Strawberries need to be cooled quickly after harvest to ensure high quality. Consider a strawberry (spherical for simplicity, 2.5 cm in diameter) with air at -1 °C blowing over it, leading to a large...

Strawberries need to be cooled quickly after harvest to ensure high quality. Consider a strawberry (spherical for simplicity, 2.5 cm in diameter) with air at -1 °C blowing over it, leading to a large surface heat transfer coefficient. The initial uniform temperature of the strawberry is 23°C. The thermal conductivity, density, and specific heat of strawberries are 0.675 W/m·C, 860 kg/m3 and 3.96 kJ/kg·C, respectively. In practice, the speed of cooling is determined by the 7 /8 cooling time, defined as the time required for the temperature at the center of the strawberry to drop by 7 /8 of the difference between the initial strawberry temperature and the air temperature. 1) Calculate the 7 /8 cooling time. 2) In a package, the strawberries downstream of cold air, i.e., further away from the source of cold air, experience slightly warmer air temperatures (air has been warmed by the strawberries upstream) and therefore do not cool at the same rate, possibly leading to quality problems. For a strawberry downstream that is experiencing an air temperature of 2°C, what would the time needed to reach the same temperature as in 1) be?