Thermal Food Processing

Infrared Heating 501
Axial Distance, z (mm)
b
o
o
Radial Distance, r (mm)
FIGURE 16.7 Penetration model of radiation energy.
The surface energy flux with wavelength l, Iλ 0 , is represented by the following
based on Plank’s law:
I
λ 0
⎡ 2πch
2 dλ
2πch
2 dλ
⎤
= φ ⎢
−
⎥
λ 5
⎣⎢
exp ( ch/ κλTh)
−1
λ 5 exp
( ch/ κλTf ) − 1
⎦
⎥
(16.12)
where f is the overall absorption coefficient, which can be estimated from a
radiation shape factor, F 21, the emissivity of the IR heater, e 1, and the emissivity
of food, e 2, as follows: 6
φεε = 1 2F21 16.3.2 SURFACE ABSORPTION MODEL (MODEL 2)
(16.13)
Assuming that irradiated energy is all converted to thermal energy at the surface
without permeating to the inside of food (Figure 16.8), the fundamental equation
is represented by the simple heat conduction equation:
∂T
∂ ∂ ∂
α r
∂t
r ∂r
∂ ∂
T ⎛ ⎞ T
=
⎝
⎜ r ⎠
⎟ z
+
⎡1
2 ⎤
⎢
2 ⎥
⎣
⎦
(16.14)
Heat generation term by infrared radiation is included in the boundary
condition, by using the Stefan–Boltzmann law:
At z = Z, k (16.15)
T ∂
=−hT ( − Ta) + ( Th −T
)
∂ z
σφ 4 4
a