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. 2020 Apr 29;18(4):e06091. doi: 10.2903/j.efsa.2020.6091

Table B.3.

Simplifications and assumptions used in the heat transfer modelling

Simplifications Assumptions
The model simulates heat transfer by conduction, disregarding any other type of heat transfer phenomena Forced convection due to aeration (forced water mixing) was not considered as it helps to homogenise the temperature distributions, avoiding the emergence of hot/warm spots (especially in tubs). Natural convection and radiation have a minor contribution compared with conduction and forced convection and were not modelled. In boxes, movement of melting water due to gravity was neither considered
The model simulates the change of phase from ice to water using the ‘Apparent Heat Capacity method’ where the latent heat is included as an additional term in the heat capacity (Bonacina et al., 1973) The following parameters were used: transition temperature (Tt) 0°C, transition interval (ΔT) 1°C and latent heat of fusion (λ) 333.5 kJ/kg. Therefore, the so‐called ‘ice domain’ is a perfect mixture of 50% water with 50% ice at the transition temperature (Tt = 0°C), where all is ice at temperatures below −0.5°C (Tt–(1/2) ΔT) and all is water above 0.5°C (Tt + (1/2) ΔT)
Only two fish, assuming an ellipsoid geometry, were explicitly modelled in each container. Instead, for the contribution of the other fish in the same container, the model considered a matrix inspired by the approximation used for porous materials Certain approximations were required to model the temperature of the surface of the tens of fish in both types of containers. Only two fish, assuming an ellipsoid geometry, were explicitly modelled in each container. The contribution of the other fish could not be modelled using the same approach as tens of ellipsoids requires fine meshes, and therefore, many equations that could not be dealt with by standard computing in terms of memory required and computational times. Instead, for the contribution of the other fish in the same container, the model considered a matrix inspired by the approximation used for porous materials made of a mixture of

  • air/fish for boxes with layers of ice on top and bottom; and

  • water/fish for tubs with one layer of ice on the top.

In this matrix, the effective thermal parameters are a linear combination of the thermal parameters of the surrounding media (i.e. air for boxes and water for tubs) and the fish in a proportion given by the volume fraction parameter. From the fraction of fish/water used on the ‘Qualitubfish’ project (Bekaert et al., 2016a), this ratio was set around 0.8
Among all the modelled fish surface temperatures distributed in space (which changed from one location to another), three t/T profiles were retrieved and reported for each container. Thus, from the large number of temperatures simulated at each time in each mesh point), the following highest temperatures were selected
  • •

    For boxes, the maximum temperatures (Tmax) are expected in the centre (in the vertical and horizontal axis), i.e. the furthest location from both ice layers on the top and bottom. Therefore, see Figure 3 for illustration, the selection was:

    • i

      Tmax on the surface of a fish located in the centre of the box;

    • ii

      Tmax on the surface of a fish located in the centre, but close to the box wall; and

    • iii

      Tmax obtained for each time within the whole food/air matrix.

  • For tubs, from the thermodynamic principles, Tmax is expected on the bottom (i.e. the furthest vertical location from the top ice layer); selected temperatures were:

    • iv

      Tmax on the surface of a fish located in the bottom centre of the tub;

    • v

      Tmax on the surface of a fish located in the bottom corner of the tub; and

    • vi

      Tmax obtained for each time within the whole food/water matrix.

For the validation of the heat transfer model, the temperature locations are selected based on the position of the hardware sensors in the ‘Qualitubfish’ project experiments (Bekaert et al., 2016a) with some adjustments due to modelling only two ice layers, whereas the experiments were carried out with three layers (see Section 2.3.2.2 for details). The fish temperatures modelled for the validation consisted of the average temperature of the whole fish, as data loggers were inserted into the fish through the gutting cut
Convective heat flux was considered without air flow As boundary condition (heat transfer between the outside surface of the container and the air of the storage/transport chamber) convective heat flux was considered with the usual heat transfer coefficient (5 W/(m2 °C)) without air flow
Initial conditions were assumed homogenous in space This means that the initial conditions were assumed homogenous in space, i.e. same temperatures for all the points in the same domain. Therefore, the initial spatial distribution of temperatures of, for example, fish, water or container material was not considered
Whenever a parameter, initial condition or boundary condition may be case dependent, the usual practice was considered Assumed values, such as the container‐specific characteristics of the tubs and boxes, are described in Table 1. The fish‐specific characteristics are provided in Table 2