Thermal Food Processing

Simulating Thermal Food Processes Using Deterministic Models 105
I Sequence of radial nodal points for numerical iteration
J Sequence of vertical nodal points for numerical iteration
jh Heating lag factor at geometric center of food container,
dimensionless
k Thermal conductivity, W/m⋅k, with reference to heat
transfer
L Length or thickness, m
R Radius of cylinder or sphere, m
r Any distance along radius from centerline, m
T Temperature, °C
Tc Temperature of cooling medium, °C
TI Initial product temperature, °C
To Pseudo-initial temperature, the temperature at which
an extension of the straight-line portion of the heat
penetration curve intersects the ordinate axis, °C
TR Retort temperature, °C
Tr Reference temperature at which Dr is measured
Tih Initial product temperature at beginning of heating, °C
Tpih Pseudo-initial product temperature at beginning of
heating (see also To), °C
T (ij)
Temperature at any grid node (i, j) in finite difference
solution to heat transfer equation, °C
Temperature at any grid node (i, j) at time t, °C
Temperature at any grid node (i, j) at time (t + ∆t), or
one time interval (∆t) later, °C
Tw Cooling water temperature, °C
t Time, min
x Spatial location within a food container, m
Z Temperature dependency factor in thermal inactivation
kinetics, temperature difference required for 10-fold
change in decimal reduction time (D value), °C thermal
diffusivity, m2 /sec
∆Fi Incremental lethality accomplished over time interval
(∆t), min
∆h Vertical height of incremental volume element ring in finite
difference solution to heat transfer equation, m
∆r Radial width of incremental volume element ring in finite
difference solution to heat transfer equation, m
∆t Time interval between computational iterations in finite
difference solution to heat transfer equation, min
product density, kg/m3 () t
T
( ij)
( t+∆t) T
( ij)