Chapter 1, Problem 1.47P

Consider a carton of milk that is refrigerated at a temperature of $T_m=5°\text{C}\text{.}$ The kitchen temperature on a hot summer day is $T_{\infty }=30°\text{C}\text{.}$ If the four sides of the carton are of height and width $L=200\text{mm}$ and $w=100\text{mm,}$ respectively, determine the heat transferred to the milk carton as it sits on the kitchen counter for durations of $t=10\text{s},60s,$ and 300 s before it is returned to the refrigerator. The convection coefficient associated with natural convection on the sides of the carton is $h=10{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ The surface emissivity is 0.90. Assume the milk carton temperature remains at $5°\text{C}$ during the process. Your parents have taught you the importance of refrigerating certain foods from the food safety perspective. Comment on the importance of quickly returning the milk carton to the refrigerator from an energy conservation point of view.