Thermodynamic Model of Meltwater Drainage during Fresh Fish Transport

Meltwater production is calculated in a semi-trailer loaded with 891 EPS boxes holding ca. 20 kg of fresh fish each.

A stacking pattern of boxes typically used in Norway is assumed. Boxes are staggered for stability and four groups of boxes are distinguished:

  1. Boxes at the top
  2. Boxes at the bottom
  3. Boxes at the side
  4. Boxes in the center
Boxes at the center have no side exposed to ambient air in the semi-trailer. Meltwater development is caluclated for each group of boxes independently.

The pathways of heat exchange considered is illustrated in the sketch below.

Figure. Pathways of heat exchange indicated by arrows.

Within each box, fish are assumed to be stacked neatly next to each other, as typically seen in gutted fish of 4 to 5 kg.

Only one quarter of a fish is modeled as a 2-dimensional domain for efficiency, and then replicated thoughout the box. The numerical domain is comprised of two columns, one column top-ice covered, the other free of top-ice, and five rows, an ice layer at the bottom, followed by two main layers of fish, one fish layer representing protruding backs, and a top-ice layer in one of the columns. The fish back forms a triangle. Two columns are used to account for the general observation that ice tends to accumulate at the ends of the box during the course of transport. An example of a domain is shown below.

Figure. Example of a modeled fish box showing box (semi-transparent, brown), fish (blue-green), and top and bottom ice (gray). Note the corrugated interface from the backs of the fish and the only partially ice-covered top ice surface.

The effect of the initial fish temperature and the temperature during transport can be investigated by dragging fish and trucks on the temperature chart.

Figure. Example of selected initial fish temperature and ambient temperature during transportation.

A large number of model parameters can be adjusted to test for model sensitivity. The default paramters are reasonable choices that replicate laboratory and field measurements well.

Meltwater production is illustrated for the first 48 hours in a chart.

Figure. Example model results for transport in a semi-trailer, showing average fish temperature (red circles), range of average fish temperatures across the four groups of boxes (vertical red "error bar" lines), cumulative meltwater production (blue line with dots), and hourly meltwater production rate in the four groups of boxes weighted by the number of boxes in each group (stacked bars).

The cumulative meltwater production is shown as a blue line, the average fish temperature as red circles, and the hourly meltwater production rate as bars. Most of the meltwater production takes place immediately after packaging. After 24 hours, the fish temperature is generally close to 0 °C and the meltwater production rate is small. Note that fish is often stored for a few hours prior to shipment. Hence, the amount of meltwater produced in the semi-trailer may be less than shown if accumulated meltwater is properly drained after loading of the semi-trailer.

Contact: Christian Petrich (


This work was funded by the Norwegian Seafood Research Fund (FHF), project number 901778.