942
INDUSTRIAL AND ENGINEERING CHEMISTRY =
A
-11~
RP
/To - t/ ___
IT - t /
Vol. 36, No. 10
H
=
90,000 /loo - 250/ X 0.393 In 1150 - 250/
s6,OOO
(24)
= 0.644 hr. = 39 min. (approx.)
The foregoing leads to the conclusion that the problems covered by this study are rather complex because of the great number of variables and constants involved. Ext,ernal circumstances may impose considerable limitat,ions on the assumptions which the designer is free to make. Some points which can be decided upon only iii a particular problem are tmherelativib sizes of the cooling system, the volume of the bat'h, and the circulating rat,e. I n this connection, economic considerations will generally dictate the best design. It doe3 not seem possible to suggest a straightforward method of procedurr. which will lead t o an optimum solution; unless data from similar cases are available, it will be necessary for the designer to assume arbitrarily the free variables and compute several arrangements from which t o choose the best. Fort,unately, however, the numerical computations, as set out in the examplw, iirc neithw involvtd tior t irnP consuming.
= heat transferred in exchanger, B.t.u./hr. hg = heat transfer coefficient from body to bath, B.t.u./(hq. ft.) (hr.) (', F,.) p = characteristic group defined by Equation 15 p = characteristic group defined by E uation 16 R = circulating rate of bath fluid, 1b.qhr. r = circulating rate of cooling fluid, Ib./hr. S = heat transfer surface in exchanger, sq. ft. SS = external surface of body, sq. ft. S , = heat transfer surface in cooler, sq. ft. T = inlet temperature of warmer fluid to exchanger, O F'. 2" = outlet temperature of warmer fluid from exchanger, O E'. t = inlet temperature of colder fluid t o exchanger, ' F. t' = outlet temperature of colder fluid from exchanger, O P. T, = int:rmediate temperature of warmer fluid in exchanger,
F.
= intermediate temperature of colder fluid in exchanger, O F'. T I = over-all heat transfer coefficient in exchanger, B.t.u./ ti
(sq. ft.) (hr.) (" F.) v = characteristic group defined by Equation 13 a = characteristic group defined by Equation 10 fi = characteristic group defined by Equation 11 y
6
e
7
6 w
= = = = = =
characteristic group defined by characteristic group defined by time, hr. temperature of body, F. characteristic group defined by characteristic group defined by
Equation 14 Equation 1 7 Equation 1 Equation 12
.iCKNOWLEL)GMENT
In conclusion, the author wishes t o thank E'. ( h r r for useful suggestions on certain technical aspects of the problem, to H. Harper for his helo in the presentation of t,he material, and.to A. C. ~ I u e l l e for r checking the galley proofs. NOMRVCI, 4TI!RE
-4
weight of h i t 1 1 fluid, Ih.
=
R = weight of body, Ih. C B = specific heat of body, B.t.u., ( 1 1 ~ () " F.1 C R = specific hi5:it 01 h t h Huiti, H.t.u./[lh,) ( " b'.) C, = specific h c i t ot cooling fluid, B.t.ii,/(lb,) iob',)
BIBLlOGRAPHY (1)
Howinan, iMueller, and Nagle, Trurts. Am. SOC..We&.
Enyrv.,
62, 283 (1940).
(2) Fishenden, Margaret, and Saunders, 0. A., "Calculation of Heat Transmission", London, H. Id. Stationery Office, 1932. (3) Grober, Heinrich, "Einfuhrung in die Lehre von der Warmeuber-
tragung", Berlin, Verlag von Juliuv Springer, 1926. (4) McAdams, W. H., "Heat Transmission", New York, MCGrawHill Book Co., 1933. (5) Schack, A. (tr. by Goldschmidt and Partridge), "Industrial Heat Transfer", New York. John Wiley & Sons. 1934.
Viscosities of Molten
COUMARONE-INDENE RESINS OMPARED to most of' the cununercially important poly-
C
meric substances, c'oumaroii[.-ind[~nercsins used in mastic flooring tile, in varnishes, and in rJxtending rubbers have low average molecular weights. Various investigators (6) have reported molecular weights of almost 4000, but most of the commercial products are included within the brief range from 550 to 800. Furthermore, it is well known (10, I d , 19) that many of the physics1 properties of these resins change sharply within t,his molecular weight range. The recent investigations of Flory' on the viscosities of molten linear polyesters ( 7 ) and of Kauzrnann and Eyring on the viscosities of linear hydrocarbons (9) have focused attention on the determination of molecular Ivtights by viscosit,y measurement,s made directly on the material without the use of a solvent,. Although there have been few other studies of the variation of the viscosity of molten synthetic- polyniers with niolecdar weight, Dunstan ( 5 ) proposed the formula: log 7 = .1.11 where 11 = Coefficient of viscosity M = molecular weight A , B = constant,s
+H
This equation was proved iiiralid by Albert for honiologous esters (8) over a narrow molecular weight range and by Flory ( 7 )
A. C. ZElTLEMOYER AND STEPHEN KUTOSH Lehigh University, Bethlehem, Pa.
for it wide molecular weight rang
