MODELLING OF HEAT TRANSFER IN HOT FILLED MILK IN COOLING TUNNEL
R.Zitny, M.Houska
Int. conf. Modelling of Thermal Properties and Behaviour of Foods during Production, Storage and Distribution, Prague 23-25 June 1997
The paper deals with mathematical modelling of cooling of milk in a processing line. Milk contained
in a cartoon box has uniform initial temperature (85 0C) after hot filling and enters a tunnel, where cooling
gas (having constant temperature -30 0 C) flows around the box with prescribed velocity. The aim of modelling
is to evaluate the cooling time corresponding to the final mean calorimetric temperature of milk 20
0 C and
first of all to ascertain whether the temperature of cooled milk has not fallen below the freezing point at any
place of box.Scheme
This is a transient natural convection problem , which cannot be solved easily and the numerical
methods have to be used for evaluation of temperature and velocities fields. Both the finite element method
(commertial package COSMOS/M) and control volume method (using FLUENT) were used in 2 and 3
dimensional models assuming laminar flow regime and temperature dependent thermophysical properties of
milk. The results are presented as time depencies of mean calorimetric and point temperatures , showing the
critical point at the corners of box.
A simplified semianalytical approach (model), based upon assumption of a linear temperature profile in a two
dimensional thermal boundary layer is suggested and compared with the numerical prediction. The model is suitable for
modelling of temperature distribution in a two- and also in a three-dimensional box.
The following figure shows time courses of mean calorimetric temperature in the box, mean temperature
at the wall and the lowest local temperature at the corner. Points correspond to the numerical solution, while
the green continuous lines describe the model approximation and the red continuous lines the analytical solution of
temperature distribution in a solid block (only mean temperatures are predicted by these approximations).
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