-sq. ft.-°F.
ν average axial velocity through vessel, ft./sec.
V velocity of coolant (heat transfer media) in coils or jacket, ft/.sec.
326 Vincent W. Uhl
w blade width for nonproximity impellers in direction parallel to the axis of rotation, see Figs. 1 and 4; for anchor and ribbon-type impellers in direction normal to the axis of rotation, see Fig. 7; ft.
w' same as u>, except if more than one blade on shaft, equals sum of widths [Eqs. (6) and (7), Table V].
χ reference number, number of baffles, Eq. (1), dimensionless y reference number, number of impeller blades, Eq. (1) dimensionless ζ thickness of vessel wall, ft.
Ζ fluid depth in vessel, ft.
β coefficient of thermal expansion of heat transfer medium, 1/°F.
8t log mean temperature difference, bulk jacket fluid to vessel outside wall, °F., Eq.(18)
JJL bulk fluid viscosity, lb./ft.-sec. or lb./ft.-hr.
μί fluid viscosity at mean film temperature, lb./ft.-sec. or lb./ft.-hr.
μ„ fluid viscosity at wall surface temperature, lb./ft.-sec.
ρ fluid density, lb./cu. ft.
π power intensity, power input/unit volume of process fluid; ft.-lb.
(force)/sec.-cu. ft.
a exponent for Reynolds number b exponent for Prandtl number c exponent for "viscosity ratio" ( Vis) e exponent for power equation, Eq. (22)
x exponent for individual factors (Table VI), Eq. (16).
m exponent for scale-up equation, Eq. (31 ) b baffle
c coil
/ at average film temperature ι impeller
j jacket wall 1 model 2 prototype m metal wall
w at wall
Note: This term only used for proximity agitators.
SUPERSCRIPTS
SUBSCRIPTS
j ( A W
DIMENSIONLESS GROUPS
-M (Vis)0-1*
Ni hjT
N u k c/x
P r k D2Np
Viscosity ratio, (Vis)
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