Thermal Food Processing

444 Thermal Food Processing: New Technologies and Quality Issues
14.2.4.3 Model for Multiparticle Mixtures in a Continuous-
Flow Heater Containing a Fluid
The model described in the previous section for a static heater has been extended
to the situation of a continuous-flow heater by Sastry. 15 Equations and assumptions
were essentially the same (Equations 14.23 to 14.35) in the introduction of fluid
and particle flow in and out of the system. Both fluid and particles will increase
in temperature (and thus conductivity) during their path through the heater, and
therefore the voltage drop must be calculated not for the whole heater, but
separately for each of the incremental sections into which the heater must be
divided for the calculations. As a consequence of this, Equations 14.23 to 14.32
have to be applied separately for each of those sections, in order to determine
the electric field. Subsequently, Equations 14.3 to 14.5 need to be applied for the
heat generation, and finally Equations 14.33 to 14.35 are applied to resolve the
thermal problem.
The simulations performed with this model allowed several important aspects
of continuous processing with OH technology to be emphasized:
• Although when a multiparticle mixture of low conductivity is present
these particles tend to heat faster than the fluid, if an isolated lowconductivity
particle crosses the system, it can be underprocessed.
• The residence time distribution and the fluid–particle heat transfer coefficient
are crucial aspects to consider when designing a continuous heater.
These results were confirmed and extended by Orangi et al., 16 who studied
a similar problem when investigating the continuous-flow sterilization of
solid–liquid food mixtures by OH.
14.2.4.4 Other Models
Other models of the behavior of particle–fluid mixtures subjected to OH have
been developed. Benabderrahmane and Pain 36 presented a model based on the
principle of a mean slip velocity between the fluid and the particles in plug flow
(the slip phase model). The existence of a difference between the velocity of the
fluid and that of the particles has been demonstrated by Lareo et al., 37 Lareo, 38
Liu et al., 39 Fairhurst, 40 and Fairhurst and Pain, 41 and therefore is considered in
this model. It also takes into consideration internal heat generation, convective
heat transfer, and heat conduction within the solid particles, thus following closely
the scheme outlined in Figure 14.2, although the heater walls are assumed to be
adiabatic. One of the main contributions of this model is that it demonstrates the
importance of the temperature gradient inside the particles. It also confirmed
results obtained earlier by other authors (see, e.g., Sastry 15 ), showing that for a
mixture of particles in a fluid, the process critical point is situated in the fluid
and not in the particles. For conventional heating processes, the critical point is
in the particles.