" o t h e r resistances" lumped into hs which include that of the heat transfer medium such as condensing steam or cooling water, the solid wall, and fouling on both sides of the wall. F o r experimental work, values of hs are obtained by one of these three methods :
1. Measurement of the temperature of the heat transfer barrier by imbedded thermocouples ( G l , C2, K 4 , O l , D l ) .
2. Use of modified Wilson plot represented by E q s . (16) and (17) below (U2, P6, C5, B3).
3. By calculation, using Eqs. (18) a n d (19) below ( C I , C 5 , R2) or other methods (B1,B4).
T w o variations of the Wilson plot technique were employed to secure hs. F o r the first method, it was recognized that
U ~ hs + K'NX ( '
where
a n d
hjOThc = K'N*
F o r test conditions which insure a fairly constant value of hS9 a plot oil/U vs.
I IN* on rectangluar coordinates will indicate a linear relationship with a slope of 1/K' a n d a j - i n t e r c e p t of l/hs. Experimental results from the use of this technique are given in Table X I . T h e second variation of the Wilson plot technique was successfully used by Cummings and West (C5) only for cooling with coils for which the working relation was
Jj = hc
+ R m + R f +
K"V08 ^
where the slope is \/K" the intercept is \jhc + Rm + Rf a n d K"V°'S = h0 c. Here the agitator geometry a n d speed were constant a n d the temperature of the vessel fluid did not vary markedly, so that hc could be considered constant.
A . HEAT TRANSFER IN JACKETS
Test information for jacket heat transfer are for condensing steam a n d cir-culating fluid media. A n analysis of the d a t a from three sources for condensing This analysis emphasizes the need for good mixing for heat transfer to viscous materials, but it also indicates that the mechanism is complicated and will be difficult t o model satisfactorily.
Table XI
Comparison of Predicted Jacket Side Heat Transfer Coefficients with Values Calculated from Test Data
Heat Heating Exptl. Exptl Calculation of h0j Method Fluid
transfer or method Uhs • from pre- of velocity
media cooling of finding experi- dicted predicting in jacket - <AT d vR e Investigator
A , zlkm
* ,
1/Λο, ment hj K((ft./sec.)Condensing Heating T.C. in 0.0034 0.0013 0.001" 0.0011 900* ca. Est. fair value Chilton et al.
steam wall N 1500 (C2)
Condensing Heating Wilson 0.0033 0.0012 0.001a 0.0011 900* ca. Est. fair value — U h l ( U l )
steam plot 1500
Condensing Heating Wilson 0.005 0.0016 Negligible 0.0034 300 200-500 Est. fair value, — Brooks and
steam plot noncon- Su(B3)
densables present
Water Cooling Wilson 0.010 0.0012 0.001a 0.0078 129* 112 Eq.(18) with 0.05 620 Uhl ( U l )
with plot K"' = 0.15
flow 114 Martinelli and
down- Boelter(Ml)
Water ward Wilson 0.0075 0.0016 Negligible 0.0059 170 180 Method not — — Brooks and
plot given in ref. Su (B3)
Water Testc — 0.0055 Negligible — 112-130 111-135 Eq. (18) with 0.03-0.11 500-1900 Brown et al.
# " ' = 0.15 (B4)
— 0.0055 Negligible — 140-220 None* See text 0.13-0.20 2200-3300
Dowtherm Heating Calculated Inform- Negligible — 40-55' 26% Eq.(18) with 0.04-0.05 800 Barton and
A with from U 0.0055- ation higher' K'" = 0.15 Williams
flow by using 0.0021 not (Bl)
312 Vincent W. Uhl
Heat trans-fer oil
up-ward
calc.
value for A,
given Negligible 14-20* [Individual 0.025-Ό.06 values checked
closely by method of
Martinelli and 0.05 Boelter(Ml)]
100 Barton and Williams
(Bl) Tetracresyl
silicate up-ward
calc.
value for hs
given Negligible 28-36*
26% higher'
250 Barton and Williams (Bl)
a Combined fouling factor for both jacket and vessel side estimated to be 0.001.
b Since the value of hQj is dependent on the estimated size of the fouling coefficient, h0j from experiment are only of-the-order values.
c Tests indicated that for heating by steam in jacket, the film coefficient for water in the vessel was about 900. Assuming the same film coefficient for cooling, values of h0j shown were calculated from the experimental values of U.
d In calculating the Reynolds number, the equivalent diameter was taken as twice the inside width of the jacket space.
e Sieder and Tate (SI) equation gives 26-46 for i VRe of 2200-3300 which is obviously not useful.
'Predicted h0j is 26% higher than from experiment in dowtherm, heat transfer oil, and tetrcresyl silicate media.
8 Summarized from test data for case of mean film temperature of 390°F. and temperature difference across fluid film, δ/, of 18 to 54°F.
5. Mechanically Aided Heat Transfer 313
314 Vincent W. Uhl
steam given in Table X I shows t h a t the value of hoj is generally very high, and because of the method of calculation, very rough. The low value of 300 for hoj from the data of Brooks and Su is expected because noncondensables were not purged from the steam.
Relations which apply for the correlation of hoj for circulating fluid media are from Colburn and Hougen (C3) and Martinelli and Boelter ( M l ) . The former, based on water flowing at velocities less t h a n 0.1 ft./sec. in a 3-in.
vertical pipe, is
where K'" = 0 . 1 5 for u p w a r d flow of heating fluid or downward flow of cooling fluid,
K!" = 0.128 for downward flow of heating fluid or u p w a r d flow of cooling fluid.
The Martinelli-Boelter relation is analytical but confirmed by experiment and unlike Eq. (18) which only includes the effect of free convection, it also reflects the influence of forced convection. Because the Martinelli-Boelter relation is t o o involved to present here, the reader is referred to the source paper or M c A d a m s (M5).
Values of jacket coefficients for sensible heat transfer derived from test work are also presented in Table X I . Besides sources for cooling water from work summarized in Table I, there are also data on heating with Dowtherm, heat transfer oil and tetracresyl silicates from Barton and Williams (Bl).
Their vessel was about 15 in. i.d. and the jacket space was 5/8 in. wide. These data in Table X I confirm the usefulness of the Colburn-Hougen and the more involved Martinelli-Boelter relations for predicting hoj where the velocity in the annular space does not exceed 0.11 ft./sec. and the Reynolds number is less t h a n 1900.
The fact that the considerable test data of Barton and Williams showed that the values of h0j were 8 0 % of that predicted by Eq. (18) is reasonable when it is realized that the considerable surface in the b o t t o m head is not vertical but almost horizontal.
N o t e that for flow beyond the viscous and in the nominal transition range with Reynolds numbers from 2200 to 3300, Brown et al. found that the values of h0j were increased to 140-200, which happens to be about four times that which would be predicted by the Sieder and Tate (SI) relations.
B. HEAT TRANSFER IN COILS
Rates of heat transfer, h0c, for fluid flowing in the straight lengths of the vertical baffle-type coils have been expected to follow the well-established relations for flow inside conduits by Sieder a n d Tate (SI).
(18)
5. Mechanically Aided Heat Transfer 315 The case of media flowing inside helical coils is another matter because the curvature enhances the heat transfer rate. The test equation which has been used was developed by Jeschke (J2) to correlate data for rates of cooling air in two helical coils of lj-in. steel tubing, one of two turns having a coil diameter, Dc, of 24.8 in. and the other of six turns having a coil diameter of 8.3 in. The flow was always turbulent with Reynolds numbers varying up to 150,000. The results show that the curvature of the coil increases the value of h0c by the factor (l + 3.5rff/Z)c). When this is incorporated into the Dittus-Boelter equation, the relation is
Data by Pratt (P5) for water in five different-sized coils and by Cummings and West (C5) for isopropyl alcohol demonstrate that Eq. (19) will predict h0c
within a few per cent for turbulent flow.
A . SCALE-UP
Scale-up is inherent in the application of available information mostly from small scale tests to equipment design. It should be recognized that for heat transfer, available correlations, v/z., Eqs. (3), (4), (8), (11), and (13), provide the basis for scale-up for most design situations. However, when there are no appropriate correlations, one needs to rely on related plant-scale data or extrapolate to plant scale the results of laboratory tests run in vessels of different sizes. The latter procedure is discussed in Chapter 3. The treatment here will be limited to situations for which existing heat transfer correlations apply.
Perhaps the most important single step in a scale-up procedure is the establishment of the process criterion. For heat transfer, this might be the same process fluid film coefficient or the same power consumption per unit volume of process fluid. It is impractical to maintain some process criteria.
For instance, it would be impossible to maintain the heat transfer rate per unit volume as the size of a jacketed vessel is increased because the surface area increases at a lower rate than the volume as scale is increased. On the other hand, this would be a reasonable criterion if coils were used.
Besides the two conditions established above for scale-up, namely, know-ledge of the extrapolation relation and définition of the process criterion, there is a third, the maintenance of geometric similitude. This last is not absolutely essential as are the first two conditions, but one can scale up with greater certainty, if geometric similitude is roughly observed.
It has been found most convenient to use power per unit volume, π, as the variable as the size or scale is increased. Subscripts 1 a n d 2 are used to
desig-(19)