To warm up some milk for a baby, a mother pours milk into a thin-walled cylindrical container whose diameter is 6 cm. The height of the milk in the container is 7 cm. She then places the container into a large pan filled with hot water at 70°C. The milk is stirred constantly, so that its temperature is uniform at all times. If the heat transfer coefficient between the water and the container is 120 W/m2·K, determine how long it will take for the milk to warm up from 3°C to 38°C. Assume the entire surface area of the cylindrical container (including the top and bottom) is in thermal contact with the hot water. Take the properties of the milk to be the same as those of water. Can the milk in this case be treated as a lumped system? Why?

Consider a stainless steel spoon ( k = 8.7 Btu/hrft°F) partially immersed in boiling water at 200 deg * F in a kitchen at 75°F. The handle of the spoon has a cross section of 0.08in * 0.5in and extends 7 inches into the air from the free surface of the water. If the heat transfer coefficient at the exposed surfaces of the spoon handle is 3 Btu/hrft²°F, determine the temperature of the tip of the spoon handle. Assume that the heat loss from the tip of the spoon is negligible.

Citrus fruits are very susceptible to cold weather, and extended exposure to subfreezing temperatures can destroy them. Consider an 8-cm-diameter orange that is initially at 15°C. A cold front moves in one night, and the ambient temperature suddenly drops to –6°C, with a heat transfer coefficient of 15 W/m2·K. Using the properties of water for the orange and assuming the ambient conditions to remain constant for 20400 seconds before the cold front moves out, determine the surface temperature of orange that night. Solve this problem using analytical one-term approximation method. The properties of the orange are approximated by those of water at the average temperature of about 5°C, k = 0.571 W/m·°C and α = 0.136 × 10–6 m2/s.   The surface temperature of orange that night is

The 10-mm-thick bottom of a 200-mm-diameter pan may be made from aluminum (k = 240 W/m-K) or copper (k = 390 W/m-K). When used to boil water, the surface of the bottom exposed to the water is nominally at 110°C and heat is transferred from the stove to the pan at a rate of 1200 W. What is the temperature of the surface in contact with the stove for each of the two materials? Aluminum: T = i °C Copper: T = °C Physical Properties Mathematical Functions