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Midplane

Figure 17. Labeling of grid nodes in matrix of volume elements on a vertical plane for application of finite differences. Source: Ref. 3, reprinted with permission, copyright 1992 by Marcel Dekker, Inc., New York.

set at retort temperature), the new temperature reached at each node can be calculated after a short time interval (At) that would be consistent with the thermal diffusivity of the product obtained from heat penetration data (fa). This new temperature distribution is then taken to replace the initial one, and the procedure is repeated to calculate the temperature distribution after another time interval. In this way, the temperature at any point in the container at any instant in time is obtained. At the end of process time, when steam is shut off and cooling water is admitted to the retort, the cooling process is simulated by simply changing the boundary conditions from retort temperature to cooling temperature at the surface nodes and continuing with the computer iterations described earlier.

dT dt d2T 1 dT d2T

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