C. Which type of heat exchanger provides a higher heat-transfer rate and by what %?
5. (6 pts) Numerical Solution for a Counter-flow Heat Exchanger (by Daisy Fuchs)
A countercurrent, shell-and-tube heat exchanger with an effectiveness of 54.3% uses a coolant fluid to cool
hot oil. You know that there is one shell pass and four tube passes. Unfortunately, some of the temperature
probes and flow meters have broken. The outlet temperature of the oil, flowing at 15 kg/s, is 60 °C, although
the inlet temperature is unknown. The coolant enters the shell side of the heat exchanger at 15 °C and exits
the heat exchanger at 45 °C. Although the exact flow rate of coolant is unknown, you do know that it is
1
greater than 9 kg/s. The specific heat of the oil is 2.2 kJ/m²-K and the specific heat of the coolant is 4.2
kJ/m²K. The overall heat-transfer coefficient (based on the outside surface area of the tubes) is 1200
W/m²-K and the outside heat-transfer area of the tubes with the correction factored applied is 26.3 m².
A. What are two different methods that you can use to solve for parameters in a shell-and-tube heat
exchanger? When would you use one method over the other?
B. What is the temperature of the hot oil at the inlet of the heat exchanger? Solve the non-linear equation
for this temperature using both the secant method in Excel and a built-in solver in Excel. Include a PDF
of your spreadsheet. Your spreadsheet should be easy to follow, have all variables labeled (including
units), and your name should be on the spreadsheet. Hint: You may need to combine the two methods
from Part A to generate an equation for the unknown entrance temperature of the oil.
C. What is the exact mass flow rate of the coolant?
D. What is the correction factor for this system? What is the outside surface area of the tubes?
E. What is the number of transfer units of this heat exchanger?
F. If the heat exchange was co-current and had the same number of transfer units, what would the
effectiveness be?
