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Figure 12. Computed distribution of sterilization (thermal-time-distribution) in liquid for the conditions in Figures 10 and 11.

without any physical or mathematical justification. Nevertheless, the f and j values measured from experiment are used to calculate sterilization time, as described in Ball and Olson (1).

### Sterilization Values and Distribution

A typical transient distribution of sterilization (TTD described previously) in a cylindrical container (35) is shown in Figure 12. This was calculated by implicitly following the liquid elements (7) throughout the duration of heating. The volume (or mass) average sterilization lies within the range of the distribution, as expected. However, the sterilization calculated based on the temperature at the slowest heating point lies completely outside the distribution. This is because all physical fluid particles stay only some time in the slowest heating zone, and no particle stays all the time in the slowest heating zone. Thus all particles in the system obtain a sterilization more than what is calculated based on the slowest heating zone. Because sterilization at the slowest heating zone is easily measured by placing a thermocouple, this is the temperature used in practice to calculate sterilization. The slowest point value in Figure 12 demonstrates that use of such slowest heating thermocouple data provides additional overprocessing (and safety) beyond the true least sterilization of a fluid.

### Effect of Non-Newtonian Liquid Behavior

For non-Newtonian (pseudoplastic) liquid with temperature-dependent viscosity, the recirculation pattern, radial and axial profile, and location of the slowest heating points were found (36) to be qualitatively similar to that of Newtonian liquid (35) discussed previously. As could be expected for the higher effective viscosity of pseudoplastic liquids, the maximum axial velocity near the wall was lower, being of the order of 10"4 m/s as opposed to 10"2 m/s for Newtonian liquid. The non-Newtonian nature itself was not expected to change the physics considerably because at the low shear rates involved in a naturally convective flow, the liquid behaves close to a Newtonian liquid.

Starch gelatinization has been included (34,40) in un-agitated heating of a canned 3.5% cornstarch dispersion. The thermorheological behavior of the starch dispersion was described in terms of three phases: (1) a pregelatin-ization phase where the magnitudes of apparent viscosity were assumed to be those of the continuous phase, (2) a gelatinization phase where the magnitudes of apparent viscosity increased, and (3) a postgelatinization phase where the magnitudes of apparent viscosity decreased. Although the spatial velocity and temperature profiles were qualitatively similar to the previous studies of unagitated heating (32), they (34,40) showed for the first time how the well-known broken heating curves (temperature-time curves with drastic changes in slope) develop during heating of starch-containing products, due to changes in the product apparent viscosity with temperature. The complex thermorheological behavior of the starch dispersion made it difficult to develop prediction equations for temperature-time histories using the commonly used f and j parameters.

### Effect of Presence of Particulates

The complexities of natural convection heating are considerably amplified when solid particles are present in the liquid food, for which little information is available. If the overall heat transfer coefficient between the solid particles inside the container and the heating medium is available, equations for conduction heating can be used to estimate the particle temperatures and insure sterility. Dimension-less Nusselt-Prandtl type correlations for the overall heat transfer coefficients between mushroom-shaped particles and water in a still retort have been provided (41), although there was considerable scatter in the data. Presence of spherical glass particles reduced natural convection in viscous liquid such as silicone, whereas the particles had very little effect on convection in thin liquid such as water (37). Smaller particles caused greater reduction in the convective flow.

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