final double pipe
TRANSCRIPT
Double- Pipe Heat Exchanger
PERFORMANCE OF A DOUBLE-PIPE HEAT
EXCHANGER
INTRODUCTION
Modern manufacturing industries employ processes that require heating and
cooling. From the preparation of the raw materials, to their processing, to the
conditioning of the final products into sellable items and even down to the treatment
of process effluents, heat transfer mechanisms are always applied. Most of the
time, heating and cooling are done using heat exchangers and a double-pipe heat
exchanger is one of the commonly used type. Being such a vital industrial tool, it is
of great importance that chemical engineering students learn the basic concepts
and theories especially the operation of a double-pipe heat exchanger. The
fundamental concepts applied will enable the students to analyze and design other
types of heat exchanger.
OBJECTIVES
1. To familiarize the students with the characteristics, parameters and problems
involved in the operation of a double-pipe heat exchanger when operated
using countercurrent or co-current flow.
2. To determine and compare measured and calculated mean temperature
difference between hot and cold water in both countercurrent and co-current
flow.
3. To compare experimental overall heat transfer coefficient obtained using data
from direct measurements with the theoretical overall heat transfer
coefficients calculated using available empirical equations.
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THEORY
Although there are several ways of transferring heat between fluids, the most
common is the use of a heat-exchanger wherein the hot fluid and cold fluid are
separated by a solid boundary. Different types of heat exchangers have been
developed. The simplest type is a double-pipe heat exchanger. This consists
essentially of two concentric pipes with one fluid flowing through the inside of the
inner pipe while the other fluid moves co-currently in the annular space. This type of
heat exchanger, however, is not recommended for processes that require very large
heating surfaces.
The heat transfer analysis of a double-pipe heat exchanger deals with the
application of several equations that relate the different parameters involved.
Consider the heat exchanger,
Where:
mh = Mass flow rate of hot fluid, lbm/hr
mc = mass flow rate of cold fluid, lbm/hr
Tc = temperature of cold fluid, °F
Th = temperature of hot fluid, °F
**subscript 1 refers to entrance conditions, 2 refers to exit conditions
To determine the rate of heat loss by the hot fluid or the heat gained by the cold
fluid, we apply a steady overall energy balance between the two ends of the heat
exchanger. On the basis of 1 lbm/sec of fluid flowing, we have,
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Double- Pipe Heat Exchanger
W + JQ = ΔZ( ggc ) + v2
2αgc + JΔH (1)
Where: W = shaft work
ΔZ( ggc ) = mechanical potential energy
v2
2α gc = mechanical kinetic energy
α = kinetic energy velocity correction factor
(α = 1.0 for turbulent flow; 0.5 for laminar flow)
Since no shaft work W, is involved, ΔZ( ggc ) and v2
2α gc, are small compared with
the thermal energy transfer. Then for one fluid, the equation reduces to,
Q = ΔH = (H2 – H1) (2)
If no change in phase involved,
ΔH = CpΔT (3)
Therefore, the rates of heat transfer for the cold and hot fluids are respectively,
qc = mcCpc(Tc2 – Tc1) (4)
qh = mhCph(Th1 – Th2) (5)
If heat losses to the surroundings are neglected,
qc = qh or (6)
mcCpc(Tc2 – Tc1)= mhCph(Th1 – Th2) (7)
To relate the heat transfer rate with the size of the heat exchanger, we apply the
transfer around the differential element of length, dL. Thus,
dq = U1(Th – Tc)dA = Uo(Th – Tc)dAo (8)
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Where: U = Overall heat transfer coefficient, Btu/hr-ft2·°F
A = heat transfer area, ft2
ΔT = temperature driving force, °F = (Th – Tc)
**subscript 1 refers to the inside of the heating surface and
subscript o refers to the outside of the heating surface
For double-pipe heat exchangers, the overall heat transfer coefficient is almost
constant along the length of the heat exchanger and the driving potential ΔT may
be considered almost linear with q so that Equation (7) can be integrated to give,
q = UiAiΔTln = UoAoΔTln (9)
where: ΔTln = Logarithmic mean temperature difference
logarithmic mean temperature difference is defined by the
equation,
ΔTln = ΔT 1−ΔT 2
lnΔT 1ΔT 2
(10)
Where: ΔT1 = Temperature approach in one end
ΔT2 = Temperature approach in the other end
The ΔTln is fairly accurate if the ΔT is linear with q or L. however, in most situations,
this relationship is not always true. Let us compare therefore the log mean
temperature difference as defined by equation (9) and the arithmetic mean
temperature difference, ΔTo defined by,
ΔTo = ΔT 1+ΔT 2
2 (11)
With the true mean temperature difference, ΔTm which is obtained directly from
equation (7) by expressing ΔT in terms of L,
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q = 2πUD∫0
L
ΔT dL = 2πUDL(ΔT)tm (12)
therefore,
(ΔT)tm = ∫0
L
ΔT dL
L
(13)
Equation (11) is evaluated using graphical or numerical integration by plotting
values of ΔT against exchanger length and getting the area under the curve. These
are then divided by the total length of the exchanger.
It is given that the experimental overall heat transfer coefficient may be calculated
based on equation (8) by determining the rate of heat transfer by direct
measurements. To determine theoretical overall heat transfer coefficient, express U i
or Uo in terms of the individual transfer coefficients by considering resistances
involved when heat travels from the hot to the cold fluid. Such a relationship,
assuming relatively clean surface, is given by:
1UoAo
= 1UiAi
= 1hiAi
+ XmkmA
+ 1hoAo
(14)
Where: xm =Thickness of the tube wall
km = Thermal conductivity of the metal
A = Average heat transfer area
If Uo is desired, equation (12) simplifies to
1Uo
= 1ho
+ XmDokmD
+ DhiDi
(15)
If Ui is desired, we get
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1Uo
= 1hi
+ XmDikmD
+ DihoDo
(16)
Since the values of the xm, Do, and km can easily be obtained from available data, the
problem now boils down to the evaluation of the individual heat transfer coefficients.
This involves the choice of a particular empirical equation based on several factors
such as mechanism of heat transfer, character of flow, geometry of the system type
of fluid involved, etc.
Since most of the conditions in this experiment can be set, the equations for h may
be limited to only several choices. Based on mechanism, we can limit it to forced
convection by using flow rates that yield turbulent flow. This will eliminate the
effects of natural convection. Based on geometry, we are limited to horizontal tubes
with fluids flowing inside the conduits, circular and annular. Based on the type of
fluid, we are limited to usng hot and cold water.
In general, for forced convection in turbulent flow, (NRE > 10,000), k may be
calculated considering the effect of tube length by
( hCpG )(Cpμ
k )3
( μμ )0 .14
= 0 .023¿¿ (17)
Where the properties Cp, μ, k are evaluated based on the arithmetic mean bulk
temperature of the fluid defined by,
Tave = T 1+T 22
(18)
The viscosity, based on the wall temperature, μw will have to be determined by
estimating Tw by iterative calculation using individual resistances evaluated by first
neglecting the effect of μw.
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If the effect of the tube length can be ignored, (L/D > 60) and the (μw/μ)0.14 is
approximately equal to 1, the simpler Dittus-Boelter Equation (Foust 13-77), given
by
NNu = 0.023(NRe)0.8(NPr)n (19)
May be applied, where n= 0.4 where the fluid is heated and 0.3 when it is being
cooled. Here, the dimensionless numbers are defined as
NNu = hDk
Nusselts’s Number
NRe = DVρμ
=DGμ
Reynold’s Number
NPr = Cpμk
Prandtl Number
Another equation which is limited to water based temperature range of 40°F to 220°
F, turbulent flow, may be used. This is given by
h = 150 (1 + .011 T) V 0 .8
( D )0 .5¿
¿ (20)
where: T = Arithmetic temperature of fluid, °F
D’ = Tube diameter, inches
Equations (15), (16) and (17) are used to determine both h i and ho. to get hi, the
corresponding inside diameter of the tube is used for D. to get ho, the D is replaced
by the equivalent diameter, De, which is four times the hydraulic radius RH, defined
to be the ratio of the cross-sectional area of the annular space to the wetted
perimeter. For an annular space,
RH = 4 (Di j2−Do t2)
π ¿¿ = 14
¿ (21)
Where: Dij = inside diameter of jacket (outer tube)
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Dot = outside diameter of inner tube
It is possible that flow with Reynold’s number less than 10,000 will be encountered.
In this case, Equations (15),(16) and (17) are no longer valid. For NRe = 2100 and for
fluids of moderate velocity.
hiaDk
=1 .75NGr 1/3 = 1.75 (mCp
L )0 .33
(22)
For NRe between 2100 and 10,000, Figure 9-22 (MC) will have to be used. Also, if the
flow is laminar, the effect of natural convection should not be discounted. This effect
can be accounted for by multiplying h ia (computed from equation (19) or figure 9-22)
by the factor
Ǿn = 2.25(1+0 .010Ng r0 .33)
logNRe(23)
NGr = DeρtβgcΔT
μt 2(24)
Where: De = equivalent diameter
β = coefficient of thermal expansion, °F-1
f = subscript indicating that fluid properties should be based on
Tf = Tw+T2
EQUIPMENT
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Figure 1. Side view of Double-pipe Heat Exchanger
Equipment Description
The double-pipe heat exchanger set-up as shown in the previous figure consists
essentially of concentric pipes welded in series. The inner is made of brass with an
inside diameter of 0.625 inch and an outside diameter of 0.815 inch. The outer tube
made of standard 1 ¼ steel pipe. The unit is composed of 12 sections in series. Each
section is approximately 50 inches long. Hot water, which comes from the nearby
tubular heat exchanger, is passed through the inner pipe and the cold water, coming
from the supply main is passed through the annular space between the tubes.
Valves are provided for reversing the direction of the cold stream to obtain either
countercurrent or co-current flow. Valves on both lines are also provided to control
the flow rates of the streams. Each section is provided with thermometer wells,
which contain small amount of oil, to measure the temperature of the streams at
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appropriate points along the heat exchanger. At the exit ends of the pipes, weighing
tanks with calibrated levels are provided for measurement of flow rates.
PROCEDURE
It is important that this experiment should be performed with proper coordination
with Experiment B2, Performance of a Tubular Heat Exchanger, since the hot water
used in this experiment is the hot water discharged from the tubular exchanger. Any
valve movement in Experiment B2 will affect the temperature and flow rate of the
hot water. Therefore, each run for both experiments should start and end
simultaneously.
1. Familiarizing yourself with the parts and operation of the equipment,
especially the use of the valves provided in the lines. Place the thermometers
at the appropriate wells provided.
2. Open the supply valve for cold water, check whether water is flowing out the
measuring tanks, if not, checks exit valves. Pressure gauge provided should
indicate a constant reading. Adjust this valve to have a feel of the range of
flow rates to be used. Approximately determine the setting so as to get six
different flow rates later for each run. The exit valves in the measuring tanks
should be open to drain the liquid to avoid overflowing when flow is not being
measured.
3. Adjust the four valves in the cold water line to get either co-current or
countercurrent flow. This is done by fully opening or closing two opposite
valves. Trace the direction of flow from inlet to exit to determine this.
4. If hot water is already available, allow this to flow through the lines by fully
opening the exit valves.
Note: you should not move any valve along the hot water line without the
consent of the people operating the tubular exchanger nor they should move
anything without you knowing it. The flow rate of the hot water is usually at
their control, so regular consultation is advised.
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5. If flow rates have been established, prepare to continue the run by regularly
checking the temperature indicated by the thermometers at regular intervals
of time to determine whether steady conditions have already been
established and by measuring the flow rates of the two streams. The flow rate
is measured by closing the first exit valve for the water level to pass between
pre-selected points in the level gauge. The more time you spend in the
measurement, the better. The volumetric flow rate is obtained by dividing the
volume of water collected by the time interval.
6. If reasonable steady state conditions have been established, record all
temperature readings and flow rates i.e., no significant changes are observed,
and the run is completed.
7. Proceed with another run by adjusting the flow rate of the cold fluid and/or
the flow rate of the hot fluid. Each run should last approximately 20 minutes.
8. Perform a total of six runs; three countercurrent and three co-current flows.
9. Tabulate all data collected, measure the length of each section accurately,
check diameter of tubes, etc.
DATA SHEET
A. CO-Current Flow Operation
Trial 1
Well Number 1st Reading 2nd Reading 3rd ReadingTH (°C) TC (°C) TH (°C) TC (°C) TH
(°C)TC (°C)
1 37 37 37 37 37 372 39.8 37 40 37 40 373 40.5 36 40.9 36.5 41 36.754 41.5 35.5 42 36 42 365 43 34 44 34.25 44 34.256 45.5 32 46 32.5 46 32.757 49 30 49.5 50 50 30
Flow Rate (kg/s) 0.266667
0.33333
0.3 0.366667
0.3 0.366667
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Trial 2
Well Number 1st Reading 2nd Reading 3rd ReadingTH (°C) TC (°C) TH (°C) TC (°C) TH (°C) TC (°C)
1 33 33 32.5 32.5 33 332 43 33 45.5 32.5 45 33.53 46.5 32 46 32 46 324 49 35 48.5 34.5 50.25 34.55 53 37 53 37 54 32.56 53.5 36.5 53.5 36 54.5 327 54 36 54 35.5 55.5 31
Flow Rate (kg/s) 0.25 0.366667 0.258333 0.375 0.25 0.366667
B. Countercurrent Flow Operation
Trial 1
Well Number 1st Reading 2nd Reading 3rd ReadingTH (°C) TC (°C) TH (°C) TC (°C) TH (°C) TC (°C)
1 38.5 39.5 38.5 38.5 38.5 392 38 29 38 29 38.5 293 41 31 40 30.5 40.5 314 43 33 42 32.5 42.5 32.55 46 34 45 34 45.5 346 48 36 47 36.5 47.5 367 50.5 38 49.5 37.5 50.5 38
Flow Rate (kg/s) 0.272222 0.355556 0.283333 0.366667 0.283333 0.366667
Trial 2
Well Number 1st Reading 2nd Reading 3rd Reading
TH (°C) TC (°C) TH (°C) TC (°C) TH (°C) TC (°C)1 42 42 42 42.5 42 422 45 42.5 45 42.5 46 42.53 46 40.5 46 40.5 46.5 40.54 48 39.5 48 39.5 47 395 50 38 49 38 49 386 50.5 37.5 49.5 37 49.5 37.5
50.5 51 37 50 36.5 51 37Flow Rate (kg/s) 0.25 0.366667 0.258333 0.375 0.25 0.366667
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ANALYSES AND CALCULATIONS
1. Plot for each run the temperature of the hot and cold fluid versus the length
of the heat exchanger indicating whether it is countercurrent flow or co-
current flow. Also, in the same graph, plot ΔT versus length. Present these
figures (1) to (6). Did you get linear behavior? Explain.
2. Using the terminal temperatures for each run, calculate the logarithmic mean
and arithmetic mean temperature differences. Based on the plot of T versus L
as given in Figures (1) to (6), calculate the true mean temperature difference
by graphical integration. Calculate also the percentage deviation of ΔTa from
ΔTtm. Tabulate the results and present as Table 1. Explain the results you got
as to the validity of the various temperature differences you obtained.
3. Calculate the heat gained by the cold fluid, qc, and the heat lost, qh. Compare
the two by solving for the difference. Tabulate the results and present this as
Table 2.
4. Using qh as the basis, calculate for the experimental Ui, by calculating first A,
and using Tln in Equation (2). Tabulate the results and present this as Table 3.
5. Calculate the theoretical Ui by first solving hi and ho using appropriate
empirical formulas. Summarize the results by preparing a table indicating the
run number, average bulk temperature, Reynolds number, Prandtl number, h
and theoretical U. also compare h obtained using Equations (14) and (15).
Present this as Table 4.
6. Calculate the percentage difference between the experimental and the
theoretical Ui. Present this as Table 5.
7. Using only the date from one run each for co-current and countercurrent flow,
calculate h using equations (13), (14), and (15). Compare by tabulating the
results. Present this as Table 6.
GUIDE QUESTIONS
1. Based on your findings, discuss the applicability of the arithmetic mean and
logarithmic temperature difference in double pipe heat exchanger
calculations. What affects accuracy?
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In computation for the temperature difference, a little variation has been
observed. The logarithmic mean temperature difference records a value of
several decimal places, which can be considered as more accurate than of the
arithmetic mean temperature difference. In a double pipe heat exchanger,
logarithmic mean difference should be used instead of arithmetic mean
difference, although a small deviations exist considering an accuracy of the
value, the former hold true. Accuracy of the measurement might due to
parallax error relative to the reader of the of the thermometer in each well on
the double pipe heat exchanger. The condition of the atmosphere or the
surroundings might intervene as well.
The behavior of a heat exchanger in variable regime can be described by a
two parameter model with a time lag and a time constant. In many studies,
the analytical calculation based on the energy balance permitted to express
the time constant in various configurations of the device operating. However,
the time lag is only experimentally determined. An empirical method for the
prediction of this parameter when a double pipe heat exchanger is submitted
to a flow rate step at the entrance.
2. Give your comments as to the validity of the theoretical and experimental
overall heat transfer coefficients you obtained.
Certain possibilities can be considered as to how the heat gained by the cold
fluid differs from the heat lost by the hot fluid, the wall resistance of the tube,
the length the fluid travels in the heat exchanger and the type of the
materials used for the pipe system.
The overall heat transfer coefficient can also be calculated by the view of
thermal resistance. The wall is split in areas of thermal resistance where
the heat transfer between the fluid and the wall is one resistance
the wall itself is one resistance
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the transfer between the wall and the second fluid is a thermal
resistance
3. What are the problems you encountered in the operation of the double-pipe
heat exchanger? How did you overcome these problems and what
recommendations can you give to streamline or improve the use of such
experiment?
The distance between the sheets in the spiral channels are maintained by
using spacer studs that were welded prior to rolling. Once the main spiral
pack has been rolled, alternate top and bottom edges are welded and each
end closed by a gasketed flat or conical cover bolted to the body. This
ensures no mixing of the two fluids will occur. If a leakage happens, it will be
from the periphery cover to the atmosphere, or to a passage containing the
same fluid.
4. Give the physical significance of NRe, NNu and NPr in relation to heat transfer
characteristics.
Reynolds Number, Nusselt, and Prandtl Numbers are significant in the
calculations and widely applicable in the heat exchange principle. NRe
determines the type of flow regime in the heat exchanger equipment as well
as in the pipeline. The flow of the fluid or the velocity affects the temperature
in somewhat considerable amount. The laminar or turbulence behavior of the
fluid also accounts to the film resistance of the fluid and thus needed to be
determined. NNu or the Nusselt number is a dimensionless quantity, which is
define as the ratio of the tube diameter to the equivalent thickness of the
laminar layer. Further, Nusselt number is the resulting correlation on the ratio
of the total heat transfer by molecular and turbulent transport to heat transfer
by molecular transport alone. The physical significance of the Prandtl number
appears that it is the ratio of the velocity to the thermal diffusivity, it is
therefore a measure of the magnitude of the momentum, diffusivity relative
to that of the thermal diffusivity. Its numerical value depends on the
temperature and pressure of the fluid, and therefore it is a true property.
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Low-Reynold’s Number turbulent flow, and laminar non-Newtonian flow. Heat
exchaner configurations and materials were examined, as were compact and
noncompact versions and heat transfer and fouling.
The Prandtl number effects on heat transfer are categorized into two
perspectives: fin perspective and array perspective. The fin perspective
Prandtl number effects explain the dependence of the periodic fully
developed Nusselt number on Prandtl number. The array perspective is
analogous to the thermal entry length perspective in duct flow. Array
perspective Prandtl number effects yield higher Nusselt numbers in the
entrance region of the offset fin array.
Nusselt numbers are measured in three counterflow tube-in-shell heat
exchangers with flow rates and temperatures representative of thermosyphon
operation in solar water heating systems. Mixed convection heat transfer
correlations for these tube-in-shell heat exchangers were previously
developed in Dahl and Davidson (1998) from data obtained in carefully
controlled experiments with uniform heat flux at the tube walls. The data
presented in this paper confirm that the uniform heat flux correlations apply
under more realistic conditions. Water flows in the shell and 50 percent
ethylene glycol circulates in the tubes. Actual Nusselt numbers are within 15
percent of the values predicted for a constant heat flux boundary condition.
The data reconfirm the importance of mixed convection in determining heat
transfer rates. Under most operating conditions, natural convection heat
transfer accounts for more than half of the total heat transfer rate.
5. Discuss briefly the relative merits of countercurrent and co-current flow of
fluids for the transfer of heat?
Countercurrent exchange along with Concurrent exchange comprise the
mechanisms used to transfer some property of a fluid from one flowing
current of fluid to another across a semipermeable membrane or thermally-
conductive material between them. The property transferred could
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be heat, concentration of a chemical substance, or others. Countercurrent
exchange is a key concept in chemical engineering thermodynamics and
manufacturing processes, for example in extracting sucrose from sugar
beet roots.
Concurrent Flow – In this exchange system, the two fluids flow in the
same direction. As the diagram shows, a concurrent exchange system has
a variable gradient over the length of the exchanger. With equal flows in
the two tubes, this method of exchange is only capable of moving half of
the property from one flow to the other, no matter how long the exchanger
is. If each stream changes its property to be 50% closer to that of the
opposite stream's inlet condition, exchange will stop because at that point
equilibrium is reached, and the gradient has declined to zero. In the case
of unequal flows, the equilibrium condition will occur somewhat closer to
the conditions of the stream with the higher flow.
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Countercurrent Flow - By contrast, when the two flows move in opposite
directions, the system can maintain a nearly constant gradient between
the two flows over their entire length. With a sufficiently long length and a
sufficiently low flow rate this can result in almost all of the property being
transferred. However, note that nearly complete transfer is only possible if
the two flows are, in some sense, "equal". If we are talking about mass
transfer, then this means equal flowrates of solvent or solution, depending
on how the concentrations are expressed. For heat transfer, then the
product of the average specific heat capacity (on a mass basis, averaged
over the temperature range involved) and the mass flow rate must be the
same for each stream. If the two flows are not equal (for example if heat is
being transferred from water to air or vice-versa), then conservation of
mass or energy requires that the streams leave with concentrations or
temperatures that differ from those indicated in the diagram.
6. Give a summary of your findings and conclusions and give recommendations,
if any.
The experiment presents the results of an experimental study of shell-side
heat transfer and flow resistance performance of multi-tube type of double-
tube heat exchanger units, which is a double-pipe heat exchanger with
smooth or roughen tubes and a segmental baffled one with smooth tubes,
using water and crude oil (a mixture of oil and water) as working fluids. The
experimental results indicate that the double-tube heat exchanger with a
spiral groove tube bundle provides superior shell-side heat transfer and
pressure drop characteristics. Double-tube heat exchanger is installed for
heating crude oil in a solar energy system.
1. Plot of Temperature vs Length of Pipe
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Length of the heat exchanger pipe
Tem
per
atur
e,o
C
Plot of Temperature vs Length of pipe
Double- Pipe Heat Exchanger
2. Computing for the Logarithmic Mean Temperature Difference
Where: ΔT1 = Tleaving temperature , hot fluid –Tentering temperature, cold fluid
ΔT2 = Tentering temperature, hot fluid –Tleaving temperature, cold fluid
LMTD = 6.6955 0C
3. Computing for the Arithmetic Mean Temperature Difference
AMTD = 6.70 0C
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Tem
pera
ture
, C
Double- Pipe Heat Exchanger
4. Comparison of LMTD and AMTD for Counter-current Flow
LMTD AMTD
Flow 1 6.6955 6.70
Flow 2 6.4499 6.450
Flow 3 6.1434 6.150
Flow 4 5.8994 5.90
Flow 5 6.2467 6.25
Flow 6 6.2467 6.25
5. Plot of Temperature vs Length of Pipe
6. Computing for the Logarithmic Mean Temperature Difference
Where: ΔT1 = Tleaving temperature , hot fluid –Tentering temperature, cold fluid
ΔT2 = Tentering temperature, hot fluid –Tleaving temperature, cold fluid
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Length of the heat exchanger pipe
Plot of Temperature vs Length of pipe
Double- Pipe Heat Exchanger
LMTD = 10.3718 0C
Computing for the Arithmetic Mean Temperature Difference
40 27 5 38 29 5
2
. . + AMTD =
AMTD = 10.500
7. Comparison of LMTD and AMTD for Counter-current Flow
LMTD AMTD
Flow 1 10.3718 10.50
Flow 2 8.6084 7.5
Flow 3 5.4389 5.5
Flow 4 3.6995 3.75
Flow 5 2.4663 2.5
Flow 6 ∞ 2.0
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