An Insulated Box That Holds Yoghurt at Its Setting Temperature for Eight Hours Without Power: A Sizing Rule from the Heat Loss

Yoghurt sets while its culture is held warm, at about 42 to 45 °C, for several hours. A household without a powered incubator must store that warmth in advance. This paper sizes the store. The stated design is a chamber of internal dimensions 0.26 x 0.26 x 0.24 m holding 1.0 kg of yoghurt in jars surrounded by a charge of hot water, insulated with polyisocyanurate board of stated conductivity 0.022 W per m per K, starting uniformly at 45 °C and cooling exponentially toward the room. The sizing rule derived from the heat loss gives the water mass for insulation thickness, hold time, and room temperature. At 60 mm of insulation the rule requires 6.59 kg of water in a 20 °C room and 3.35 kg in a 30 °C room; adopting charges of 7.0 kg and 3.5 kg holds the band for 8.43 and 8.28 hours respectively, ending at 42.14 and 42.09 °C. Thinner insulation is not a saving: at 20 mm the required charge in a 20 °C room is 21.78 kg, which does not fit the chamber at all, while at 100 mm it falls to 3.55 kg. The stated cost of the 60 mm box is USD 37 (panels USD 24, tape and adhesive USD 4, inner container and jars USD 9). A stated smaller charge of 3.0 kg of water in the 60 mm box at 20 °C leaves the band after 4.22 hours and stands at 39.62 °C at eight hours - about half the required hold - and even in a 30 °C room it leaves the band at 7.36 hours. SIMULATED, NOT MEASURED.