Tank contents are being cooled by water circulating through an external heat exchanger. 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
Batch circulation rate, W, is 25,000 pounds per hour
Initial temperature, T1, 250 degrees Fahrenheit
Specific heat, C, is 0.5 BTU per pound per degree Fahrenheit
External Heat-exchanger 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 an external heat exchanger using non-isothermal medium. Temperature of the fluid at any time, theta,
is given in terms of y, where y is given as (K4 minus 1 over M)
times (W times lower case w times lower case c over (K4 lower case w
times lower case c – upper case W times uppercase C) times theta.
K4 is given as e to the power UA times (1 over (upper case W times upper case C) –
1 over (lower case w times lower case c)).
Plugging in the values of U, A, lower case w, lower case c, upper case
W, and upper case C, K4 is found to be 0.748.
For theta equal to 5 hours, y is calculated as 1.254.
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 132 degrees Fahrenheit.