E5.16 External Exchanger, Non-Isothermal Cooling

Example 5.16: A tank contains 50000 lb of a fluid at 250 °F. The tank is equipped with an external cooling coil having heating area of 100 ft² and overall heat transfer coefficient of 145 Btu/(h·ft²·°F). The batch materials are circulated at the rate of 25000 lb/h. Specific heat of tank fluid is 0.5 Btu/(lb·°F). What is the temperature of tank contents after 5.0 h, if 10000 lb/h of cooling water are flowing at 85 °F?

Solution: This is a case where tank contents are being heated by an external heat-exchanger.

Initial temperature of the tank contents, T₁ = 250 °F

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

Specific heat of hot fluid, C = 0.5 Btu/(lb·°F)

Mass of the tank contents, M = 50000 lb

Mass flow rate of cooling water, w = 10000 lb/h

Circulation rate of the tank contents, W = 20000 lb/h

Heat transfer coefficient of the external coil, U = 145 Btu/(lb·°F)

Heat transfer surface of the external coil, A = 100 ft²

Heating time, θ = 5 h

The value of the parameter, K₄ can be found to be

And dimensionless temperature, y, can be found as

And the final temperature of the tank contents, T₂, can be calculated as