A thin-wall cylindrical vessel (1 m in diameter) is filled to a depth of 1.2 m with water at an initial temperature of 15°C. The water is well stirred by a mechanical agitator. Estimate the time required to heat the water to 50°C if the tank is suddenly immersed into oil at 105°C. The overall heat transfer coefficient between the oil and the water is 284 W/(m2 K), and the effective heat transfer surface area is 4.2 m2 .

Question

GIVEN

• A thin wall cylindrical vessel filled with water is suddenly immersed into oil

• Diameter of vessel (D) = 1 m

• Depth of water is vessel = 1.2 m

• Initial temperature (To) = 15°C

• Final temperature (Tf) = 50°C

• Oil temperature (T?) = 105°C

• The overall heat transfer coefficient between the oil and water ( )h = 284 W/(m2 K)

• The effective heat transfer surface area (A) = 4.2 m2 FIND

• The time required to heat the water to 50°C

ASSUMPTIONS

• The thermal capacitance of the cylindrical vessel is negligible

• The temperature of the water is uniform

• The oil temperature remains constant

SKETCH

Answer 1

the temperature-time relationship is