Food Biochemistry and Food Processing (2 edition)

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38 Thermal Processing Principles 737

0 102030405060708090100110

Temperature (oC)

Time (min)

fc

Tpic

Tic

Tcw+1

Tcw+10

Tcw+100

Tcw+1000^1000

100

10

1

Figure 38.8.Heat penetration curve on semi-log paper during

cooling phase.

versus time. The beginning of cooling time (time zero) is con-

sidered the end of heating time. The cooling rate index (fc)is

calculated from the negative reciprocal slope of cooling curve

and the cooling lag factor (jcc) from the intercept of the equation.

Ball calculated the process time based on straight-line equa-

tion of heating curve and integrating the effect of process time

over the kinetic data of microbial destruction. He developed ta-

bles (Table 38.6) and graphs to relate process time and process

Table 38.6.fh/UVersus LoggValues for the Ball

Method

fh/U Loggfh/U Logg

0.4 −1.79 5 0.742

0.5 −1.29 6 0.805

0.6 −0.949 8 0.894

0.7 −0.736 10 0.955

0.8 −0.544 20 1.112

0.9 −0.392 30 1.187

1 −0.273 40 1.235

1.2 −0.09 50 1.27

1.3 −0.019 60 1.296

1.4 0.042 70 1.318

1.5 0.097 80 1.336

1.6 0.146 90 1.352

1.7 0.183 100 1.365

1.8 0.229 120 1.388

1.9 0.265 140 1.406

2 0.298 160 1.422

3 0.525 180 1.435

4 0.655 200 1.447

lethality. These were based on relating two parameters:g(tem-

perature difference between heating medium and product at the

end of heating) as a measure of process time andfh/U(ratio

of heating rate to sterilization value) as the measure of process

lethality.

The lag factor for cooling cycle is important, because a sig-

nificant contribution of sterilization takes place during the early

part of the cooling period. Ball (1923) assigned a value of 1.41

forjccand also assumedfh=fcso that the needed information

can be obtained just from the heating curve. The values forfc

tend to be largerfhbecause of the slower heat transfer with water

compared to steam. Considering these factors, Ball related di-

mensionless ratiofh/Uversusgand expressed their relationship

in the form of tables and figures. With the above assumptions,

and experimentally obtained heating parameters (fh,jch,Ich),

process calculations can easily be accomplished. Table 38.7 is

an illustration of how process time (B) can be calculated. It can

be seen it is necessary to get the input from Table 38.7 for find-

ing the value of loggfromfh/U. As discussed before, the retort

does not reach the desired retort temperature immediately after

the steam is turned on, rather needs a finite heating time to come

to operating temperature (CUT). On the basis of the assumed

42% effectiveness for the CUT, the operator’s process time (Pt)

is obtained from the Ball process time (B) (Equation 36).

B=Pt+ 0 .42CUT (36)

The operator’s process timePtis the time interval from the

time the retort reaches the desired process temperature to the

time the steam is turned off. The CUT correction concept is only

applied in Formula Methods, because in General Methods, the

effect of the length of the CUT will be automatically included

in the calculated lethality value because all the temperatures

used in the calculation will reflect the effect of heat flowing into

the product during the CUT. The stepwise procedure for calcu-

lating process lethality using Ball formula method is shown in

Table 38.8.

Stumbo’s Method

Stumbo’sfh/Uversus loggtables (Stumbo 1973) includes the

contribution from both the heating and cooling lags. These tables

were developed after considering some restrictive assumptions

made by Ball (1923).

Generally, the Formula Method assumptions were

1. Ball assumed a constant hyperbolic lag factor of 1.41
   (jcc=1.41) for the cooling conditions, which is not the
   same in many cases. Early part of the cooling curve con-
   tributes significantly to the process lethality and hencejcc
   is very important. Stumbo and Longley (1966) published
   tables that considered variations in cooling lag factor in-
   stead of assuming it to be constant (Table 38.9).


2. This is one of the assumptions made by Ball (1923) as-
   suming the heating rate is equal to cooling rate during
   thermal processing time at the slowest heating part. Com-
   monly under practical conditionfh<fcc, which is more