1. principles of the model in a good accuracy to make predictions about
Modelling Condensation and Atmospheric Evaporation on Fruit and Vegetable
Surfaces after Cooling
M. Linke , K. Gottschalk and M. Geyer
Institute of Agricultural Engineering Potsdam - Bornim, Germany
Re-warming of fruits and vegetables after cooling is characterised by heat and mass transfer processes affecting the produce quality (due to microbial growth) at unfavourable environmental conditions
A mathematical model is developed for the determination of the amount of condensed water and the dwell time on fruit surfaces dependent on environmental air conditions
The model describes in a first step the heat and mass transfer processes on single fruits
The process of diffusion of humidity in air and proceed of temperature is the basis for the model
To validate the model some important basic interactions at single produce items under laboratory conditions were measured
The objective is to minimize the negative influences of condensation after cooling by controlling the air flow conditions close to the produce surface
condensation and
atmospheric evaporation
mass flow
heat flow
mass flow
mass flow
heat flow
atmospheric evaporation
and transpiration
principles of the model
validation
calculation
transpiration
E : mass loss rate
A : surface
m : mass
t : time
0 : begin of experiment
1 : end of experiment
= (1+x) / (RA+x RV) · p/T
mass density of humid air
j = - Dair d/dr
= - Dair · d/dx · dx/dr
mass flow density
x : air humidity
j : mass flow density
mass flow density
coupling heat
D : diffusion coefficient vapour in air
r : radial coordinates
q =  (Tsurface – T)
heat flow density
T : temperature
q : heat flow density
Data acquisition system, recording measured values from a highly sensitive balance, a non-contact surface temperature sensor, and a combined air temperature / relative humidity sensor
Calculation of the mass flow density j
during condensation (until 20 min) and atmospheric evaporation (after 20 min)
spherical diffusion equation for air humidity
 =  / T
xs : humidity at saturation point
0 : rel. humidity at far distance
R0 : radius of sphere
r : radial distance
 : heat transfer coefficient
 : heat conductivity
T : boundary layer thickness
x(r) = xs · 0 (1- R0/r) + xs · R0/r
solution of spherical diffusion equation
q = - j  h
Environmental conditions:
- unrestricted natural convection air temperature 21.5 °C
- relative air humidity 60 % r.H initial surface temperature 1.0 °C
h : latent heat
model for the mass flow density
The model represents the condensation and evaporation process on single fruit (plums)
in a good accuracy to make predictions about
the occurrence and duration of these processes along the time after cooling
max. amount of water
surface temperature
dwell time
of surface water
Model calculation of condensation and atmospheric evaporation (surface temperature and changes in relative weight)
Changes in relative weight, surface temperature, and dew point temperature after cooling (measured values)
Institute of Agricultural Engineering Bornim e.V., Max-Eyth-Allee 100, D Potsdam, Germany, Tel ,
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