Tank contents are being cooled by water circulating through a cooling coil installed inside the tank. What would be the temperature of the tank fluid after 5 hours, if the following data applies?
Water: Mass flow rate,
w, is 10,000 pounds per hour.
Inlet temperature, t1, 85 degrees Fahrenheit
Specific heat, Lower case c, is 1.0 BTU per pound per degree
Fahrenheit
Fluid: Mass, M, is 50,000 pounds
Initial temperature, T1, 250 degrees Fahrenheit
Specific heat, C, is 0.5 BTU per pound per degree Fahrenheit
Cooling coil data:
Heat-transfer coefficient, U, 145 BTUs per pound per square
foot per degree Fahrenheit
Heat-transfer surface, A, 100 square feet.
Solution:
It is a very specific case where tank contents are being
cooled by a coil-in-tank using non-isothermal medium. Temperature of the fluid at any time, theta, is given in terms of
y, where y is given as (w times lower case c over (M times uppercase C) times
(K2 minus 1) over K2 times theta.
K2 is given as e to the power UA over (w lower
case c). Plugging in the values of U,
A, w, and lower case c, K2 is found to be 4.263.
For theta equal to 5 hours, y is found to be 1.531.
Temperature of the tank contents after time, theta, is equal
to lower case t1 plus (T1- lower case t1)
times exp (minus y). This yields T2
as 121 degrees Fahrenheit.