School Meal Cold Chain: A Phase-Change Box That Holds Milk and Cooked Protein at or Below 5 °C for a Six-Hour Kitchen-to-School Journey

Central kitchens that cook school meals for several schools must move the perishable components — here, a 250 mL milk carton and a 150 g cooked protein portion for each of 60 children, 24.0 kg in total — to a school and hold them safely until they are served, often without refrigeration at the school or in the vehicle. This paper sizes a passive box for that journey: scheduled at 6 hours (1.5 hours of transport and 4.5 hours of waiting) at a 32 °C ambient, with the load held at or below a safe temperature of 5 °C throughout, and sized against an 8-hour design target so that ordinary delays have margin. The design is a box of internal dimensions 0.60 × 0.40 × 0.40 m insulated with 40 mm of expanded polystyrene (U = 0.90 W/m²/K) and carrying 6 kg of phase-change material (PCM) melting at 2 °C with a latent heat of 230 kJ/kg, frozen overnight to −6 °C. A transient lumped enthalpy model holds the load at 2.0 °C through 8 hours, completes melting at 8.87 hours, and does not cross 5 °C until 11.20 hours; the identical box without PCM crosses 5 °C at 1.32 hours. Overnight re-freezing of the PCM requires 1,518.6 kJ (0.422 kWh) of cooling per box in the worst case, or 3.80 kWh of cooling and 2.37 kWh of electricity per night for a nine-box fleet serving 500 children, which two 250 W chest freezers deliver in 7.59 hours but one freezer cannot deliver in an overnight window (15.19 hours). The system costs $293 in capital per box and $68.71 per box per year in total, or $1.15 per child per year ($0.0064 per child per meal) over 180 school days. The failures are as important as the headline: PCM dispatched only half re-frozen crosses 5 °C at 6.53 hours, and at 5.49 hours on a 38 °C day — before a delayed service is complete — and a box whose PCM is half frozen and which is opened 30 times crosses at 4.97 hours, inside the scheduled journey itself.