Question

You are working for a camping gear manufacturer and your boss has asked you to design a new portable cooler. The portable cooler will have the shape of a rectangular prism, with a height of 25 cm, a width of 20 cm and a length of 35 cm. The walls of the cooler will be composed of a thin inner liner (negligible resistance to heat transfer), a gap containing water, and an outer insulating wall having a thickness of 20 mm and a thermal conductivity of 0.025 Wm−1K −1. The idea is to place the cooler inside a freezer before a long trip so that the water trapped inside the wall freezes. The contents could then be maintained at a low temperature because the melting ice would be able to absorb a relatively large quantity of heat transferred from the warm surroundings. Assuming that you would like the ice to take approximately 5 hours to melt on a typical day, how thick would you make the ice layer? You may neglect all multi-dimensional heat transfer effects, and all radiation effects. You may also assume that on a typical day the outside surface temperature of the cooler would be maintained at 30◦C. The latent heat of fusion of ice can be assumed to be 334.0 kJ/kg and the density of the ice is 916.7 kg/m3

Answer 1