Thermal Food Processing

Modeling Thermal Processing Using Computational Fluid Dynamics (CFD) 145
colder and the wall of the cylindrical section is heated (the top may also be
heated), then the circulation should start from the hot side wall surface and
move up to the top due to buoyancy effect, and then drop down to the lower
region due to the gravity effect. As such, when all the sides are heated, including
the bottom plate, there are at least two recirculation regions that compete
against each other, forming the pattern shown in Figure 5.3c. For different
physical properties of the fluid of concern, and the variation in the height-todiameter
ratio, the ratio of the size of the side region circulation to that of the
bottom region should vary.
The above interpretation is schematically shown in Figure 5.3 and Figure 5.4.
Figure 5.5 clearly shows how the velocity generated affects the location of the
lowest temperature region (SHZ or CZ).
As is evident in Figure 5.4, the main fluid flow pathway corresponds nicely
to the whereabout of the coldest zone. Figure 5.5 shows more explicitly such a
phenomenon, while the effect of natural convection may be grossly viewed in a
one-dimensional manner, i.e., a one-dimensional heat transfer affected by an
overall downward fluid (at a velocity generated due to natural convection effect)
(see Figure 5.6). This velocity is determined by the Grashof (Gr) number and
Prandtl (Pr) number. 27
y=H
y=0
y
Fluid in
Fluid out
FIGURE 5.6 An equivalent one-dimensional system simulating the effect of natural convection
on the development of SHZ or CZ (X.D. Chen, unpublished results, 2004).
V
T CP
T w
T w