I would like build a package with frozen food products (to -18 °C). The products are small balls of pizza dough (diameter of 4 cm). Total dough ball weight is 10 kg (333 balls, 30 grams each).
I'm going to put them into a styrofoam package with dry ice (sealed and insulated) that has inner dimensions 33 x 23 x 28 cm and a wall thickness of 3.5 cm. The dough balls will be stored from 2 to 5 days.
The data for the dry ice:
- 16 mm granules
- Sublimation temperature: -78.5 °C
- Density: 1.1 – 1.4 g / cm^3
External temperature where the box is stored:
a) 10 °C.
b) 21 °C.
My question:
How much dry ice should I include to have all balls still frozen, i.e. have them in a temp. around -2°C, in the case when:
a) time of storage = 3 days
b) time of storage = 5 days
Best Answer
Everything inside the sealed box will reach an equilibrium temperature of -78.5C for as long as there is dry ice inside. You are still missing a few assumptions such as the conductivity of the box (typically 3.3x10-3 W/m/K) and the heat capacity of your dough (assumed to be same as ice).
Once everything has reached that temperature, just to overcome "cold losses", at 10C outside, you need between 1.8 and 2.3 kg for 3 days and between 2.9 and 3.7g for 5 days. At 21C, between 1.9 and 2.5 kg at 10C, 3.3 and 4.2 kg at 21C. You will need an additional amount to chill all the contents (air included) down from -18C to -78.5C, which comes to at least 2.2 kg.
All of this is based on a simplified model and is likely an underestimate.
One problem as @keshlam pointed out is the sublimated dry ice in a sealed container and the pressure build up. Also, between 18% and 28% of your box will be filled with dry ice. 10kg of dough as a single lump will take up another 5% of your cavity, before you consider packing efficiency of spheres. All that leaves you with not a lot of room for gas expansion.
Without any dry ice, if everything is chilled to -18C first, your sealed box should just about keep the dough balls frozen for 3 days at 10C outside.