Table of Contents
Executive Summary
2
Introduction
Background
Experimental Apparatus and Procedures
Safety
Assumptions
Calculation Flowcharts
Theory
5
5
7
10
10
11
15
Discussion
Experimental Objectives
Trend Analysis
Error Analysis
23
23
23
27
Results
29
Conclusions
36
Recommendations
38
Bibliography
39
Appendix A
Operating Instructions
40
40
Appendix B
Table of Nomenclature
42
42
Appendix C
Jacketed Tank
Calculations
Graphs
Sample Calculations
Concentric Tube Parallel Flow
Calculations
Sample Calculations
Concentric Tube Counter Flow
Calculations
Sample Calculations
44
44
44
45
46
48
48
49
52
52
53
Appendix D
Raw Data
56
56
1
Executive Summary
Buff Facilities Optimization Group has contracted with Team Excellence to
determine the advantages and disadvantages of two types of heat exchangers.
Specifically, Buff Facilities Optimization Group has asked Team Excellence to determine
the amount of time required to process 50 liters of water from 20oC to 35oC in each unit.
When performing the heat exchanger analysis, we obtained measurements from
two types of equipment which include:

A jacketed stir-tank

A concentric tube in parallel and counter flow
All measurements obtained throughout these experiments, allowed us to determine the
overall heat transfer coefficients, effectiveness and amount of time required to heat 50
liters of water from 20oC to 35oC by each apparatus. We were then able to recommend
which heat exchanger would perform best for the clients’ desired use.
Through our analysis of a jacketed stir-tank and a concentric tube heat exchanger
Team Excellence has concluded that the concentric tube will perform best for our clients’
specified needs. We determined made this determination by evaluating the effectiveness,
overall heat transfer coefficient both theoretically and experimentally and most
importantly the time required to heat 50 liters of water from 20 degrees Celsius to 30
degrees Celsius. The concentric tube heat exchanger proved to perform best throughout
the experiment and all evaluation procedures. Also, we determined that in the case of
limited area available for the heat exchanger itself, the concentric tube takes up a
considerably less amount of space than does the jacketed stir-tank heat exchanger.
2
Through our analysis, Team Excellence has determined that the jacketed stir-tank
is a very inefficient apparatus. The jacketed tank has a considerable amount of heat loss
out of the top of the tank resulting in an increase in the overall heat transfer coefficient,
UA, and a decrease in the effectiveness. This apparatus also takes a considerable amount
of time to heat 50 liters of water from 20 degrees Celsius to 35 degrees Celsius, on the
order of 180 to 205 minutes. The complete results for the jacketed stir-tank are as
follows:
Table I: Jacketed Stir Tank Results
Run 1
Run 2
Uexp A(W/K)
Uth A(W/K)
ε
t (s)
t (min)
72.32
114.41
174.52
240.71
0.0370
0.0431
12268.00
10811.02
204.47
180.18
The large values of the theoretical and experimental overall heat transfer coefficient lead
to a rather large decrease in the effectiveness of the system. The effectiveness for run 1 is
about 0.037 and for run 2 the effectiveness is about 0.043. The effectiveness is a measure
of how well the system operates and should lie between 0.10 and 0.30, where 0.03 to 0.04
is basically unacceptable.
In contrast to the jacketed tank, the concentric tube heat exchange preformed very
well throughout all evaluations and experimental procedures. We ran the concentric tube
in both parallel flow and counter flow. The effectiveness of the concentric tube for both
types of flow was between 0.11 and 0.22, which is considerably higher than the jacketed
tank with an effectiveness of 0.03 to 0.04. The concentric tube has minimal heat loss
resulting in a significant decrease in the amount of time required to heat 50 liters of water
from 20 degrees Celsius to 35 degrees Celsius when compared to the jacketed tank. The
jacketed tank took about 180 to 205 minutes to heat the water, while the concentric tube
3
on average took about 30 minutes, independent of the type of flow used. The complete
results are as follows:
Table II: Concentric Tube in Parallel Flow Results
Run 1
Run 2
Run 3
UAexp (W/K)
46.03
40.39
50.34
ε
0.2056
0.1761
0.2197
UAther (W/K)
49.23
44.00
56.70
t (s)
1983.23
2313.60
1832.47
t (min)
33.05
38.56
30.54
t (s)
1767.25
2116.03
1763.65
t (min)
29.45
35.27
29.39
Table III: Concentric Tube in Counter Flow Results
Run 1
Run 2
Run 3
UAexp (W/K)
47.25
41.91
49.05
ε
0.1062
0.1826
0.2156
UAther (W/K)
53.36
34.84
36.68
By evaluating tables I, II and III we clearly see the best arrangement for our clients would
be to use the concentric tube in counter flow using run 3. Run 3 of our experiment for the
concentric tube in counter flow had a cold water flow rate of 2.68 L/min and a hot water
flow rate of 4.21 L/min. The effectiveness for this procedure was 21.56%, which is within
expected range and a considerably good value. The amount of time required to heat 50
liters of water from 20 degrees Celsius to 35 degrees Celsius is about 29.4 minutes,
which is about 6 to 7 times less than that of the jacketed tank.
4
Introduction
Background
Buff Facilities Optimization Group has contracted with Team Excellence to
determine the overall heat transfer coefficients, effectiveness and the advantages and
disadvantages of two types liquid-liquid of heat exchangers. Specifically, Buff Facilities
Optimization Group has asked Team Excellence to determine the amount of time
required to process 50 liters of water from 20oC to 35oC in each unit.
The analysis of heat exchangers involves many aspects of heat and mass transfer.
Convection caused by internal and external flow, conduction, radiation, condensation and
evaporation are all important concepts to consider. Industrially, heat exchangers are
widely used to increase the conversion of reactants to products by increasing or
decreasing the reactor temperature.
The first apparatus evaluated by Team Excellence was a jacketed tank heat
exchanger. This apparatus consists of a water reservoir and stir propeller surrounded by a
tube of hot flowing fluid. The path of heat transfer for a jacketed tank is from the tube to
the bath and also from the fluid motion caused by stirring the water bath. In this system
we have convection through the tube.
The second apparatus evaluated by Team Excellence was a concentric tube heat
exchanger in parallel and counter flow. A concentric tube is a tube within a tube or a
double pipe. In this system, hot and cold fluids move in the same (parallel flow) or
opposite (counter flow) directions. In our case, the hot fluid runs through the outer tube
while the cold fluid runs through the inner tube keeping in mind that this can run
5
opposite. The heat transfer of a concentric tube is between hot and cold fluids throughout
the tube and consists of convection.
To determine the amount of time required to heat the water from 20oC to 35oC we
first determined the overall heat transfer coefficient, UA. The overall heat transfer
coefficient was determined by use of inlet and outlet temperatures and flow rates for both
hot and cold fluids. The temperatures of all fluids throughout this experiment were
measured by thermocouples at all inlet and outlet areas. Using the centerline temperatures
we were then able to determine the heat capacity, viscosity, thermal conductivity and
Prandtl number for each fluid. These values, assumed to be constant, are then used to find
the experimental and theoretical overall heat transfer coefficients and the effectiveness of
each system.
After determining the overall heat transfer coefficient we were then able to
determine the effectiveness and time required to heat water from 20 degrees Celsius to 35
degrees Celsius by each system. By comparing these values we were then able to give our
recommendation of which heat exchanger would work best for our clients’ desired use.
6
Experimental Apparatuses and Procedures
When performing the heat exchanger analysis, we obtained measurements from
two types of equipment. These measurements allowed us to determine the amount of time
required to heat 50 liters of water from 20oC to 35oC by each apparatus. We also
determined the advantages and disadvantages of each heat exchanger as well as the
effectiveness and overall heat transfer coefficients. The two types of equipment involved
in our analysis were a jacketed tank and a concentric tube in both parallel and counter
flow. Operating instructions for both apparatuses can be found in Appendix A.
The jacketed tank experiment consisted of a water reservoir and stir propeller
surrounded by a tube of hot flowing fluid, as seen in Figure 1 on page 8. There are
thermocouples at the inlet and outlet areas of the tube and a thermocouple in the bath
itself. Also, there is a control box that measures the flow rate of hot water through the
tube. The computer records measurements of temperature and the fluid flow rate through
the tube. The propeller speed remains constant during each experiment and is measured
by a hand-held tachometer.
The concentric tube was the second heat exchanger that we evaluated. The
concentric tube consists of a tube within a tube connected to the flow rate control box that
is connected to both hot and cold water sources, as seen in Figure 2 on page 9. The inlet
and outlet temperatures, for both hot and cold flow, are measured by thermocouples and
recorded by the LabView program. The fluid flow rates remain constant throughout each
experiment, but are varied for each separate experiment. These flow rates are measured
and recorded by LabView.
7
HOT WATER
RESERVOIR
HOSE
COLD WATER
PUMP
CONTROL BOX
Valves
Hot Water
Flowmeter
LabView
Cold Water
Flowmeter
Drain
Thermocouples
20”
12”
HEAT EXCHANGER
HOT WATER OUT
TOP VIEW
COLD WATER OUT
HOT WATER IN
COLD WATER IN
Figure 1: Jacketed Stir Tank Heat Exchanger
8
HOT WATER
RESERVOIR
HOSE
COLD WATER
PUMP
LabView
CONTROL BOX
Valve
s
Hot Water
Flowmeter
Cold Water
Flowmeter
Drain
COLD WATER OUT
¾” Copper Pipe,
½” Copper Pipe
20”
12”
16”
HOT WATER
OUT
12”
HOT WATER
IN
Thermocouples
COLD WATER
IN
Figure 2: Concentric Tube Heat Exchanger
9
Safety
There are a couple of obvious safety concerns involved with this lab. First and
most importantly, this experiment involves water and electricity, which are a dangerous
combination. It is important to keep the area as dry as possible and report any leaking
equipment immediately.
Also, in regards to the flow meter, which has a temperature limit of 50 degrees C
and a flow rate limit of 10 L/minute. Deviations above these limits could lead to the
burning out of electrical equipment, but more importantly mixing of water and electricity.
Assumptions
To calculate values associated with this experiment, the following assumptions were
made:
Jacketed Tank

Negligible kinetic and potential energies

Constant fluid properties

Negligible tube to wall thermal resistance and fowling factors

Fully developed flow conditions
Concentric Tube

Negligible heat loss to the surroundings

Negligible kinetic and potential energies

Constant fluid properties

Negligible tube to wall thermal resistance and fowling factors

Fully developed flow conditions
10
Calculation Flowcharts
Jacketed Tank
All calculations completed throughout the analysis of the jacketed tank are as follows:
Experimental Overall Heat Transfer Coefficient Determination
mh = mass flow rate of hot fluid
mc = mass flow rate of cold fluid
Di = diameter of tank (jacketed)
Do = diameter of helical tubes (jacketed)
Di = inner diameter of annulus (concentric)
Do = outer diameter of outer tube
(concentric)
Do,i = inner diameter of outer tube
(concentric)
 = viscosity
Re = Reynolds number
Nu= Nusselt Number
Pr = Prandtl Number
hi = heat transfer coefficient for inner fluid
ho = heat transfer coefficient for outer fluid
k = thermal conductivity
Cp = heat capacity
= density
U = overall heat transfer coeff.
q = heat transfer rate
 = efficiency
Tm = (Tc,i + Tc,o)/2
Tmf = mean temperature of cold fluid final
Tm,i = mean temperature of cold fluid initially
Tci = temperature of cooling water in
Tco = temperature of cooling water out
Thi = temperature of hot water in
Tho = temperature of hot water out
T∞ = temperature of water in tank
Nr= stir speed of propeller
Lp = length of propeller
t = time
Ai = area of heat transfer inside
Ao = area of heat transfer outside
Energy Balance:
.
mc C p
dT
 UA(Tm  T )
dt
Let
θ = Tmf -T∞
θi = Tm,i - T∞
d θ = dT
Integrating:
Ln θ / θi = 1/(UA/mc *Cp)
*t
Measure Tco, Tci, T
Plot ln θ / θi vs time
Slope =1/ (-UA/ mc /Cp)
Calculate U:
U =1/ ( -slope* mc *Cp/A)
Compare the calculated U
values to theoretical U
obtained using the following
literature correlations
11
Jacketed Tank Calculation Flow Chart Continued
Theoretical Overall Heat Transfer Coefficient
 L2 p N r  

hi 
* 0.54 * 
Di



kf
2 3 
 cp 

* 
k


 13 
ho 
kf
Do
 
*  b 
 w 
1
1
1
1


UA hi Ai ho Ao
Effectiveness of Jacketed Tank
Cmin = mc*Cpc
qactual = mccp,c(Tc,o-Tc,i)
qmax = Cmin(T∞-Tc,i)
qactual/qmax
12
4 mc
Re 
D
* .23 * Re .8 * Pr 3 * (
Theoretical U can be calculated:
Calculate effectiveness:
.
0.14
 b .14
)
w
Concentric Tube
All calculations completed throughout the analysis of the concentric tube are as follows:
Experimental Overall Heat Transfer Coefficient
Tlm 
q  mc c p ,c (Tc ,o  Tc , I )
(Th ,o  Tc ,o )  (Th,i  Tc ,i )
ln(( Th,o  Tc ,o ) /(Th,i  Tc ,i ))
Experimental U can be
calculated:
q  UATlm
Theoretical Overall Heat Transfer Coefficient
Re 
4m h
Di 
Nui  .023 Re
hi  Nu i
4 5 
Hydraulic diameter
D h  Do  Do , i
Pr 0.4 
Re o 
k
Di
4m c
Dh 
Nuo  .023 Re
4 5 
ho  Nu o
Theoretical U can be
calculated:
1
1
1


UA hi Ai ho Ao
13
Pr 0.4 
k
Dh
Concentric Tube Calculation Flow Chart Continued
Effectiveness of Concentric Tube
Cmin = mc*Cpc or
Cmin = mh*Cph
qactual = mccp,c(Tc,o-Tc,i)
qmax = Cmin(Th,i-Tc,i)
Calculate effectiveness:
qactual/qmax
14
Theory
When performing the heat exchanger analysis, we obtained measurements from
two types of equipment. These measurements allowed us to determine the advantages and
disadvantages of each heat exchanger as well as the effectiveness and overall heat
transfer coefficients. Most importantly were are able to use the above findings to
determine the amount of time required to heat 50 liters of water from 20oC to 35oC by
each apparatus. The two types of equipment involved in our analysis were a jacketed tank
and a concentric tube in both parallel and counter flow.
An overall heat transfer coefficient is needed in order to determine the
effectiveness of each unit. The overall heat transfer coefficient is a quantity of the rate at
which heat is transferred and is calculated differently for each heat exchanger. Given
energy balances and appropriate correlations, a theoretical overall heat transfer
coefficient, found in literature, can be compared to an experimentally measured overall
heat transfer coefficient yielding the effectiveness of the system.
The overall heat transfer coefficient, UA, is dependent upon the different modes
of heat transfer. These three modes consist of conduction, convection and radiation. For
the two apparatuses that we analyze we can ignore the effects of conduction and
radiation. Instead, we will concentrate on two different forms of convection:

convection due to internal flow

convection due to external flow
A general correlation for the overall heat transfer coefficient, UA, is as follows:
R" f ,i ln( Do / Di ) R" f ,o
1
1
1





UA hi Ai
2kL
Ao
h0 Ao
Ai
15
eq. (1) [1]
eq. (1) relates the inverse of the overall heat transfer coefficient, UA, to the heat transfer
of the individual heat transfer modes as a sum of the resistances. The first term in
equation (1) represents the inverse of the convection coefficient due to internal tubular
flow, hi, multiplied by the internal tube’s surface area, Ai. The second term represents the
fouling factor inside of the tube, R”f,i. The fouling factor is a measures the buildup of a
film or other deposits that could affect the heat transfer rate. The third term in equation
(1) measures the effect of conduction through the tube. Di and Do are the inner and outer
tube diameters, L is the length of the tube and k is the thermal conductivity of the tube.
The fourth term in equation (1) is a measurement of the fouling factor outside of the tube,
R”f,o, divided by the outside surface area of the tube, Ao. The last term is the inverse of
the convection coefficient due to condensation, ho, multiplied by the outside surface area
of the tube, Ao. Measuring, calculating or using literature values for all of the above
quantities will result in determining a theoretical value for the overall heat transfer
coefficient, UA.
Jacketed Tank
Convection in a heat exchanger is due to heat transfer occurring between two
fluids in motion at different temperatures separated by a bounding surface layer. In order
to calculate the theoretical value of the internal convection coefficient, hi, the following
correlation is needed. A convection coefficient, hi, correlation for internal flow is as
follows:
hi 
kf
Di
* .54 * (
L2p N r 

2
)3 *(
Cp
k
16
1
)3 *(
 b .14
)
w
eq. (2)
[2]
eq. (2) takes into account both the thermal conductivity of the fluid, kf, the length of the
propeller, Lp, the stir speed of the propeller, Nr, the density of the fluid,  , the heat
capacity of the fluid, Cp, and the viscosity,  , of the fluid.
The next value to calculate is that of the convection coefficient due to external
flow, ho; which can be calculated using the following correlation:
ho 
kf
.8
D0
1
3
* .23 * Re * Pr * (
 b .14
)
w
eq. (3) [2]
eq. (3) contains the Reynold’s number, Re, that relates the tube diameter to the flow rate.
The Reynold’s number, Re, can be calculated by the following equation for a jacketed
tank:
.
4 mc
Re 
D
eq. (4)
[1]
.
where m c in eq. (4) is the mass flow rate of the water. Equation (3) also contains the
Prandtl number, Pr, which is a dimensionless ratio of the kinematic viscosity of the fluid
and the fluid’s thermal diffusivity.
Pr 


eq. (5)
[1]
Once equations (4) and (5) are calculated, a value for ho can then be generated.
We will now consider the fouling factor, R”f, terms in equation (1). A common
value for the fouling factor for water is 0.0001 m2K/W, which we can divide by the premeasured outer area of the tube. The fouling factor inside of the tube, R" f ,i , is unknown.
Once equations (2), (3), (4), and (5) have been calculated, a theoretical overall
heat transfer coefficient, UA, can be obtained by use of equation (1).
17
An experimental overall heat transfer coefficient, UAexp, is to be determined next,
which will require an energy balance around the fluids being cooled and heated. For the
jacketed tank:
.
mc C p
dT
 UA(Tm  T ) eq. (6) [1]
dt
where Tm in equation (6) is the mean temperature of the cold fluid and T is the
temperature of the water in the tank. Since the temperature distribution is dependent on
the time, integration is necessary. To simplify terms, let:
  Tm, f  T
 i  Tm,i  T
d  dT
Substitution and integration leads to:
mc * C p

)
* t eq. (7)
i
 UA
Ln(
The plot of ln(

) versus time will give a slope equal to mc*Cp / (-UA). With this value
i
of the slope in hand, we are then able to solve for the experimental overall heat transfer
coefficient, UA.
Having obtained both the theoretical and experimental overall heat transfer
coefficients, the effectiveness can now be calculated using the following correlation:

q actual UAexp

q max
UAtheor
eq.(8) [1]
qactual is the heat transfer rate through the system and is found using:
.
qactual  mc C p,c (Tc,o  Tc,i ) eq. (9) [2]
18
qmax is the maximum heat transfer rate possible through the system and can be obtained
using:
.
qmax  mc C p,c (T  Tc,i ) eq. (10)
[2]
Values obtained from equations (9) and (10) are inserted into equation (8). The resulting
value of the effectiveness, , will quantify the quality of experimental data and the
apparatus itself.
Lastly, the time taken to drain the tank needs to be calculated. The time can be
obtained from a relationship involving the volumetric flow rate and the volume. This
equation takes the form:
t
V
eq. (11)
o
[1]
This time correlation will be used to determine the amount of time required to heat 50
liters of water from 20 degrees Celsius to 35 degrees Celsius. Therefore, the volume, V,
will be 50 liters. The volumetric flow rate, vo, is determined by use of the following
correlation:
o 
qc
eq. (12)
C pc  c T
[1]
where Cpc is the heat capacity of the fluid,  c is the density of the fluid and T is the
temperature difference 15 degrees Celsius of the fluid. Substitution of these known
values into equation (11) will give the requested draining time.
19
Concentric Tube
The theoretical overall heat transfer coefficient for the concentric tube is also
calculated using equation (1). The differences are in the method for calculating the
convection coefficients, hi and ho. The internal convection coefficient, hi, can be
calculated using an internal flow equation:
4
5
Nu  .023 * Re * Pr .4 eq. (13)
[2]
This correlation contains both the Reynolds number, Re, and the Prandtl number, Pr,
which can be found using equations (4) and (5) respectively. Once the Nusselt number,
Nu, is known, we can find the internal tube flow convection coefficient, hi using the
following correlation:
hi 
Nu * k
D
eq. (14)
[2]
The outer tube flow convection coefficient, ho, can also be obtained using equations (13)
and (14). The difference lies in the calculation of the Reynolds number. The procedure
for calculating the Reynolds number still follows equation (2), except this time the
diameter is different. For this correlation we need the hydraulic diameter, Dh, which is the
difference between the tube’s outer diameter and inner diameter. After calculating the
hydraulic diameter, the remaining calculations are straightforward.
The fouling factors, Rf”, and the effects of conduction are calculated in the same
manner as for the jacketed tank. With all of this information, it is now possible to obtain a
value for the theoretical overall heat transfer coefficient, UA.
The experimental overall heat transfer coefficient can be found by performing an
energy balance:
20
q  UATlm eq. (15)
[2]
q is the heat transfer rate through the concentric tube and can be found by performing the
following energy balance:
.
q  mc * C p,c (Tc,o  Tc,i ) eq. (16)
[2]
.
Equation (16) contains the mass flow rate of the cold fluid, m c , the heat capacity of the
cold fluid, Cp,c, and the temperature difference, final minus initial, (Tc,o-Tc,i). The last
value needed in order to calculate the experimental overall heat transfer coefficient,
UAexp, is the log mean temperature difference, Tlm . The log mean temperature is
defined numerically as:
Tlm 
(Th ,o  Tc ,o )  (Th ,i  Tc ,i )
ln(( Th ,o  Tc ,o ) /(Th ,i  Tc ,i )
eq. (17) [2]
It is now possible to calculate the experimental overall heat transfer coefficient, UA,
using equation (15). This value is then compared the theoretical value obtained earlier to
determine the effectiveness,, by the following equation:

q actual UAexp

q max
UAtheor
eq. (18)
[2]
where qactual in equation (18) is determined from equation (9) and qmax can be calculated
using equation (10). When calculating qmax, a value of Cmin is necessary. The value of
Cmin is either:
.
C min  mc * C p ,c
or
.
C min  mh * C p ,h
21
Cmin along with the values calculated from equations (9) and (10) are then used to
determine the effectiveness,, of the system found in equation (18).
Again, the time taken to drain the tank needs to be calculated. The time can be
obtained from a relationship involving the volumetric flow rate and the volume. This
equation takes the form:
t
V
eq. (11)
o
[1]
The volume is already a known quantity of 50 liters given by the clients. The volumetric
flow rate can be found from the following correlation:
o 
qc
eq. (12)
C pc  c T
[1]
where Cpc is the heat capacity of the fluid,  c is the density of the fluid and T is the
temperature difference of 15 degrees Celsius. Substitution of these known values into
equation (12) will determine the amount of time required to heat 50 liters of water from
20 degrees Celsius to 35 degrees Celsius or any other specified rates.
22
Discussion
Experimental Objectives
The objective throughout this experiment is to analyze two types of heat
exchangers to determine the experimental and theoretical overall heat transfer coefficient
and effectiveness of each heat exchanger. Also, determine which heat exchanger can heat
50 liters water from 20 degrees Celsius to 35 degrees Celsius in the shortest amount of
time. These findings will help us to determine which heat exchanger will perform best for
the clients’ specified use.
Trend Analysis
A few trends were evident in our analysis of the heat exchangers. The jacketed
tank heat exchanger seemed to have more heat transfer as the stir speed increased. This
trend, shown in Figure 3 below, was the expected result, because as the stir speed
increases the convection coefficient of the water bath increases, which results in an
increase in the heat transfer rate.
Experimental UA and Effectiveness versus Stir Speed for Jacketed Tank
140
Ex
per 120
im
ent
100
al
UA
(W/ 80
K)
60
0.05
0.045
0.04
Eff
0.035 ect
ive
0.03 ne
0.025 ss
0.02
0.015
40
0.01
20
0.005
0
0
100
120
140
160
180
200
Stir Speed (rpm)
Figure 3: Experimental UA and effectiveness versus the stir speed.
23
Effectiveness
Exp UA
Another trend for the jacketed tank was that the time required to heat 50 liters of
water by 15 degrees Celsius increased with a decrease in stir speed, which directly
corresponds to the heat transfer rate, as seen in Figure 4 below. This decrease was the
expected result that the time would decrease with an increase in the heat transfer rate.
Time versus Stir Speed for the Jacketed Tank
210
205
t (min)
200
195
190
185
180
175
100
120
140
160
180
200
Stir Speed (rpm)
Figure 4: Jacketed tank plot of time versus stir speed.
The results for the concentric tube heat exchanger exhibited trends that were
similar for the counter flow and the parallel flow cases. The trends followed a
polynomial curvature, indicating that either a maximum or a minimum occurred
corresponding to changes in flow rate. The heat transfer rate increased when the flow
rate difference increased from a minimum of 0 kg/s to a maximum of 0.025 kg/s and then
proceeds to decrease. These observations can be seen in Figure 5 for parallel flow and
Figure 6 for counter flow below:
24
60
0.3
50
0.25
40
0.2
30
0.15
20
0.1
10
0.05
0
0
0.01
0.02
0.03
0.04
Effectiveness
Exp UA
Effectiveness and Experimental UA versus Difference between
Cold and Hot Water Flow Rates for Parallel Flow
Effectiveness
Exp UA
0
0.05
Difference (kg/s)
Figure 5: Effectiveness and experimental UA versus difference between cold and hot water flow rates for
parallel flow.
60
0.3
50
0.25
40
0.2
30
0.15
20
0.1
10
0.05
0
0
0.01
0.02
0.03
0.04
Effectiveness
Exp UA
Effectiveness and Experimental
UA versus Difference between Cold and Hot Water Flow Rates for Counter
Flow
Exp UA
Effectiveness
0
0.05
Difference (kg/s)
Figure 6: Effectiveness and experimental UA versus the difference between the cold and hot water flow
rates for counter flow.
As seen in Figures 5 and 6 above, the effectiveness and overall heat transfer coefficients
exhibit maximum values of 0.217 and 48.74 W/K, respectively, at a flow rate difference
of 0.025 kg/s.
Starting at a flow rate difference of 0, the heating time also exhibits a polynomial
trend as seen in Figure 7 for parallel flow and Figure 8 for counter flow below.
25
Time versus the Difference between the Cold and Hot Water
Flow Rates for Paralell Flow
45
40
35
t (min)
30
25
20
15
10
5
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Difference (kg/s)
Figure 7: Time versus the difference between the cold and hot water flow rates for parallel flow.
Time versus Difference between the Cold and Hot Water Flow
Rates for Counter Flow
45
40
35
t (min)
30
25
20
15
10
5
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Difference (kg/s)
Figure 8: Time versus the difference between the hot and cold water flow rates for counter flow.
As seen in Figures 7 and 8 above the time is a maximum at flow rate difference of 0 it
then decreased to a minimal until reaching a difference of 0.025 kg/s and then increases
as it reaches a difference of 0.045 kg/s. This trend was the expected result of increasing
the heat transfer rate, which should decrease the amount of time needed to heat a cold
water stream from 20 degrees C to 35 degrees C.
26
Error Analysis
In this experiment, the main source of error was from our assumption that each
heat exchanger was adiabatic. This assumption was more accurate for the concentric tube
heat exchanger than for the jacketed stir-tank heat exchanger.
The adiabatic assumption was more accurate for the concentric tube because the
theoretical values for the overall heat transfer coefficient, UA, were closer to the
experimental values than when comparing the same the values for the jacketed stir-tank.
However, not one of our experiments had exactly the same experimental overall heat
transfer coefficient, UA, as the theoretical overall heat transfer coefficient, UA. This
situation demonstrates that neither heat exchanger was completely adiabatic. Heat loss
was evident from the experimental overall heat transfer coefficient, UA, being smaller
than the theoretical overall heat transfer coefficient, UA, which means that there was
other heat transfer occurring rather than just convection from the hot water to the cold
water in the heat exchanger.
Also, the jacketed stir-tank was less adiabatic than the concentric tube heat
exchanger because the jacketed tank had a significant amount of heat loss through the top
of the tank. The only barrier between the top of the tank and the ambient air was a piece
of aluminum foil. Although, the foil helped decrease the amount heat loss, it is not a
great insulator because it conducts heat quite rapidly. Therefore, heat was lost by
conduction through the aluminum out of the top of the tank combined with convection
from the air.
The concentric tube heat exchanger had some heat loss, but less than the jacketed
stir-tank. The heat was probably lost by conduction through the copper walls of the
27
concentric tube heat exchanger. In contrast to the jacketed stir-tank, there was more
metal in between the air and the water inside the concentric tube heat exchanger. This
increase in metal thickness insulated the heat exchanger more efficiently. Also, copper
conducts heat less heat than aluminum foil resulting in less heat transfer. One other
factor in the favor of the adiabatic assumption for the concentric tube heat exchanger was
that the hot water ran through the outer annulus and the cold water ran through the inner
of the annulus. This situation allowed for maximum heat transfer between the cold and
hot water. If the hot and cold were switched, then the heat from the hot water would have
a longer distance to conduct through the copper to the outside air, which would decrease
heat loss.
Overall, neither heat exchanger was totally adiabatic, but the concentric tube had
less heat loss than the jacketed stir-tank. In order for the adiabatic assumption to be
valid, each heat exchanger would have to be insulated very well and vacuum tight to
avoid convection from air. This task would be quite expensive and time consuming.
Another easier way to analyze the heat exchangers is to account for the heat loss. The
heat loss can be accounted for by measuring the temperature of the air and the
temperature of the surface of the heat exchanger being exposed to the air. These
observations would allow for an overall energy balance to be performed and calculate the
more accurate theoretical overall heat transfer coefficient, UA.
28
Results
Jacketed Tank
The first step in the analysis of the jacketed tank heat exchanger was to evaluate
the experimental overall heat transfer coefficient, UA, and effectiveness as a function of
the stir speed of the stir propeller in the tank, as shown in Figure 3 below.
Experimental UA and Effectiveness versus Stir Speed for Jacketed Tank
140
0.05
0.045
0.04
100
0.035
0.03
80
0.025
60
0.02
0.015
40
Effectiveness
Experimental UA (W/K)
120
Effectiveness
Exp UA
0.01
20
0
100
0.005
0
120
140
160
180
200
Stir Speed (rpm)
Figure 3: Experimental UA and effectiveness versus the stir speed.
Figure 3 demonstrates that the stir speed directly affects the overall heat transfer
coefficient and the effectiveness of the jacketed tank. As shown in Figure 3, decreasing
the stir speed caused the effectiveness of the heat exchanger to decrease, meaning that the
heat transfer between the cold and hot fluid also decreased. Also, Figure 3 demonstrates
that the overall heat transfer coefficient, UA, increased with an increase stir speed, which
corresponds to an increase the heat transfer between the cold and hot fluid. This situation
makes sense physically, since the increase in stir speed should increase the convection
inside the stir tank, hence increasing the overall heat transfer. Considering these findings,
29
we thought that the time to heat 50 liters of water by 15 degrees Celsius would decrease
with an increase in stir speed, as Figure 4 below shows this assumption is true.
Time versus Stir Speed for the Jacketed Tank
210
205
t (min)
200
195
190
185
180
175
100
120
140
160
180
200
Stir Speed (rpm)
Figure 4: Jacketed tank plot of time versus stir speed.
Figure 4 shows that the time needed to heat 50 liters of water from 20 degrees Celsius to
30 degrees Celsius actually decreased with the stir speed, and thus decreased with the
heat transfer rate. This result makes sense because an increase in heat transfer should heat
up the water faster. However, evaluating the heat loss out of the top of the tank, stirring
the tank more should cause less heat loss to the surroundings resulting in a higher UA
value. The preceding situation causes faster stir speeds to heat the water faster. The
jacketed stir tank definitely takes a large amount of time to heat 50 liters of water than the
concentric tube. According to our calculations, the time required for heating the water by
15 degrees Celsius is about 180 to 205 minutes.
The theoretical overall heat transfer coefficient, UA, was calculated for each stir
speed of the jacketed tank and the results are given in Table IV.
30
Table IV: Jacketed Stir Tank Results
Run
Speed
Theoretical UA(W/K)
1
115 rpm
174.52
2
192 rpm
240.71
Uncertainties +/-1 rpm
+/-.05
Experimental UA (W/K)
72.32
114.41
+/-.05
Table I shows that the experimental overall heat transfer coefficient, UA, was marginally
less than the theoretical overall heat transfer coefficient, UA. This situation was more
than likely due to the assumption that the apparatus operated adiabatically. While
minimizing heat loss from the top of the tank with aluminum foil, we were unable to
completely prevent heat loss. Therefore, our adiabatic operation assumption is flawed.
Concentric Tube
The parallel flow concentric tube heat exchanger analysis begins by evaluating
the experimental overall heat transfer coefficient, UA, and effectiveness as they relate to
the difference between the cold water and hot water flow rates, as shown in Figure 5.
60
0.3
50
0.25
40
0.2
30
0.15
20
0.1
10
0.05
0
0
0.01
0.02
0.03
0.04
Effectiveness
Exp UA
Effectiveness and Experimental UA versus Difference between
Cold and Hot Water Flow Rates for Parallel Flow
Effectiveness
Exp UA
0
0.05
Difference (kg/s)
Figure 5: Effectiveness and experimental UA versus difference between cold and hot water flow rates for
parallel flow.
31
Figure 5 shows that the experimental overall heat transfer coefficients, UA, and
effectiveness increase as the difference between the hot and cold water flow rates
increase. This increase occurs until UA and the effectiveness reach a maximum value at a
flow rate difference of about 0.025 kg/s, they then begin to decrease. The time to heat 50
liters of water by 15 degrees Celsius was also calculated for this condition and is depicted
in Figure 7 below.
Time versus the Difference between the Cold and Hot Water
Flow Rates for Paralell Flow
45
40
35
t (min)
30
25
20
15
10
5
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Difference (kg/s)
Figure 7: Time versus the difference between the cold and hot water flow rates for parallel flow.
Figure 7 shows that the time to heat the 50 liters of water decreases as the heat transfer
rate and effectiveness increase. By evaluation of Figures 5 and 7, the optimum difference
between the hot and cold flow rates for parallel flow is to about 0.025 kg/s. According to
our calculations, the time required for heating the water by 15 degrees Celsius in the
parallel flow concentric tube is about 30 minutes.
The theoretical overall heat transfer coefficient, UA, was calculated for the
parallel flow concentric tube heat exchanger, and the results are in the following Table V.
32
Table V: Concentric Tube Parallel Flow Results
Run
Difference (kg/s)
Theoretical UA (W/K)
1
2
3
Uncert.
Experimental UA (W/K)
49.23
44.00
56.7
+/-.05
0.046
0.0003
0.0254
+/-.005
46.03
40.39
50.34
+/-.05
The theoretical overall heat transfer coefficients, UA, for the parallel flow were only
slightly larger than the experimentally determined values. This suggests that there was
minimal heat loss from this heat exchanger to the surrounding. Therefore, our assumption
of adiabatic operation holds true.
The concentric tube heat exchanger was also evaluated for counter flow operation.
The effectiveness and experimental overall heat transfer coefficient, UA, versus the
difference between the flow rates is shown in Figure 6.
60
0.3
50
0.25
40
0.2
30
0.15
20
0.1
10
0.05
0
0
0.01
0.02
0.03
0.04
Effectiveness
Exp UA
Effectiveness and Experimental
UA versus Difference between Cold and Hot Water Flow Rates for Counter
Flow
Exp UA
Effectiveness
0
0.05
Difference (kg/s)
Figure 6: Effectiveness and experimental UA versus the difference between the cold and hot water flow
rates for counter flow.
Figure 6 has a similar trend to Figure 5. As the difference between the cold and hot water
flow rates increased the overall heat transfer coefficient, UA, and effectiveness increased
to a certain maximum point, again around 0.025 kg/s. Therefore, the heat transfer rate for
33
the concentric tube is independent of the type of flow. The difference in flow rates of the
concentric tube should be about 0.025 kg/s to achieve optimal heat transfer. The time to
heat 50 liters of water was calculated for the counter flow case and is illustrated in Figure
8 below.
Time versus Difference between the Cold and Hot Water Flow
Rates for Counter Flow
45
40
35
t (min)
30
25
20
15
10
5
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Difference (kg/s)
Figure 8: Time versus the difference between the hot and cold water flow rates for counter flow.
Figure 8 demonstrates that the time to heat the 50 liters of water is a minimum at a flow
rate difference of 0.025 kg/s. Also, Figure 8 shows that the time started to slightly
increase with an increase in flow rate difference. The time to heat the water was again
much less than the jacketed stir tank, taking around 28 minutes as opposed to 180 to 205
minutes.
The theoretical UA values were calculated for the counter flow case and are
summarized in Table VI.
Table VI: Concentric Tube Counter Flow Results
Run
Difference (kg/s)
Theoretical UA (W/K)
1
52.98
0.0438
2
34.56
0.0006
3
36.36
0.0245
Uncert.
+/-.05
+/-.005
34
Experimental UA (W/K)
46.97
41.66
48.74
+/-.05
Table VI shows that the theoretical overall heat transfer coefficient, UA, values were
slightly larger than the experimental UA values. This situation shows that the adiabatic
assumption is not completely accurate.
35
Conclusions
The concentric tube heat exchanger heated the water in a shorter amount of time
than the jacketed stir-tank. This situation makes sense because the jacketed stir-tank is a
batch process. A batch process has a large amount of fluid volume on the inside of the
tank compared to a much smaller amount of volume of hot fluid flowing through the
tubes surrounding the tank. This tank has much less surface area of heat transfer than the
concentric tube. The concentric tube has more surface area of heat transfer because the
hot fluid is flowing constantly over the cold fluid. A similar amount of volume flows
through the outer and inner annulus of the concentric tube, allowing for much greater
heat transfer. For these reasons the experimental and theoretical overall heat transfer
coefficient, UA, for the jacketed-stir tank is much larger than that of the concentric tube.
By evaluating complete results listed in tables I, II and III below, with a heating
time of about 29.4 minutes we clearly see the best arrangement for our clients would be
to use the concentric tube in counter flow Run 3. Run 3 of our experiment on the
concentric tube in counter flow had a cold water flow rate of 2.68 L/min and a hot water
flow rate of 4.21 L/min. The effectiveness for this procedure was 21.56%, which is within
expected range and a considerably good value.
Table I: Jacketed Stir Tank Results
Run 1
Run 2
Uexp A(W/K)
Uth A(W/K)
ε
t (s)
t (min)
72.32
114.41
174.52
240.71
0.0370
0.0431
12268.00
10811.02
204.47
180.18
t (s)
1983.23
2313.60
1832.47
t (min)
33.05
38.56
30.54
Table II: Concentric Tube in Parallel Flow Results
Run 1
Run 2
Run 3
UAexp (W/K)
46.03
40.39
50.34
UAther (W/K)
49.23
44.00
56.70
36
ε
0.2056
0.1761
0.2197
Table III: Concentric Tube in Counter Flow Results
Run 1
Run 2
Run 3
UAexp (W/K)
47.25
41.91
49.05
UAther (W/K)
53.36
34.84
36.68
37
ε
0.1062
0.1826
0.2156
t (s)
1767.25
2116.03
1763.65
t (min)
29.45
35.27
29.39
Recommendations
Overall, we have two different recommendations for the use of the heat
exchangers based on the clients’ needs. If the clients desire to run the apparatus
continuously or for long periods of time, the concentric tube heat exchanger would be
their best option. The concentric tube is the best choice for this situation because it does
not require any downtime for setup or shut down; the opposite is true for the jacketed stirtank. Likewise, if the clients wish to heat large amounts of water at any one time quickly,
then their best option would be a concentric tube heat exchanger because of its ability to
heat large amounts of water quickly. One other concern for the clients to consider is how
much space they have available for the heat exchanger. Concentric tube heat exchangers
are generally smaller than jacketed stir-tanks and are therefore the best option when
dealing with a limited amount of space.
The best arrangement for our clients would be to use the concentric tube in
counter flow use run 3. Run 3 of our experiment on the concentric tube in counter flow
had a cold water flow rate of 2.68 L/min and a hot water flow rate of 4.21 L/min., which
corresponds to a flow rate difference of 0.025 kg/s. The effectiveness for this procedure
was 21.56%. The time required to heat water from 20 degrees Celsius to 35 degrees
Celsius is 29.4 minutes using the above arrangement.
38
Bibliography
1. Chemical Engineers’ Handbook
Perry, Robert; Chilton, Cecil H.
McGraw-Hill Book Company
New York, 5th edition 1973
Section 11
2. Fundamentals of Heat and Mass Transfer
Incropera, Frank P.; DeWitt, David P.
John Wiley & Sons, Inc.
New York, 5th edition 2002
Chapter 11
39
Appendix A
Operating Instructions: Modular Heat Exchanger
Set Up for Jacketed Tank
1) Verify all drains are closed and then fill the water reservoir on the main cart of the
heat exchanger with a mixture of hot and cold water from the sink.
2) Set the main cart for the heat exchanger next to the spigot and drain. Verify all
valves are closed and all switches are off.
3) Make the following electrical connections: plug the thermocouple control box into
the large extension cord hanging by the vertical I-beam, verify all connections,
plug the military connecter into the labview.
4) Turn the unit on.
5) Set the hot water setpoint using the “up” and “down” arrows on the “heater
control”.
6) Open the bypass valve and turn on the pump and both heaters. Allow water to
circulate until the desired temperature is met.
Set up for Concentric Tube Heat Exchanger
1) Attach thermocouples directly to the heat exchanger entrance and exit.
2) Place one flowmeter downstream of the heat exchanger on the hot stream and one
upstream of the exchanger on the cold side.
3) Connect a hose to the “cold water in” port on the right side.
4) Connect the “cold water out” port to the inlet of the cold flowmeter.
5) Connect the exit of the flowmeter to a thermocouple fitting and then to the cold
water inlet in the heat exchanger.
6) Connect the cold water exit of the heat exchanger directly to the second
thermocouple fitting.
7) Connect this fitting to the clear tubing labeled “drain” and return to floor drain.
8) Connect the “hot water out” port to a thermocouple fitting and connect the fitting
directly to the hot water inlet on the heat exchanger.
9) Connect a second thermocouple fitting to the hot water exit of the heat exchanger
and then to the inlet of the “hot” flowmeter.
10) Plug flowmeter cables into the back of the control box.
11) Open LabView.
12) Enter thermocouple channels and time intervals when we want data taken.
Operation
1) Start the flow of water.
2) Turn on the cold water, close the bypass valve, and open the “cold water out”
valve, the “hot water out” valve, and the “hot water return” valve. Use regulators
to monitor flowrate, never exceeding 10 L/min.
3) Verify that the temperatures and flowrate data are visible.
40
4) If after a while the tank heaters cannot keep up with cooling capability of the
exchanger, circulate the water in the tank until the temperature stabilizes.
Clean Up
1)
2)
3)
4)
Turn off all heaters, pumps and the main power switch.
Disconnect all wires and tubing.
Drain each side of the exchanger, the water reservoir, and each piece of tubing.
Clean up any water on the floor.
41
Appendix B
Nomenclature
Description
Symbol
Units
Value
area of heat transfer inside
m2
calculated
area of heat transfer outside
m2
calculated
A (tubes) surface area of helical tubes
m2
calculated
A (tank)
h (tank)
surface area of jacketed tank
height of the jacketed tank
m2
m
calculated
measured
Di
inner diameter of the tubes
m
measured
m
m
m
m
m
m
m
kg/s
kg/s
measured
measured
measured
calculated
measured
measured
measured
specified
specified
Ai
Ao
Do
outer diameter of the tubes
D (tank) diameter of jacketed tank
Do (tubes) outer diameter of the helical tubes
Dh
hydraulic diameter of tubes
L (tubes) length of the jacketed tank tubes
L
length of the concentric tubes
Lp
propeller length
m (dot), c mass flow rate of cold fluid
m (dot), h mass flow rate of hot fluid
μ
Re
Nu
Pr
viscosity
reynolds number
nusselt number
prandtl number
hi
convective heat transfer coefficient of inside
W/m2K
calculated
convective heat transfer coefficient of outside
W/m2K
calculated
k
Cmin
thermal conductivity
minimum heat capacity rate
W/m2K
W/K
looked up
calculated
Cp
heat capacity
J/kgK
looked up
density
kg/m3
looked up
U
overall heat transfer coefficient
W/m2K
calculated
qactual
heat transfer rate from experiment
W
calculated
qmax
ε
maximum heat transfer rate possible
effectiveness
Th (bar)
centerline temperature of hot fluid
K
calculated
Tc (bar)
centerline temperature of cold fluid
K
calculated
Tm
mean temperature
K
calculated
Tm,f
final mean temperature of cold fluid
K
calculated
Tm,i
initial mean temperature of of cold fluid
K
calculated
Tci
temperature of cooling water in
K
specified
Tco
temperature of cooling water out
K
specified
ho
ρ
N*s/m2
looked up
dimensionless calculated
dimensionless calculated
dimensionless calculated
42
W
calculated
dimensionless calculated
Symbol
Nomenclature (cont)
Description
Units
Value
Thi
temperature of hot water in
K
specified
Tho
T∞
temperature of hot water out
temperature of water in tank
K
K
specified
specified
Nr
t
stir speed of propeller
time
ΔTlm
log mean temperature
K
calculated
V (tank)
volume of jacketed tank
m3
measured
V
volumetric flow rate for concentric tube
m3 /s
calculated
rpm
measured
seconds calculated
43
Appendix C
Jacketed Tank Calculations
Jacketed Tank Parameters
h (tank)
0.2445
m
D (tank)
0.2020
m
A (tank)
0.1552
m2
Lp
0.0630
m
Do (tubes)
0.0160
m
L (tubes)
11.23
m
A (tubes)
0.5645
m
V(tank) =
6.231
L
Temperature (oK)
Stir Motor
Run 1
Run 2
Flow (L/min)
4.12
4.17
Tc,o
284.09
283.04
Tc,i
283.20
282.04
T(inf)
307.22
305.21
Speed (rpm)
115
192
Run 1
Run 2
Tc (bar)
283.65
282.54
Cp,c (J/Kg K)
4191.2
4193.2
mu (N s/m2)
1.27E-03
1.32E-03
k (W/m K)
0.644
0.643
Pr
9.16
9.48
Run 1
Run 2
mdot,c (kg/s)
0.06873
0.06948
Time(s)
2116.015
2340
Slope
-8.00E-07
-5.00E-07
Uexp A(W/K)
72.32
114.41
Run 1
Run 2
hi (W/m2/K)
1147.45
1595.27
ho (W/m2/K)
15628.13
15493.17
1/UA (K/W)
0.00573
0.00415
Uth A(W/K)
174.52
240.71
Run 1
Run 2
Cmin (W/K)
4.801
4.856
qactual (W)
4.270
4.848
qmax (W)
115.29
112.53
ε
0.03704
0.04308
V (L/s)
Run 1
Run 2
0.004075645
0.004624912
t (s)
12268.00
10811.02
Uexp A(W/K)
Uth A(W/K)
ε
t (s)
t (min)
72.32
114.41
174.52
240.71
0.0370
0.0431
12268.00
10811.02
204.47
180.18
Run 1
Run 2
44
p (kg/m3)
1000
1000
Ln(Theta/Theta i) versus Time for 115 rpm
1
0.8
y = -8E-07x + 0.0012
0.6
Ln(Theta/Theta i)
0.4
0.2
0
0
500
1000
1500
2000
2500
-0.2
-0.4
-0.6
-0.8
-1
Time (s)
Ln(Theta/Theta i) versus Time for 192 rpm
1.000000
0.800000
y = -5E-07x + 0.0008
0.600000
Ln (Theta/Theta i)
0.400000
0.200000
0.000000
0
500
1000
1500
-0.200000
-0.400000
-0.600000
-0.800000
-1.000000
Time (s)
45
2000
2500
46
47
Concentric Tube Parallel Flow
Concentric Tube Parameters
Ai
0.0264
m2
Ao
0.0425
m2
Di
0.0138
m
Dh
0.0084
m
Do
0.0222
m
L
0.6100
m
Temperature (K)
Run 1
Run 2
Run 3
Flow 0 (L/min)
5.44
2.67
2.66
Flow 1 (L/min)
2.71
2.72
4.24
Tc,o
286.68
289.90
291.83
Th,o
316.83
318.81
320.79
Tc,i
282.50
282.59
282.56
Th,i
326.36
327.14
327.44
Run 1
Run 2
Run 3
Tc (bar)
284.59
286.25
287.20
Cp,c (J/Kg K)
4189.7
4187.8
4186.8
µ (N s/m2)
1.24E-03
1.19E-03
1.16E-03
k (W/m K)
0.589
0.592
0.594
Prc
8.93
8.5
8.26
ρc (Kg/m3)
1000
1000
1000
Run 1
Run 2
Run 3
Th (bar)
321.60
322.98
324.11
Cp,h (J/Kg K)
4180.6
4181.2
4181.6
µ (N s/m2)
5.61E-04
5.48E-04
5.37E-04
k (W/m K)
0.642
0.643
0.644
Prh
3.658
3.56
3.48
ρh (Kg/m3)
988.53
987.95
987.56
Run 1
Run 2
Run 3
m(dot),c (Kg/s)
0.0906
0.0445
0.0443
m(dot),h (Kg/s)
0.0446
0.0448
0.0697
qc (W)
1588.32
1361.51
1718.99
qh (W)
1778.93
1560.48
1939.71
qmean (W)
1683.62
1461.00
1829.35
Delta Tlm
36.58
36.17
36.34
Run 1
Run 2
Run 3
ReD,c
7343.1
7544.3
11979.5
NuD,c
47.8
48.4
69.4
hi,c (W/m2 K)
2225.3
2252.9
3236.8
ReD,h
11075.10
5664.75
5791.09
NuD,h
94.96
54.46
54.79
ho,h (W/m2 K)
6658.59
3837.80
3874.67
Cmin (J/s*K)
186.66
186.24
185.55
qmax (W)
8187.45
8297.30
8326.80
V (m3/s)
2.5211E-05
2.1611E-05
2.7286E-05
V (L/s)
0.02521
0.02161
0.02729
UAther (W/K)
49.23
44.00
56.70
ε
0.2056
0.1761
0.2197
t (s)
1983.23
2313.60
1832.47
t (min)
33.05
38.56
30.54
Uther (W/m2 K)
Run 1
1842.50
Run 2
1650.57
Run 3
2130.48
Run 1
Run 2
Run 3
UAexp (W/K)
46.03
40.39
50.34
48
49
50
51
Concentric Tube Counter Flow
Concentric Tube Parameters
Ai
0.0264
m2
Ao
0.0425
m2
Di
0.0138
m
Dh
0.0084
m
Do
0.0222
m
L
0.6100
m
Temperature (K)
Run 1
Run 2
Run 3
Flow 0 (L/min)
5.35
2.69
2.68
Flow 1 (L/min)
2.75
2.76
4.21
Tc,i
281.92
282.02
282.29
Th,o
317.35
318.53
320.81
Tc,o
286.69
289.94
291.83
Th,i
326.73
326.89
327.14
Run 1
Run 2
Run 3
Tc (bar)
284.30
285.98
287.06
Cp,c (J/Kg K)
4196.7
4188
4186.9
µ (N s/m2)
1.25E-03
1.20E-03
1.17E-03
k (W/m K)
0.589
0.592
0.593
Prc
9.013
8.57
8.3
ρc (Kg/m3)
1000
1000
1000
Run 1
Run 2
Run 3
Th (bar)
322.04
322.71
323.98
Cp,h (J/Kg K)
4180.8
4181
4181.6
µ (N s/m2)
5.5701E-04
5.5044E-04
5.3800E-04
k (W/m K)
0.642
0.643
0.644
Prh
3.63
3.58
3.49
ρh (Kg/m3)
988.34
988.04
987.56
Run 1
Run 2
Run 3
m(dot),c (Kg/s)
0.0891
0.0449
0.0447
m(dot),h (Kg/s)
0.0453
0.0455
0.0692
qc (W)
1782.44
1488.64
1786.07
qh (W)
1779.18
1589.95
1832.72
qmean (W)
1780.81
1539.29
1809.39
Delta Tlm
37.69
36.73
36.89
Run 1
Run 2
Run 3
ReD,c
6484.86
3400.73
3472.96
NuD,c
62.11
36.32
36.47
hi,c (W/m2 K)
2613.27
1535.93
1544.71
ReD,h
12957.58
13160.24
20485.33
NuD,h
66.03
66.57
94.13
ho,h (W/m2 K)
5298.63
5350.87
7577.50
Cmin (J/s*K)
374.06
187.92
187.07
qmax (W)
16761.75
8432.01
8390.72
V (m3/s)
2.82926E-05
2.36292E-05
2.83503E-05
V (L/s)
0.02829
0.02363
0.02835
UAther (W/K)
53.36
34.84
36.68
ε
0.1062
0.1826
0.2156
t (s)
1767.25
2116.03
1763.65
t (min)
29.45
35.27
29.39
Uther (W/m2 K)
Run 1
1750.12
Run 2
1193.38
Run 3
1283.13
Run 1
Run 2
Run 3
UAexp (W/K)
47.25
41.91
49.05
52
53
54
55
Appendix D
56