E5.15 External Exchanger - Non-isothermal Cooling

Example 5.15: A tank contains 50000 lb of a fluid at 250 °F. The tank is equipped with a cooling coil having a heat-transfer surface of 100 ft². The overall heat transfer coefficient from the coil to the tank is 145 Btu/(h·ft²·°F). Specific heat of the fluid is 0.5 Btu/(lb·°F). What is the temperature of tank contents after 5 h, if 10000 lb/h of cooling water are flowing at a temperature of 85 °F.

Solution: This is a situation where tank contents are cooled with a medium, which exits the internal coil and different temperatures.

Mass of the tank contents, M = 50000 lb

Initial temperature of tank contents, T₁ = 250 °F

Inlet temperature of the cooling medium, t₁ = 85 °F

Heat transfer coefficient of the cooling coil, U = 145 Btu/(h·ft²·°F)

Heat transfer area of the internal coil, A = 100 ft²

Specific heat of tank contents, c = 0.5 Btu/(lb·°F)

Specific heat of water, C = 1 Btu/(lb·°F)

We can find the parameter K₂ as follows

Knowing the value of K₂, we can determine

Plugging in the values of t₁ and T₁, we can find