CHE425: Problem set #1
1. 1) Run the program Microplant as an Established Troubleshooter and turn in the last
display of the program.
You need to copy the Microplant folder from the CHE425 distribution folder into your H:
drive or your flash drive. Open the Microplant folder and double click on Microplant.exe to
run the program. Turn in the last page of the program with performance number.
2) 1A process fluid having a specific heat of 3500 J/kgK and flowing at 2 kg/s is to be cooled
from 80oC to 50oC with chilled water (specific heat of 4180 J/kgK), which is supplied at a
temperature of 15oC and a flow rate of 4.0 kg/s. Assuming an overall heat transfer coefficient
of 2000 W/m2K, calculate the required heat transfer areas for the following exchanger
configurations: (a) parallel flow, (b) counter flow, and (c) shell-and-tube, one shell pass and
2 tube passes.
Ans: Parallel flow, A(m2) = 2.624
Counter flow, A(m2) = 2.434
Shell and tube HX, A(m2) = 2.523
3) 1A counter flow, concentric tube heat exchanger is designed to heat water from 20 to 80oC
using hot oil, which is supplied to the annulus at 180oC and discharged at 140oC. The thin-
wall tube has a diameter of Di = 20 mm, and the overall heat transfer coefficient is 500
W/m2K. The design condition calls for a total heat transfer rate of 3000 W.
(a) What is the length of the heat exchanger?
(b) After 3 years of operation, performance is degraded by fouling on the water side
of the exchanger, and the water outlet temperature is only 65oC for the same fluid flow rates
and inlet temperatures. What are the corresponding values of the heat transfer rate, the outlet
temperature of the oil, and the overall heat transfer coefficient (P. 11.161).
Ans: (a) 0.871 m (b) 2250 W, 150 oC, 336 W/m2K
4. 2Hot exhaust gases are used in a shell-and-tube exchanger to heat 2.5 kg/s of water from 35
to 85°C. The gases, assumed to have the properties of air, enter at 200°C and leave at 93°C.
The overall heat transfer coefficient is 180 W/m2K. Using the effectiveness–NTU method,
calculate the area of the heat exchanger. For a single shell with 2, 4,… tube passes, the
appropriate formula are
E 1 2 / (1 Cr )
E = (1 Cr )
2 1/ 2
NTU = (1 + C 2)-1/2 ln E 1
r
Ans: 40.9 m2
1
Incropera and DeWitt, Fundamentals of Heat and Mass Transfer, Wiley, 6th ed., 2007
2
Incropera and DeWitt, Fundamentals of Heat and Mass Transfer, Wiley, 6th ed., 2007
5. 2In open heart surgery under hypothermic conditions, the patient’s blood is cooled before
the surgery and rewarmed afterward. It is proposed that a concentric tube, counterflow heat
exchanger of length 0.5 m be used for this purpose, with the thin-walled inner tube having a
diameter of 55 mm. The specific heat of the blood is 3500 J/kgK.
m
(a) If water at Th,i = 60°C and h = 0.10 kg/s is used to heat blood entering the exchanger at
Tc,i =18°C and mc = 0.05 kg/s, what is the temperature of the blood leaving the exchanger?
The overall heat transfer coefficient is 500 W/m2K.
(b) The surgeon may wish to control the heat rate q and the outlet temperature Tc,o of the
blood by altering the flow rate and/or inlet temperature of the water during the rewarming
process. To assist in the development of an appropriate controller for the prescribed values of
m c m m
and Tc,i, compute and plot q and Tc,o as a function of h for 0.05 h 0.20 kg/s and
values of Th,i = 50, 60, and 70°C (Use Matlab and put your name on the graph using the Title
command). Since the dominant influence on the overall heat transfer coefficient is associated
with the blood flow conditions, the value of U may be assumed to remain at 500 W/m2K.
Should certain operating conditions be excluded?
Ans: 26.8oC
6. An enthalpy-concentration diagram is given in Figure 1 for a mixture of n-hexane (H), and
n-octane (O) at 101 kPa. Using this diagram, determine the following:
(a) Composition of vapor at bubble-point for 30 mol% nC6.
69 mol% nC6 and 31 mol% nC8
(b) Energy to vaporize 60 mol% of a mixture initially at 100oF with 20 mol% nC6 .
16,500 Btu/lbmol.
(c) Vapor and liquid compositions resulting from part (b).
equilibrium liquid phase composition is at point D, which is 7.5 mol% nC6 , while the
equilibrium vapor composition is at point F, which is 28.5 mol% nC6
7. An enthalpy-concentration diagram is given in Figure 1 for a mixture of n-hexane (H), and
n-octane (O) at 101 kPa. Using this diagram, determine the following:
(a) Temperature and compositions of liquid and vapor, where F1 = 950 lb/h of 30 mol
% nC6 at 180oF is adiabatically mixed with F2 = 1,125 lb/h of 80 mol% nC6 at 240oF.
204oF. The equilibrium vapor is located at point V, while the equilibrium liquid is located at
point L. The equilibrium vapor has a mole fraction of 0.75 for nC6 and 0.25 for nC8. The
equilibrium liquid has a mole fraction of 0.35 for nC6 and 0.65 for nC8.
(b) Energy and resulting phase compositions when a mixture of 60 mol% nC6 at
260oF is cooled and partially condensed to 200oF.
Q = 27,700 - 17,700 = 10,000 Btu/lbmol mixture.
The composition of the equilibrium vapor at point V is 77 mol% nC6. The composition of
equilibrium liquid at point L is 38 mol% nC6 . The amounts of vapor and liquid can be
obtained by material balances and the molar percent vapor = 53%.
(c) Compositions and relative amounts of the two phases when the equilibrium vapor
from part (b) is further cooled to 180oF.
In the diagram, the equilibrium vapor from part (b), shown at F, is cooled to 180oF to point M
in the two-phase region. This mixture splits into equilibrium vapor, V, and equilibrium
liquid, L. The composition of V is 92 mol% nC6. The composition of L is 60 mol% nC6 and
the mole % of equilibrium vapor = 60%.
