Last Rev.: 11 JUN 08
SHELL & TUBE HEAT EXCHANGER : MIME 3470
Page 1
Grading Sheet
~~~~~~~~~~~~~~
MIME 3470—Thermal Science Laboratory
~~~~~~~~~~~~~~
Laboratory № 14
~~~~~~~~~~~~~~
SHELL-AND-TUBE HEAT EXCHANGER
~~~~~~~~~~~~~~
Students’ Names / Section №
POINTS
5
APPEARANCE, ORGANIZATION, ENGLISH/GRAMMAR
ORDERED DATA, CALCULATIONS & RESULTS
ORDERED DATA
CALCULATE HOT & COLD AVERAGED MEAN TEMPS, Tm
INTERPOLATED PHYSICAL DATA AT APPROPRIATE TEMPS
CALCULATE HOT AND COLD FLOW RATES, Cmax, Cmin, and Cr
CALCULATE TUBE-SIDE HEAT TRANSFER COEFFICIENT
CALCULATE AVERAGE FLOW AREA ON SHELL SIDE
CALCULATE SHELL-SIDE HEAT TRANSFER COEFFICIENT
INTERPOLATE C1 & m BOTH VERTICALLY & HORIZONTALLY
CALCULATE OVERALL HEAT TRANSFER COEFFICIENT
CALCULATE NTU
CALCULATE EFFECTIVENESS
CALCULATE OUTLET HOT WATER TEMPERATURE
CALCULATE OUTLET COLD WATER TEMPERATURE
CALCULATE PERCENTS ERROR
SUMMARY TABLE OF RESULTS
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
DISCUSSION OF RESULTS
HOW GOOD IS THE NTU METHOD?
EXPLAIN SOURCES OF ERROR
CONCLUSIONS
ORIGINAL DATASHEET
TOTAL
COMMENTS
d
GRADER—
5
5
5
5
100
SCORE
TOTAL
Last Rev.: 11 JUN 08
SHELL & TUBE HEAT EXCHANGER : MIME 3470
MIME 3470—Thermal Science Laboratory
~~~~~~~~~~~~~~
Laboratory №. 14
SHELL-AND-TUBE HEAT EXCHANGER
~~~~~~~~~~~~~~
LAB PARTNERS: NAME
NAME
NAME
SECTION
№
EXPERIMENT TIME/DATE:
NAME
NAME
NAME
TIME, DATE
IMPORTANT—When using the Heat Exchanger Performance Test
Bench, there are some important items to remember for your
safety and the safety of others.
they make many passes. This experiment employs a shell-and-tube
heat exchanger consisting of two tube passes and one shell pass.
THEORY: HEAT EXCHANGER ANALYSIS
Thermodynamics and the First Law dictate the overall energy
transfer in a heat exchanger. There are two widely used methods
of heat exchanger analysis, the NTU-Effectiveness method and the
Log-Mean-Temperature-Difference (LMTD) method. These are
briefly discussed below.
Log-Mean-Temperature-Difference (LMTD) Method
For a heat exchanger between two fluids with given inlet and outlet
temperatures, there are three equations for the rate of heat transfer, Q,
Q = Rate of heat transfer, W
= m 1c p T1,i  T1,o
1. Make sure the proper inlet and outlet valves are open before the
heat exchanger is operated. Failure to do this will pressurize the
system and rupture the heat exchanger seams. As a rule of
thumb, do not close any of the outlet ball valves more than half
way. In particular, make sure the outlet valves that allow the
water to go to the drain are open prior to turning on water.


m 2c p T2,i  T2,o 
2

T1,i  T2,o   T1,o  T2,i 
UA
1
=
=
 T1,i  T2,o 
ln

 T1,o  T2,i 


2. For meaningful data, bleed taps will need to be opened and
closed to allow air to escape while the experiment is going
on. Outlet valves may be closed SLIGHTLY to help keep the
heat exchanger full.
OBJECTIVE of this experiment is to measure the two inlet temperatures and the mass flows through the shell and tubes, in order to predict
the two outlet temperatures using the NTU method and compare these
predicted values with actual measured outlet temperatures.
INTRODUCTION—Many engineering applications involve a
process of heat exchange between two fluids. Heat exchangers are
devices used to promote the heat transferred between two fluids; e.g.,
a car radiator and the condenser units on air conditioning systems.
Space heating, air conditioning, power production, and chemical
processing are typical areas of application.
There are many heat exchanger designs. The laboratory setup for
this experiment contains three heat exchanger types: a shell-and-tube
exchanger, a concentric tube exchanger, and a tube bank exchanger
in cross flow. This particular experiment employs the shell-and-tube
type heat exchanger (see Figure 1). A shell-and-tube heat exchanger
is constructed of tubes that are attached on each end by a plate, called
the tube sheet, through which the tubes pass. One fluid streams into
the inlet of the heat exchanger, flows through the tubes, and exits
through the tube sheet at the opposite end of the heat exchanger.
Page 2
Tlm
where,
m j = mass flow rate of fluid j, kg/s
cp
j
= specific heat of fluid j, J/(kgK)
T = temperature, C
i  inlet
o  outlet
U = overall heat transfer coefficient, W/(m2K)
A = area of surface across heat transfer occurs, m2
For known specific heats, U, A, and entering temperatures, the
three equations above can be solved for three unknowns—T1,o, T2,o,
and Q —by successive substitution of one of the equations for Q onto
another. It is a simple matter to use the log-mean-temperaturedifference method of heat exchanger analysis when the fluid inlet
temperatures are known and the outlet temperatures are specified or
readily determined from the energy balance expressions. The value
of Tlm for the exchanger may then be determined. However, if only
the inlet temperatures are known, use of the LMTD method requires
an iterative procedure. In such cases, it is preferable to use an
alternative approach, termed the NTU-Effectiveness method.
NTU-EFFECTIVENESS METHOD—Often, when working with a given
heat exchanger one must predict the outlet temperatures given the
inlet temperatures. As the dimensions of the exchanger are known, the
NTU-effectiveness method is a popular way to perform this task. This
is an easy method to calculate the overall heat transfer rate, Q. The
number of (heat) transfer units, NTU, is a dimensionless parameter
which precipitates form the heat exchanger analysis and is defined as:
NTU 
Figure 1—Schematic of shell-and-tube exchanger
A shell encloses the internal volume where the tubes are housed.
Another, fluid flows through the shell and heat is exchanged between
the tube-side fluid and the shell-side fluid. In a power plant, most heat
exchangers are of the shell-and-tube design. The number of passes
commonly presents a further description of a shell-and-tube heat
exchanger. A single pass means the fluid flows straight through the
entire heat exchanger without changing direction and so, in this
design, the fluid moves past the length of the heat exchanger only a
single time. In a two-pass heat exchanger the fluid in the tubes goes in
one end, flows to the other end, reverses direction then flows back to
the same end that the fluid entered through a second set of tubes.
Thus, the fluid travels the full length of the heat exchanger twice.
Similarly, multiple pass heat exchangers are so named because
where
UA
,
C min
(1)
U – Overall heat transfer coefficient (W/m2K)
A – Area of heat transfer (m2)
C cp
CC = m
(2a)
– Cold fluid heat capacity rate
 H cp
CH = m
(2b)
 C
 H
– Hot fluid heat capacity rate
Cmin = min(CC, CH)
– Smaller of the two heat capacity rates (W/K)
Cmax = max(CC, CH)
– Larger of the two heat capacity rates (W/K)
Last Rev.: 11 JUN 08
SHELL & TUBE HEAT EXCHANGER : MIME 3470
Note that NTU is a function of geometric and material properties,
and the mass flow rates. It does not include any fluid temperatures.
Using the calculated NTU, the effectiveness of the heat exchanger, ,
can be calculated from tables where the effectiveness formulae for
different heat exchanger arrangements can be found. In such tables,
another dimensionless term that precipitates from the analyses
appears. This is the heat capacity rate ratio, Cr = Cmin/Cmax. For a
shell-and-tube exchanger with one shell pass and some multiple of
two tube passes, the effectiveness is






Hot water inlet thermometer
Cold water
inlet
thermometer
Cold water
outlet
thermometer
1
2 1/ 2 

1 / 2 1  e  NTU 1 C r


  21  C r  1  C r2
 .
2 1/ 2
 NTU 1 C r


1 e


Heat Exchanger Effectiveness—is defined as
Q
Actual rate of heat transfer 
  actual 
Qmax
 Maximum possible rate of heat transfer that an 


 exchanger of infinite heat transfer area

 would have if it had the same inlettemps, flow 




rates, & specific heats as actual case


The maximum heat transfer occurs in the fluid with the least
capacity to absorb or give off heat. This is the fluid with the
minimum value of m C p = Cmin. If this fluid is the cold fluid, its

Page 3
Distance between Tube Sheets, 16-1/8
(inside face to inside face)
5 Baffles, 1.2 thick. Equally spaced to form 6
chamber. 23 tube penetrations per baffle.
30 Tubes, each 0.25 diameter
neglect wall thickness
Hot water
Shell: 5 OD
outlet
thermometer
4.5 ID

The width of the
flow course
varies & thus
the average
velocity
temperature cannot rise above the hot-side, inlet temperature.
Alternately, if the fluid is the hot fluid, it cannot be cooled below
the cold-side, inlet temperature. Thus,
Q
Qactual
.
  actual 
Qmax
m c p
Thot,in  Tcold,in
 min 

As the actual heat transfer is the same for both fluids—one
gaining thermal energy and the other loosing an equal amount—
the actual heat transfer rate is defined by both
Qactual  m c p TC,o  TC,i
and
 C 

Qactual  m c p  TH ,i  TH ,o  .
H
These last two relations yield the outlet temperatures desired.
LABORATORY PROCEDURE
1. Verify the dimensions and features of Figure 2.
2. Generally, small flow rates will generate better results but may
take longer to reach steady state. Also, do not let the air that comes
out of entrainment accumulate in shell. Use bleed taps as needed.
3. For a hot water flow of about 15% of the maximum rotameter
reading and a cold water flow of about 30%, take inlet and outlet
temperatures of both flows until no further changes in temperature are noted. This is the steady-state condition—use only the
associated flow rates and temperatures for calculations.
DETAILED COMPUTATIONAL PROCEDURE
The NTU method will be described using just one tube; but that
single tube could represent an entire tube bundle. The NTU method
calculation procedure for a shell-and-tube heat exchanger follows:
1. a. Determine cold and hot water flow rates, m H and m C (from
rotameter readings), and their specific heats, c p and c p (look
H
C
up values based on the average of the inlet and outlet temperatures). The units of mass flow, m , are kg/s and those of
specific heat, cp, are J/(kgK). [NOTE: Some tables list specific
heat as kJ/(kgK)—so always check units!!]
ST
SL = 0.475
ST = 0.548
SD = 0.548
SL
SD
Figure 2— Experimental apparatus with dimensional data
b. Calculate a temperature specific energy flow known as the
heat capacity rate, C, for both the cold and hot flows
C cold  m cold c pcold  The larger of these is C max
.

C hot  m hot c phot  and the smaller C min
c. Calculate the heat capacity rate ratio, Cr = Cmin/Cmax.
2. Calculate the heat transfer coefficients at the inside and outside
surfaces of the tubes, hinside and houtside. These are used to compute
the overall heat transfer coefficient, U. (See Figure 3)
houtside
hinside
Figure 3—Heat transfer coefficients at inside and outside tube surfaces
a. Flow Inside Tubes: Even though there are many tubes in the
bundle and there are parallel and counter flows in this two-pass
exchanger, the calculation may be performed by considering the
flow in just one of the tubes WITH THE CAVEAT THAT one must
account for the direction of the flow. That is, half of the tubes are
associated with parallel flow and half the tubes are associated
with counterflow. Thus, the mass flow in the equivalent tubes is
m total tube- side flow
 m inside1 tube
N 2
where, N = total number of tubes.
Last Rev.: 11 JUN 08
SHELL & TUBE HEAT EXCHANGER : MIME 3470
From simple flow relations, it is known that the velocity
inside a single tube is
m
Vinside  inside
A
where, A = cross sectional area of one tube.
Given this velocity, a Reynolds number ( Re  VinsideD  )
can be computed to indicate whether the inside flow is
laminar or turbulent. This will most likely be fullydeveloped, laminar flow. For such with constant surface
temperature, Ts, and Pr ~ 0.6 :
Nu D  3.66
where fluid properties are based on the mean (or bulk)
temperature across a cross section, Tm.
If the flow is fully developed, turbulent (Re  10,000),
n  0.4, Ts  Tm
.
Nu D  0.023 Re 4D/ 5 Pr n 
n  0.3, Ts  Tm
Tube-side fluid properties should be evaluated at the
average of the mean temperatures, Tm 
Tm,i  Tm,o
2
.
b. Shell Flow Outside of Tubes: For the staggered tube
arrangement of the experiment shown in Figure 4, use the
following expression for the average Nusselt number
1/ 3
.
Nu D  1.13C1 Re m
D,max Pr
(3)
Use Table 1 to determine m and C1. Note in the report which
values of m and C1 were used. This relation applies when there
are more than 10 tubes in a bundle (NL  10), 2000 < ReD,max <
40,000 where ReD,max is defined below, and Pr  0.7. average
mean temperature of the fluid, Tm , as defined above.
the fluid moving form the A1 to the A2 planes. In this case,
Vmax  ST 2S D  D Vavg , otherwise it occurs at A1 and
Vmax  ST
ST  DVavg .
Note: The average velocity of flow over the tube is not
constant as the shell is not wall-sided but circular. Thus,
one needs to use some average value of area. To use the
relations for staggered tube arrangements, a free-stream, shellside, fluid velocity must be determined. As the sides of the shell
are circular, this free-stream velocity varies. Thus, an average
free-stream velocity must be determined based on an average
width of the shell, wavg. This can be obtained from simple
integration as
r
1


2
2
2
2 r  x
dx

r  1

w av g 
1.25
C1
m
—
—
—
—
—
—
—
—
0.518
0.556
0.451
0.568
0.404
0.572
0.310
0.592
1.5
C1
—
—
0.497
—
0.505
0.460
0.416
0.356
2.0
m
—
—
0.558
—
0.554
0.562
0.568
0.580
C1
—
0.446
—
0.478
0.519
0.452
0.482
0.440
r
 1 dx

0
A t this point, wav g is determined and an answer could be listed as
w av g  1.571
A llternately , the expression abov e could be selected and then
choose SYMBOLIC S: EVA LUA TE : SYMBOLIC A LLY
from the menu to y ield
w av g 
C1
0.213
0.401
—
0.518
0.522
0.488
0.449
0.428
m
0.636
0.518
—
0.560
0.562
0.568
0.570
0.574
Table 1—Constants of for airflow over a staggered tube bank
SD
SL
D
ST
Vavg, T
A2
A1
Figure 4—Staggered tube arrangement
Re D ,max  Vmax D /  is defined for the maximum velocity
occurring within the tube bank, Vmax, which occurs at one of
two locations—either in way of A1 or A2 (see Figure 4). The
maximum velocity will occur at A2 if 2S D  D   ST  D  .
The factor of 2 results from the bifurcation experienced by
1
2
r 
Multiplying this with the distance between baffles gives an
average cross-sectional area, Aavg, for the flow and the
average velocity, Vavg, can be determined from V = AavgVavg.
3. a. Calculate the overall heat transfer coefficient, U
1
U
1
1
t
  

hinner
k
h

 tubes
outer



0
Assumetubes
are thin- walled
& very conductive
3.0
m
—
0.571
—
0.565
0.556
0.568
0.556
0.562

0
ST/D
SL/D
0.600
0.900
1.000
1.125
1.250
1.500
2.000
3.000
Page 4
where, t = the tubing thickness
Then NTU is
This value

NTU 
should be
Cmin
dimensionl ess

Now, the heat exchanger effectiveness, , can be determined.
For one shell pass and two tube passes the effectiveness is
UAtube surface




1/ 2

 NTU 1 C r2

2 1/ 2 1 e
  21  C r  1  C r
2 1/ 2

1  e  NTU 1 C r








1
.
PHYSICAL PROPERTIES—As the liquid (water) is moving, it
must be under a slight pressure. This experiment is interested in the
properties of liquid water density and specific heat which are both
functions of temperature and pressure. However, at low pressures,
one may assume that density and internal energy are approximately
equal to their saturated liquid values at the same temperature; i.e.,
(T, p)  f(T) and u(T, p)  uf(T). Thus, density can be defined.
Enthalpy is, h(T, p)  hf(T) + [p – psat(T)]/f(T). At a room temperature
of, say, 70F (~21C), psat = 0.02487bar. Compared to atmospheric
pressure of 1.01325bar, this is small and negligible. Thus,
h(T, p)  hf(T) + p/f(T). At the temperature assumed, the density of
water is 998kg/m3. At small pressures, say 2atm = 2.02bar,
p/f(T) = 0.202 kJ/kg while hf(T) = 88.14 kJ/kg. Thus, a fair approximation of enthalpy is h(T, p)  hf(T). Finally, the definition of specific
heat is h = c(T) T; thus, C (T, p)  C f(T).
Last Rev.: 11 JUN 08
SHELL & TUBE HEAT EXCHANGER : MIME 3470
FOR THE REPORT
1. Be sure to clearly state/show the calculations along with any
assumptions made on the Mathcad worksheet in the order
appearing on the grading sheet. Of course, you may have other
intermediate calculations.
Page 5
2. Indicate sources of error in equations as they apply to the shelland-tube heat exchanger in the lab, as well as sources of error in
the measurements.
3. Discuss how good is the NTU method.
Last Rev.: 11 JUN 08
SHELL & TUBE HEAT EXCHANGER : MIME 3470
Page 6
ORDERED DATA, CALCULATIONS, and RESULTS The object below is reduced to 70% of full size.
MATHCAD OBJECT--DOUBLE CLICK TO OPEN
DA TA
Look Up (& Interpolate) Phy sical Properties For The 2 Mean Temperatures C alculated A t The Right
1a. Determine Flow Rates Of Hot A nd C old Fluids
1b. C alculate Heat C apacity Rates, The MA X & MIN Heat C apacity Rates,
& The Heat C apacity Rate Ratio
2a. C alculate Heat Transfer C oefficient For Tube Side
2b. C alculate Heat Transfer C oefficient For Shell Side
3a. C alculate Heat Exchanger Effectiv eness
3b. C alculate Outlet Temperatures
The Measured Outlet Temperatures Were
Last Rev.: 11 JUN 08
SHELL & TUBE HEAT EXCHANGER : MIME 3470
DISCUSSION OF RESULTS
Discuss how good is the NTU method.
Indicate sources of error in equations as they apply to the shelland-tube heat exchanger in the lab, as well as sources of error in
the measurements
CONCLUSIONS
Page 7
Last Rev.: 11 JUN 08
SHELL & TUBE HEAT EXCHANGER : MIME 3470
Page 8
APPENDICES
APPENDIX A—DATA SHEET FOR SHELL-AND-TUBE HEAT EXCHANGER LAB
Time/Date:
___________________________
Lab Partners:
___________________________
___________________________
___________________________
___________________________
Verify supplied dimensions given in Figure 2. Is anything else needed?
Is the hot flow on the tube side or shell side? ______________
Rotameter max flow rate: ________________
Run
Cold
Volumetric
Flow Rate, VC
Hot
Volumetric
Flow Rate, VH
( % of max
rotameter rating)
( % of max
rotameter rating)
Hot Outlet
Temperature, T H ,o
Hot Inlet
Temperature, TH ,i
Cold Outlet
Temperature, TC ,o
Cold Inlet
Temperature, TC ,i
(C)
(C)
(C)
(C)
1
2
3
4
5
APPENDIX B—PHYSICAL PROPERTIES TABLE