ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT V
=
y
=
g+ fi p 7 7 0
(2) MacLeod, A. A , , Ph.D. dissertation in chemical engineering, Carnegie Institute of Technology, 1951. (3) hTikuradse, J., V D I - F o r s c h u n g s h e f t , 356, 1 (1932).
bulk average linear fluid velocity, ft./sec. distance from tube wall or plate surface to point of measurement in fluid, f t . = friction distance parameter y u*p / p , dimensionless = viscosity of fluid, lb./(sec.)(ft.) = density of fluid, lb./cu. ft. = local shearing stress in the fluid, poundals/sq. ft. = skin friction at the tube wall or plate surface, poundals/ sq. f t .
Subscripts P denotes flow in smooth tubes or pipes F denotes flow between smooth, parallel plates literature cited (1) Corcoran,
UT.H., Page, F., Jr., Schlinger, W. G . , and Sage, B. H., IXD.ENG.CHEM.,44,410 (1952).
(4) Page, F., Jr., Corcoran, W. H., Schlinger, W. G., and Sage, B. H., IND.ENG.C H E M . 44, , 419 (1952). ( 5 ) Page, F., Jr., Schlinger, W. G., Breaux, D. K., and Sage, B. H., I b i d . , p. 424. (6) Prandtl. L.. 2. Ver. dezct. Ina., 77. 107 (1933).
(7) Prengle, R. S., Ph.D. disiertation in chemical engineering, Carnegie Institute of Technology, 1953. (8) Rothfus, R. R., Monrad, C. C., and Senecal, V. E., IND.ENG.
CHEM.,42, 2511 (1950). (9) Rothfus, R. R., and Prengle, R. S., I b i d . , 44, 1683 (1952). (10) Schlinger, W. G., and Sage, B. H., I b i d . , 45,2636 (1953). (11) Senecal, V. E., and Rothfus, R. R., C h e m . Eng. Progr., 49, 533 (1953). (12) Stanton, T. E., and Pannell, J. R., Trans. Roy. SOC.(London), A214, 199 (1914). RECEIVED for review September 8, 1954.
ACCEPTED October 5, 1954.
Temperature Tolerance in Frozen Food Processing Effective Temperatures in Thermally Fluctuating Systems SIGMUND SCHWIMMER
AND
LLOYD L. INGRAHAM
W e r f e r n Utilization Research Branch, Agricultural Research Service,
U. S. Department of Agriculture, Albany 6, Calif.
H. M. HUGHES University o f California, Berkeley, Calif.
C
ALCULATIONS of reaction rates in nonisothermal systems have been applied to such diverse problems as the pyrolysis of hydrocarbons in the petroleum industry ( 7 ) , thermal death rates in the food canning industry ( 6 ) , and effective scalding temperatures for enzyme inactivation in the frozen food industry (6). I n connection with temperature tolerance studies on frozen foods at Albany, Calif., laboratories of the Western Utilization Research Branch of the U. S. Department of Agriculture (,?), investigators have been concerned with the prediction of effective temperatures as related to chemical and organoleptic evaluations of the quality of the frozen foods. A theory is presented in this paper that permits calculation of reaction rates and effective temperatures in some simple periodically fluctuating temperature systems, used in the temperature tolerance studies, in which the reactions have known constant temperature coefficients in the range of interest. This theory may be of value in other industrial processes where temperature fluctuations affect the final product. Calculations from this theory permit the presentation of some simple charts that afford a rapid comparison of the mean temperature with the effective temperature. The effective temperature is that constant temperature at which the rate of the reaction of interest is equal to the mean reaction rate when the system is subjected to the given fluctuating temperature cycle. The theory presented in this article is similar t o that proposed by Hicks ( I ) , who developed an equation for the estimation of sinusoidal diurnal temperature fluctuations on reaction rates as applied to foods stored a t ambient temperatures. The present discussion may be considered as an extension of the Hicks theory, 1 Present address, Department of Biometry, School of Aviation Medicine, Randolph Field, Randolph, Tex.
June 1955
in that it develops equations for two additional modes of temperature fluctuation and provides a more convenient means for calculations of effective temperature for the sinusoidal variations by restricting the calculation to the one parameter, &A. The Hicks considerations involve &A and A separately, so that results of calculation from his equation can be presented only in tabular form. Relationships allow prediction of effective temperatures and reaction rates
Systems in which the temperature undergoes three modes of fluctuation-saw-toothed, square, and sine waves-have been analyzed. These cycles are illustrated in Figure 1, which also the mean temperature; T,, the effective temperature; shows TO, A , the amplitude (half the range of maximum and minimum temperatures); and B, one quarter of the period of fluctuation. Saw-Toothed Wave. During one half-cycle of amplitude A and duration time 2B, A T=To+-i! -B
