TURBULENT HEAT TRANSFER IN VISCOELASTIC LIQUIDS
Experimental results of heat transfer for turbulent flow of viscoelastic liquids in tubes are compared with momentum transfer results under the same conditions. A marked decrease of the heat transfer efficiency is observed with respect to the Newtonian case, even larger than the corresponding drag reduction phenomenon.
of small amounts of polymeric materials to a solreduction effect-namely, the decrease of pressure losses in turbulent flow through tubes. This effect has been attributed to viscoelasticity (Astarita, 1965; Metzner and Park, 1964). Solutions displaying the drag reduction effect also have anomalous turbulent heat transfer behavior: The heat transfer coefficient between the tube wall and the bulk of the liquid is lower than in the pure solvent. The authors have recently presented (Astarita and Marrucci, 1966) a theoretical analysis of the heat transfer problem, as well as preliminary data supporting the theoretical results. This note presents a more complete set of data, particularly with regard to the rheological properties of the solutions which have been investigated. These data clearly show that the heat transfer reduction is even more conspicuous than the drag reduction. The experimental technique, as well as an interpretation of the phenomenon considered, is available (Astarita and Marrucci, 1966). DDITION
A vent is known to result in the so-called drag
Correlation of Data
Two aqueous solutions of ET-597 (a polymeric water-soluble drag reducing agent manufactured by the Dow Chemical Co.)
T= 7 1 O C 0.2
#/
have been investigated, the concentrations of polymer being 600 and 1000 p.p.m. by weight, respectively. A capillary viscometer was used to determine the shear stress-shear rate curve in the temperature range of interest. The viscometric curves a t 71' C. are given in Figure 1. A small but significant intercept is observed on the stress axis; in the range of interest, the viscometric behavior is that of a Bingham fluid, with a yield stress of the order of 10 dynes per square centimeter. The coefficient of rigidity, q-i.e., the slope of the shear stress-shear rate curve-is larger than the viscosity of water; because of the smallness of the yield stress, the rigidity, 7, is little different from the apparent viscosity, p , a t shear stresses exceeding a few tens of dynes per square centimeter. Slip phenomena a t the wall are not present, inasmuch as rheological data obtained with capillaries of different diameters are correlated by the same line. T h e logarithm of q is plotted against the reciprocal temperature in Figure 2. The energy of activation for the rigidity is weakly dependent on concentration and slightly lower than the energy of activation for viscosity of water. Heat transfer data for turbulent flow of purely viscous Bingham fluids have been correlated by Thomas (1960, 1961). T h e Colburn factors, jQ, show no shift with tube diameter, and are correlated by the usual Newtonian equation j, = f/2 when the rigidity is used instead of the viscosity. Heat transfer data obtained in a 1.2-cm. i.d. tube with a heated length of 120 cm. have therefore been reduced to j, factors by using the rigidity a t the appropriate temperature level. Because of the small yield stress of the solution in-
1000 PPM. 0.15 ry
E
--&
-
n*
0.5 0
05
7.5
1
2
2.5
2.9
l&EC FUNDAMENTALS
3.3
34
r
D
470
32
3.1
2 , O3 K - l
BL. 164, sec:f Figure 1 . Viscometric curves at 71 ' C.
30
Figure 2.
Dependence of rigidity on temperature
\
-$z Jq Newtonian
7
d‘i 5
104
4
2
6
+roo
7 ‘\
,
6
5
. . . ‘,04
2
4
I
S
6
8
Re
Re
Figure 3. Pressure drop and heat transfer data in water and in 600 p,p.m. solution of ET-597
Figure 4. Pressure drop and heat transfer data in 1000 p.p.m. solution of ET-597
vestigated, the l a values i,hus calculated are little different from the values which woulcl be obtained by using the apparent viscosity. I n the paper by Astarita and Marrucci (1966), the data have been correlated by using a viscosity value such as that obtained with a n Ostwald-Fenske viscometer ( 7 , = 0.02 g sq cm ), which proved to be much larger than both 7 and p in the 7,-range of the data (0.04 + 0.16 g.f/sq. cm.). T h e heat transfer reduction efect was therefore in part masked. Pressure drop data have been obtained, a t the same temperature levels as the corresponding heat transfer data, and have been reduced to f i iction factors //2. The independent variable (flow rate) has been reduced to a Reynolds number, Re, again on the basis of he rigiditv. Friction factor and Colburn factor data are reported in Figures 3 and 4 I n Figure 3, data obtained with water are included for comparison; the line marked “//2 = j~ Newtonian” is the usual Nen tonian correlation which, according to the resul s of Thomas, is also acceptable for purely viscous Bingham fluids. The data in Figures 3 and 4 clearly show the drag reduction a n 1 the heat transfer reduction effects. T h e latter is even more conspiclous than the former: over the whole range of R e values, iU < f / 2 . For values of R e of the order of l o 4 the f / 2 results lie on the Newtonian curve, while the J Q values are muc I smaller than would be predicted by the Newtonian cor1 elation. The data in Figure 4 also show that the transition to turbulent flow is delayed. In contrast with the reduction effects, the delayed transition is not necessarily attributed to viscoelasticity, because a similar behavior was observed by Thomas (1960, 1961) At lower values of Re, t h e j Q data are correlated by the laminar flow line for the appropriate lengthdiameter ratio; if the correction required for Bingham fluids is applied (Pigford, 1955; Hirai, 1957; Metzner et al., 1957; Thomas, 1960) the agreement with the two data points a t the lowest Reynolds numbers is remarkable
T h e j Q values a t the end of the transition region are lower than the accepted purely viscous correlation by a factor as large as 5 , and lower than the corresponding//2 values by a factor of about 2. These are very significant effects, and the following conclusion can be drawn : “Solutions displaying the drag reduction effect are characterized by an even more conspicuous reduction of the turbulent wall-to-fluid heat transfer coefficient.” Nomenclature
D (
= tube diameter, cm.
L
=
= =
Re =
T V
= =
17
=
p
= =
friction factor Colburn factor tube length, cm. Reynolds number temperature, K . average velocity, cm./sec. coefficient of rigidity, poises viscosity, poises wall shear stress, g.f/sq. cm.
literature Cited
Astarita, G., IND.ENG.CHEM.FUNDAMENTALS 4, 354 (1965). Astarita, G., Marrucci, G., XXXVI CongrZs Internationale de Chimie Industrielle, Bruxelles, 1966. Hirai, E., Chem. Eng. ( J a p u n ) 21, 17 (1957). Metzner, A. B., Park, M. G., J . Fluid Mech. 20, 291 (1964). Metzner, A. B., Vaughn, R. D., Houghton, G. L., A.I.Ch.E. J . 3, 92 (1957). Pigford, R. L., Chem. Eng. Pro,gr. Symp. Ser., No. 17, 51, 79 (1955). Thomas, D. G., A.2.Ch.E. J . 6 , 631 (1960); see corrected Figure 5, 7, 6s ( 1 961 ). GIUSEPPE M A R R U C C I GIANNI ASTARITA Chemical Engineering Department University of Naples Naples, Italy
RECEIVED for review October 31, 1966 ACCEPTEDMarch 13, 1967
VOL.
6
NO. 3
AUGUST
1967
471
