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Department of Mechanical and Industrial Engineering
MEC701 HEAT TRANSFER
LABORATORY MANUAL
Prepared by: Dr. D. Naylor
January 2014
TABLE OF CONTENTS
Table of Contents ...................................................................................................................1
Lab Report Instructions..........................................................................................................2
Lab # 1:
Thermal Conductivity and Contact Resistance ......................................................................3
Lab # 2:
Numerical Solution of Steady Two-dimensional Heat Conduction ......................................8
Lab # 3:
Forced Convection from A Cylinder in Cross Flow ..............................................................14
Lab # 4:
Free Convection .....................................................................................................................19
Lab # 5:
Concentric Tube Heat Exchanger ..........................................................................................25
Appendix:
General Safety Rules and Regulations for the Laboratories ..................................................33
January 2014
Ryerson University
Department of Mechanical & Industrial Engineering
MEC701 - Heat Transfer
LAB REPORT INSTRUCTIONS
1. All lab reports for MEC701 must be prepared in accordance with the Department Guidelines for Lab
Reports. This document is available from the course website:
http://www.ryerson.ca/~dnaylor/MEC701/MEC701.html
2. All reports are to be word processed. Detailed hand calculations should be placed in an appendix.
Also, be sure to include the raw experimental data in an appendix.
3. All lab reports must use the Standard Lab Report Cover Page, available at:
http://www.ryerson.ca/~dnaylor/MEC701/MEC701.html
In order to get a mark, the lab cover must have your original signature. By signing the report you attest
that you have contributed to this written lab report and confirm that all work contained in this project
report is your group’s own work. Any copying or plagiarism found in this work will trigger an
Academic Misconduct charge, including failing grades, suspension, and possibly expulsion from the
University under Ryerson Policy #60, which can be found online at:
http://www.ryerson.ca/senate/policies/pol60.pdf
4. All group members must contribute to, and check, the contents of each report. It is NOT
ACCEPTABLE to “partition” the lab work such that one group member takes sole (or nearly sole)
responsibility for the content of a lab report. This is academic misconduct, since you are attempting to
get marks for work that you did not contribute to in a meaningful way. Simply attending the lab is not
sufficient!
5. The reports will be marked out of 10, with the following marking scheme:
Lab Report:
2/10 Pre-Lab Report
7/10 Report Technical Content
1/10 Spelling, Grammar, and General Appearance (of Graphs, Figures, etc.)
6. A penalty of 1 mark out 10 per day will be applied for late submission of lab reports. Late Pre-Lab
reports will not be accepted.
7. You must attend the laboratory in order to receive a mark. Attendance will be taken by the lab
demonstrator at the beginning of the lab. So, you must arrive on time, and stay for the duration of the lab
in order to get marks for the lab.
2
Ryerson University
Department of Mechanical & Industrial Engineering
MEC701 - Heat Transfer Laboratory
LAB #1: THERMAL CONDUCTIVITY AND CONTACT RESISTANCE
1. OBJECTIVE
The objective of this lab is to measure the thermal conductivity of two materials using a heat conduction
apparatus. An additional objective is to measure the thermal contact resistance at the joint of a
composite bar.
2. THEORY
Fourier’s law of heat conduction states that the local heat flux is proportional to the local temperature
gradient. Fourier’s law can be written as:
(1)
where the constant of proportionality is the thermal conductivity, k W/(mK).
Steady one-dimensional conduction along a bar with constant cross sectional area (A) is shown in Figure
1. If the temperatures (T1 and T2) are known at two locations spaced a distance L apart, Eq. (1) can be
integrated to give the conduction heat transfer rate:
(2)
Figure 1: One-dimensional heat conduction along a bar.
3
Figure 2 shows steady-state heat conduction along a composite solid bar made of two different
materials. It is important to realize that there may be a substantial drop in temperature at the interface.
This apparent discontinuity in temperature is caused by thermal contact resistance.
The interfacial resistance to heat transfer is caused by surface roughness, as depicted in Figure 2. Heat
transfer across the interface occurs by conduction at the contact points as well as by conduction and
radiation across the interstitial fluid. In theory, for perfectly smooth surfaces there would be no thermal
resistance (and no temperature difference) across the interface.
Figure 2: Interfacial temperature difference caused by contact resistance.
During steady heat conduction along a composite bar, the thermal contact resistance at the interface is
defined as:
(3)
where (TA - TB) is the interfacial temperature difference and A is the cross sectional area. Contact
resistance is often expressed in terms of an interfacial contact coefficient hc (W/m2K) defined in a
similar way as Newton’s law of cooling:
(4)
Rearranging equation (4) gives:
(5)
4
3. APPARATUS
Measurements will be made using the Cussons Thermal Conductivity Apparatus. A schematic diagram
of the Cussons Apparatus is shown in Figure 3. The two test specimens (25 mm diameter) are shown
clamped into the apparatus. The specimens are heated electrically at the upper end and cooled at the
lower end by a flow of water. To reduce heat losses, an insulation jacket (not shown) surrounds the
specimens.
The conduction heat transfer rate is calculated by measuring mass flow rate and temperature rise of the
cooling water supplied to the lower end of the bar. At steady state conditions, the total heat transfer rate
is:
(6)
where is the mass flow rate of the cooling water, and cp is the specific heat of liquid water. The inlet
temperature and outlet temperature of the cooling water are measured using glass thermometers. The
mass flow rate is measured using a stop watch, bucket, and weigh scale.
Steady-state temperature measurements are made at the four locations shown in Figure 3 using type K
thermocouples. Using these temperature and heat transfer rate measurements, the thermal conductivity
of each sample (kA, kB) and the interfacial contact coefficient (hc) can be calculated using equations
presented above.
Figure 3: Schematic diagram of the thermal conductivity apparatus.
5
4. PROCEDURE
Composite Bar (Aluminum/Stainless Steel) Measurement Procedure
(i)
Place the aluminum and stainless steel specimens together in the apparatus, as illustrated in
Figure 3. Check that all four thermocouples are in place and cover the apparatus with the
insulating jacket.
(ii)
Turn on the cooling water supply and switch the heater to full power. Set the flow rate of
cooling water to about 0.1 litres per minute using the flow meter. Wait for the hot end (T4) to
reach 180 oC, then reduce the power to about 0.35 amps.
(iii)
Allow the apparatus to reach steady-state. Monitor the specimen and cooling water
temperatures to confirm that steady conditions have been achieved.
(iv)
Once at steady-state, time the collection of the cooling water in the container provided.
Record the specimen temperatures (T1 to T4), and the cooling water temperatures (Tin, Tout)
every two minutes. At the fourth reading (after six minutes) stop collecting the cooling
water. Weigh the amount of water collected.
5. CALCULATIONS & DISCUSSION
Your lab report should include the following:
(i)
Using appropriately averaged cooling water temperature readings calculate heat transfer rate
through the composite bar. Plot the temperature distribution in the composite bar and deduce the
interfacial temperature difference (TA-TB). Using this result, calculate interfacial contact
coefficient (hc) and the thermal contact resistance (Rc). Show the detailed calculation procedure
in your report.
(ii)
Calculate the thermal conductivity of the aluminum and stainless steel specimens and compare
the values to those published in the textbook. Based on your measurement is the aluminum bar
made from pure aluminum or an alloy? Show the detailed calculation procedure in your report.
(iii)
Even though there is an insulation jacket, heat will be lost along the length of the two specimens.
Does the heat loss from the side of the bars cause the measured thermal conductivities to be high
or low relative to their true values? Do you expect this error to be larger for the aluminum or
stainless steel bar? Discuss and explain this source of experimental error.
6
6. EXPERIMENTAL DATA SHEET
Composite Bar (Aluminum/Stainless Steel) Test
Time
0 min.
2 min.
Water Temp. In
Water Temp. Out
T1
T2
T3
T4
Mass of Empty Container:
Mass of water collected:
Collection time:
7
4 min.
6 min.
Ryerson University
Department of Mechanical & Industrial Engineering
MEC701 - Heat Transfer Laboratory
LAB #2: NUMERICAL SOLUTION OF STEADY TWO-DIMENSIONAL HEAT
CONDUCTION
1. OBJECTIVE
This lab will give students experience solving two-dimensional steady-state heat conduction problems
using the finite difference method. Students will perform a heat transfer analysis on a simple twodimensional shape with convection boundary conditions.
2. THEORY
The governing equation for steady-state, two-dimensional heat conduction in a solid with constant
thermal conductivity is:
0
(1)
Exact mathematical solutions of Eq. (1) are available only for a limited number of simple geometries
and boundary conditions. For most practical applications we must resort to an approximate numerical
solution.
2.1 The Finite Difference Method
In the finite difference method, the solid is subdivided into an orthogonal grid of nodes, as shown in
Figure 1. Rather than solving for the entire continuous temperature field, the temperature is determined
only at the discrete nodal points. In this way, the partial differential equation is reduced to a set of
approximate linear algebraic equations, which can be solved simultaneously.
In this lab, a commercial spreadsheet program (Excel) will be used to solve the set of simultaneous
equations for the temperature at each node. Each cell of the spreadsheet will be used to represent a nodal
point in the finite difference grid. Then, once all the finite difference approximations and boundary
condition information have been entered into the cells, the set of simultaneous equations can be solved
automatically using Gauss-Seidel iteration. The finite difference equations below are presented in a
form most suitable for solution on a spreadsheet.
8
Figure 1: Orthogonal finite difference grid
2.2 Finite Difference Approximations
The following finite difference approximation applies to all interior nodes (i.e., all nodes not on the
boundary):
(2)
The following approximation applies to all nodes on a plane surface with convection:
∆
(3)
∆
9
The following approximation applies to all nodes on an interior corner with convection:
∆
(4)
∆
The following approximation applies to all nodes on an exterior corner with convection:
∆
(5)
∆
Note that all of the above equations apply only for uniform equal node spacing in the x and y directions
(Δx=Δy).
10
3. TEMPERATURE FIELD SOLUTION PROCEDURE
(i) Sketch the finite difference grid to scale. One cell in the spreadsheet will be used for each node.
Label each node according to its spreadsheet cell reference, e.g. C4. Indicate all boundary conditions on
the sketch.
(ii) Determine the finite difference expression that applies to each node in the grid where the
temperature is unknown (see Section 2.2 above). In order to reduce the number of nodes, be sure to
make use of symmetry in the problem. Note that a line of symmetry is treated as an adiabatic surface.
Why?
(iii) Set up the spreadsheet to allow “circular references”. This is done in Excel by selecting the Office
Button (at the top left of the screen). Then left click on “Excel Options”, followed by “Formulas”. Check
the box to “Enable Iterative Calculations”. It is recommended to set the “Maximum Iterations” equal to
1.
(iv) Enter the appropriate equation or known boundary temperature into each cell. For example, the
formula for an interior node at cell D4 would be (C4+D3+E4+D5)/4. Generally speaking, you only need
to enter a formula once, using relative cell references. The copy feature of the spreadsheet can be then
used to repeat the formula as needed. Absolute cell references (e.g. $A$2) should be made to the cells
that contain the “constants” of the problem (ho , To, kb, etc.), since this information is usually contained
in fixed cells.
Warning! Save your file often!
(v) Once all the equations and boundary conditions have been entered, iterate the set of simultaneous
equations by pressing the “recalculate” function key (F9 in most spreadsheet programs). Continue to
press the “recalculate” key until the temperature field has converged to the desired accuracy.
Some familiarity with spreadsheet-type programs has been assumed. A short spreadsheet tutorial will be
given at the beginning of the lab for those students that are unfamiliar with spreadsheets.
11
4. ASSIGNED PROBLEM: HEAT TRANSFER THROUGH A CHIMNEY
Figure 2 shows the square cross section of a tall brick chimney. A flow of hot gases maintains the inside
surface of the chimney at 285°C. The outer surface is cooled by forced convection (ho=18 W/m2K) in
ambient air at To= 22°C. The thermal conductivity of the brick is kb=2.1 W/mK. The objective is to
calculate: (i) the steady state temperature field in the brick chimney, and (ii) the steady state heat transfer
rate across the chimney wall (per metre of height).
Note that the horizontal dimension of the chimney is given in terms of variables, w and t. Each lab
section will be assigned a different geometry:
(a) w= 2.0 m, t= 1.5 m
(b) w= 2.0 m, t= 2.0 m
(c) w= 3.0 m, t= 1.5 m
Only one geometry needs to be solved. The Teaching Assistant will indicate the geometry assigned for
your lab section.
Figure 2: Square cross section of a tall chimney.
The following calculations are required:
(a) Calculate the two-dimensional temperature field in the brick chimney using a finite difference grid
size of Δx=Δy=0.5m. Make use of symmetry to reduce the number of nodes in your grid.
(b) From the converged temperature field computed above, calculate the total heat transfer rate per metre
of chimney height. One possible method is to sum the convective heat transfer rate over the “n” nodes
on the outer surface of the chimney:
12
∑
Δ
(7)
where Tj and ΔAj are the temperature and surface area associated with each node on the outer surface of
the chimney. This summation can be done automatically using the spreadsheet function @SUM.
(c) Repeat parts (a) and (b) with a finite difference grid size of Δx=Δy=0.25m. What is the percentage
change in the heat transfer rate? Which result is more accurate? Why?
(d) As a check on your results, estimate the heat transfer rate per metre of chimney using a one
dimensional thermal resistance method. Calculate the thermal resistance of your chimney geometry
using a conduction shape factor from your textbook:
.
.
1.4
(8)
where L is the depth of the chimney. Be sure to show and explain your one-dimensional calculation
method in your report.
5. RESULTS AND PRESENTATION
Your report should include:
• Your spreadsheet files for both grids (on CD)
• A labeled sketch of the finite difference grids (coarse and fine)
• An explanation of how lines of symmetry were treated in the calculation
• One-dimensional thermal resistance calculation (in appendix).
• A summary of the numerical results
• A brief discussion of results (one page maximum). Be sure to answer ALL the questions that
are posed above.
13
Ryerson University
Department of Mechanical & Industrial Engineering
MEC701 - Heat Transfer Laboratory
LAB #3: FORCED CONVECTION FROM A CYLINDER IN CROSS FLOW
1. OBJECTIVE
The objective of this lab is to determine the convective heat transfer rate from a circular cylinder in a
cross flow of air. Experimental measurements will be made using a lumped capacitance transient
cooling technique. Using the experimental data, an empirical correlation will be derived and compared
to published results.
2. INTRODUCTION
Forced convection from a circular cylinder in a cross flow of fluid is encountered in wide range of
engineering applications. As shown in Figure 1, the fluid has free stream velocity U∞ and free stream
temperature T∞. The flow direction is perpendicular to the axis of the cylinder. The cylinder has
diameter D and uniform surface temperature TS.
Figure 1: Forced convection from a circular cylinder in cross flow.
Some theoretical solutions to this problem have been obtained for low Reynolds number. However, at
moderate and high Reynolds number, an unsteady turbulent wake forms behind the cylinder making
mathematical solution of the governing equations extremely difficult. Hence, in the range of most
practical applications, heat transfer correlations are based on experimental measurements.
14
3. THEORY
For external forced convection problems, experimental heat transfer data has been found fit a
relationship of the following form:
�
where
ℎ𝐷
����
𝑁𝑢𝐷 = 𝑘 = 𝐶𝑅𝑒𝐷𝑚 𝑃𝑟 1/3
(1)
����𝐷 is the average Nusselt Number
𝑁𝑢
ReD is the cross flow Reynolds number, ReD = ρU∞D/μ
Pr is the fluid Prandtl number, Pr = μcp/k
In Equation (1), the constant C and exponent m are obtained from a least-squares best fit to experimental
data. The values of C and m for several Reynolds number ranges are given in Table 1. To partially
correct for property variations, all fluid properties should be evaluated at the film temperature:
Tf = (Ts +T∞)/2.
Table 1: Constants of Equation (1).
ReD Range
0.4 - 4
4 - 40
40 - 4,000
4,000 - 40,000
40,000 - 400,000
C
0.989
0.911
0.683
0.193
0.027
m
0.330
0.385
0.466
0.618
0.805
4. APPARATUS
The convective heat transfer rate will be measured using the Plint Cross Flow Apparatus. The primary
component of this apparatus is a low speed wind tunnel. A sketch of the wind tunnel is shown in Figure
2. The wind tunnel has a 12.7 cm x 12.7 cm cross section and is equipped with a gate on the outlet of the
fan to control the air velocity. A traversing pitot tube is used to measure the air velocity in the tunnel.
The test cylinder has a diameter of 1.242 cm and is instrumented with a single thermocouple. The
middle section of the cylinder is made of copper and has a length of 9.5 cm. Cylindrical end pieces made
of phenolic are attached to the copper cylinder to reduce axial conduction. An annular heater is used to
heat the cylinder prior to each test.
15
Figure 2: Low speed wind tunnel
5. EXPERIMENTAL PROCEDURE
(i) Turn on the wind tunnel fan. With the flow control gate approximately 50% open, traverse the pitot
tube over the cross section of the wind tunnel to check the velocity profile. (In a properly designed wind
tunnel, the velocity should be uniform over most of the tunnel cross section.)
(ii) Check that the copper test cylinder is polished. Insert the copper cylinder into the annular electric
heater. Comment on the influence of radiation heat transfer in your report. Why should the cylinder
highly polished to give the best results?
(iii) With the wind tunnel fan on, open the flow control gate fully. Record the pitot tube manometer
deflection, the inlet air temperature, and the barometric pressure.
(iv) Once the cylinder temperature reaches 80°C to 85°C, quickly insert the cylinder into the wind
tunnel.
(v) Using the data acquisition system, record the cylinder temperature as it cools.
(vi) Repeat steps (iii) to (v) for several gate settings. Get at least five cooling curves at different air
velocities. Use the pitot tube to get even velocity increments between data sets.
(vii) Repeat one test, matching the test conditions as closely as possible. In your report, comment on the
experimental reproducibility.
16
6. DATA ANALYSIS
(a) Using a lumped capacitance analysis, the temperature variation of the cylinder with time (t) can be
shown to be:
𝜃
𝜃𝑖
𝑇−𝑇∞
= 𝑇 −𝑇 = 𝑒
𝑖
where
∞
� 𝐴𝑠
ℎ
�𝑡
𝜌𝑉𝑐𝑝
−�
(2)
Ti is the initial cylinder temperature at t=0 seconds (°C)
T∞ is the ambient temperature (°C)
ℎ� is the average heat transfer coefficient (W/m2K)
As is surface area of the copper cylinder (m2)
ρ is the density of the copper cylinder (kg/m3)
cp is the specific heat of the pure copper cylinder (J/kgK)
V is the volume of the copper cylinder (m3)
Taking the natural logarithm of Equation (2) gives:
𝜃
�𝐴
ℎ
𝑙𝑛 �𝜃 � = − �𝜌𝑉𝑐𝑠 � t
𝑖
(3)
𝑝
For each set of cooling data, plot ln(θ/θi) versus time t and fit a straight line to the data. Referring to
Equation (3), use the slope of this best fit line to calculate the average heat transfer coefficient (ℎ�) for
each air velocity. For each set of data, calculate the air velocity from the pitot tube manometer reading.
(b) Calculate the Reynolds number, Prandtl number and average Nusselt number for each data set.
Evaluate the fluid properties at the average film temperature, (𝑇�𝑆 + T∞)/2.
����𝐷 ) versus ln(ReD). Fit a straight line to the data and use the slope and y-axis intercept to
(c) Plot ln(𝑁𝑢
calculate the constant C and exponent m for your experimental data. On the same graph, plot the
empirical correlation from your textbook.
(d) Plot the average heat transfer coefficient (ℎ�) versus the free stream air velocity, U∞. How much does
the convective heat transfer rate increase if the free stream air velocity is doubled?
(e) Measurement errors caused by blockage effects are always present in an enclosed wind tunnel. The
test model reduces the cross section for flow, causing the air velocity near the model to be artificially
high. Using the ℎ� versus U∞ graph, estimate the approximate percentage error in ℎ� caused by wind
tunnel blockage.
17
7. RAW EXPERIMENTAL DATA
Barometric Pressure: ______________ mmHg
Test #1
Test #2
Test #3
Test #4
Test #5
Test #6
(repro. test)
Air Temp:
Manometer:
Time
Temp.
(s)
(oC)
Air Temp:
Manometer:
Time
Temp.
(s)
(oC)
Air Temp:
Manometer:
Time
Temp.
(s)
(oC)
Air Temp:
Manometer:
Time
Temp.
(s)
(oC)
Air Temp:
Manometer:
Time
Temp.
(s)
(oC)
Air Temp:
Manometer:
Time
Temp.
(s)
(oC)
18
Ryerson University
Department of Mechanical & Industrial Engineering
MEC701 - Heat Transfer Laboratory
LAB #4: FREE CONVECTION
1. OBJECTIVE
The objective of this lab is to measure the free convective heat transfer coefficient for a horizontal
cylinder and a vertical flat plate. Measurements will be made in air using a transient cooling technique
and the data will be compared to published empirical correlations.
2. INTRODUCTION
From common experience we know that a heated fluid tends to rise. In the presence of the Earth’s
gravitational field, density differences within the fluid produces buoyance forces that drive the flow.
This buoyancy-induced flow is called free convection or natural convection. The fluid velocities
associated with free convection are usually smaller than those associated with forced convection. For
this reason, the heat transfer coefficient for free convection is generally much lower than for forced
convection. Although the heat transfer coefficient is low, free convection has the advantage of being
reliable, inexpensive, and quiet.
Free convection is encountered in a wide range of engineering applications, such as electronics cooling,
nuclear safety systems, and domestic baseboard heating. In many systems, free convection provides
the largest thermal resistance and therefore has a strong influence on the total heat transfer rate.
3. THEORY
Consider a horizontal cylinder of diameter D and a vertical flat plate of height L, shown in Figure 1.
Both objects have surface temperature TS and are immersed in a large body of quiescent fluid at
temperature T4. Most fluids expand when heated. So, the heated fluid near the surface of the object will
be less dense than the surrounding fluid. This fluid will rise, producing a thermal boundary layer on the
surface, and thermal plume above the object.
Figure 1: Free convection from an isothermal horizontal cylinder and an isothermal vertical plate.
19
It has been found that the free convective heat transfer can be predicted by the following empirical
relationship:
(1)
where
is the average Nusselt Number and Ra is the Rayleigh number. In Eq. (1), C and n are
empirical constants, determined from experiments or analysis. The fluid properties in Eq. (1) should
be evaluated at the film temperature, (TS+T4)/2.
The characteristic dimension used in the Nusselt number and Rayleigh number depends on the
geometry of the problem. For free convective heat transfer the dimension that has the biggest effect on
the convective heat transfer rate is the overall height of the object. So, for a horizontal cylinder, the
characteristic length is the diameter D. Similarly, for a vertical plate, the characteristic length is the
height, L. Using these characteristic dimensions, for the horizontal isothermal cylinder, Eq. (1)
becomes:
(2)
Similarly, for the vertical isothermal plate, Eq. (1) becomes:
(3)
The value of the constant “C” and the exponent “n” depend on the Rayleigh number, and are different
for each geometry. The course textbook should be consulted to get the empirical correlations.
4. APPARATUS
The apparatus consists of a long aluminum cylinder and a square aluminum plate, which are hung on
plastic threaded rods. A single thermocouple is embedded in each specimen in order to measure the
temperature of the object as it cools. Note that both the plate and the cylinder have been polished to
give a low surface emissivity. Table 1 provides the physical data for each test specimen.
5. EXPERIMENTAL PROCEDURE
To avoid any interaction with the plume from the horizontal cylinder, the experiment for the vertical
plate should be done first. Note that the room air must be relatively still (quiescent) in order to get good
results. So, it is important that the apparatus is not be set up near any sources of air disturbance, such
as the ventilation diffuser. For the same reason, you should avoid moving about the room during the
experiment.
20
Use the following procedure:
(i) Record the ambient temperature and the atmospheric pressure.
(ii) Uniformly heat the vertical plate to a temperature of between 160-170 °F, using a hot air gun.
(iii) After the heating is complete, wait 2 minutes for the plate’s internal temperature to become
uniform, before recording the initial temperature.
(iv) Allow the plate to cool, recording the plate’s temperature every 2 minutes, for 16 minutes.
(v) Repeat with the steps (ii) through (iv) for the horizontal cylinder.
Table 1: Physical data for the cylinder and plate test specimens.
Plate
Material:
Orientation with
respect to gravity:
Cylinder
Aluminum Alloy
2024-T6
Material:
Vertical
Aluminum Alloy
2024-T6
Orientation with
respect to gravity:
Horizontal
0.4505 kg
Mass:
0.8002 kg
Mass:
Height:
15.24 cm
Diameter:
2.46 cm
Width:
15.24 cm
Length:
35.6 cm
Depth:
1.27 cm
Emissivity:
Emissivity:
0.04
0.04
6. DATA ANALYSIS PROCEDURE
This experiment is based on the “lumped capacitance” assumption. The experiment has been designed
such that the resistance to heat conduction inside each specimen is much smaller than the external
convective resistance. So, the internal temperature variation inside the solid test specimen will be small,
and can be recorded by a single thermocouple.
Let Ti represent the instantaneous temperature of the specimen at time t. Then, the instantaneous heat
transfer rate from the specimen can be expressed as:
(4)
where m is the mass of the specimen, Cp is the specific heat of aluminum, A is the surface area of the
specimen. The specimen cools by convection and radiation. Thus, in Eq. (4) the total heat transfer rate
from the specimen is set equal to the sum of the convective and radiative heat transfer rates at the
surface. Equation (4) can be solved for the average convective heat transfer coefficient, :
21
(5)
In this experiment, the cooling rate will be estimated from the temperature of the specimen taken at 120
second intervals ()t=120 seconds). Over each time interval, the cylinder cools from temperature Ti to
temperature Ti+1. Using the measured temperature at these time intervals, the cooling rate can be
approximated as:
(6)
Over this time interval, the average specimen temperature is taken to be
. Using this
average temperature and the cooling rate from Eq.(6), the average convective heat transfer coefficient
can be calculated using Eq. (5) as:
(7)
where
is the average surface temperature of the time interval. Similarly, over this time
interval, the average Rayleigh number can be calculated using the average specimen temperature
as:
(8)
where H is the appropriate characteristic dimension. As mentioned previously, for the horizontal
cylinder, H=D. For the vertical plate H=L. Note that the air properties are evaluated at the average film
temperature over the time interval,
.
7. RESULTS AND PRESENTATION
Your lab report should include the following:
( i) Using the analysis procedure above, calculate the average Nusselt number and the Rayleigh number
at each time step for both test specimens. Be sure to interpolate for the properties of air at the mean film
temperature,
, at each time step. Include a full sample calculation for the first time step
for both geometries.
(ii) For both test specimens, calculate the average Nusselt number at each time step predicted by
empirical correlations. Consult your textbook. Calculate the percentage difference between the
22
measured and predicted values. Discuss the most likely reason for the difference between the measured
and predicted values.
For each geometry, present a summary of your experimental data and the empirical correlation values
in a table, as shown below.
Table 2: Summary of Results
Time
Step
i
Measured Average
Heat Transfer
Coeff.,
(W/m2K)
Predicted
Average
Heat Transfer
Coeff.,
(W/m2K)
Difference
Between
Measured &
Predicted
(%)
Experimental
Rayleigh
Number,
Ra
Measured
Average Nusslt
Number
1
2
3
4
5
6
7
(iii) Plot the average Nusselt number against the Rayleigh number, using a log scale for both axes. You
can expect a substantial amount of scatter in the data. So, you should plot both sets of data (horizontal
cylinder and vertical plate) on the same graph, along with the two empirical correlations.
(iv) The current experiment is based on the lumped capacitance method. For a typical value of the
measured average heat transfer coefficient, calculate the Biot number. Do this calculation for both the
plate and the cylinder. Is the lumped capacitance method valid? Comment on whether or not it is
acceptable to use a single thermocouple to measure the transient temperature in each specimen.
(v) Other issues to consider and discuss: Does radiation play a significant role? Why were the cylinder
and plate polished?
Use of an Excel spreadsheet is recommended for these repetitive calculations. If you use Excel, be sure
to include an electronic copy on CD with your report (as well as a full sample calculation for each
geometry).
23
8. RAW EXPERIMENTAL DATA
(i) Cylinder Experiment
Cylinder Orientation: Horizontal
Barometric Pressure:
Initial Room Temperature:
Index
i
Time
t
(s)
1
0
ii) Plate Experiment
Plate Orientation: Vertical
Barometric Pressure:
Initial Room Temperature:
mmHg
°F
Instantaneous
Cylinder Temp.
Ti (°F)
Index
i
Time
t
(s)
1
0
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
24
Instantaneous
Plate Temp.
Ti (°F)
mmHg
°F
Ryerson University
Department of Mechanical & Industrial Engineering
MEC701 - Heat Transfer Laboratory
LAB #5: CONCENTRIC TUBE HEAT EXCHANGER
1. OBJECTIVE
The objective of this lab is determine the overall heat transfer coefficient of a concentric tube heat
exchanger in counter flow mode. The measured overall U-value will be compared to the U-value
predicted by theory, using empirical correlations.
2. APPARATUS
The Technovate concentric tube heat exchanger will be used for the experimental measurements.
A schematic diagram of the heat exchanger is shown in Fig. 1. Hot water flows inside the round pipe
and cold water flows in the outer annulus. The hot water enters via the upper tube and exits via the
lower tube. The direction of the cold water flow can be switched, so that either parallel or counter
flow modes can be achieved. The flow will be set in counter flow mode for this experiment.
As shown in Fig. 2 the dimensions of the heat exchanger are:
Inside Diameter of the Inner Pipe:
Outside Diameter of the Inner Pipe:
Inside Diameter of the Outer Shell (Annulus):
Total Length of Both Pipes:
Di =14.3 mm
Do =15.9 mm
DS = 25.4 mm
L = 2130 mm
Note that the total length of 2130 mm includes both passes.
3. THEORY
The total heat transfer rate provided by a heat exchanger is given by:
(1)
where Uo is the overall heat transfer coefficient based on Ao (W/m2K)
Ao is the outside surface area of the inner pipe, BDoL (m2)
)Tlm is the log mean temperature difference (K)
In Eq. (1), the overall heat transfer coefficient is defined based on the outside surface area of the
inner tube, Ao.
25
Figure 1: Schematic diagram of the concentric tube heat exchanger in counter flow mode.
Figure 2: Cross section of the concentric tube heat exchanger.
26
The log mean temperature difference ()Tlm) depends on the temperature difference between the
fluid streams at each end of the heat exchanger. For counter flow, the log mean temperature
difference is:
(2)
3.1 Experimental Measurement of the Overall Heat Transfer Coefficient (Uo)
The total heat transfer rate can be calculated for the hot and cold water streams, as follows:
(3)
(4)
Under ideal condition, the heat transfer rate from the hot stream will equal the heat transfer rate to
the cold stream. However, because of errors in the measurement of the mass flow rates and fluid
temperatures (and minor heat losses to the ambient), these heat transfer rates will not be identical.
So, the measured overall heat transfer coefficient (Uo) should be calculated using the average heat
of the hot and cold side transfer rates. Using Eq. (1), the measured overall heat transfer coefficient
(Uo) can be computed as:
(5)
3.2 Calculation of the Overall Heat Transfer Coefficient (Uo) using Empirical Correlations
The overall heat transfer coefficient depends upon the average heat transfer coefficients associated
with the flow in the inner pipe and in the annulus of the heat exchanger. Using a thermal resistor
network, it can easily be shown that Uo is given by:
(6)
where hi is the average heat transfer coefficient inside the inner pipe (W/m2K)
ho is the average heat transfer coefficient inside the outer annulus (W/m2K)
Ao/Ai is the outside-to-inside area ratio of the inner pipe.
Under normal experimental conditions, it is expected that the Reynolds number in both the inner
pipe and the annulus will exceed -2300. So, the flow is expected to be turbulent.
27
The average heat transfer coefficients in the pipe and in the annulus can be calculated based on fully
developed turbulent flow. The following correlation (by Gnielinski (1976)) is recommended:
(7)
where ReD is the Reynolds number of the flow
Pr is the fluid Prandtl number
f is the Darcy friction factor
In Eq. (7), the fluid properties are evaluated at the mean bulk temperature.
For smooth pipes, the friction factor can be calculated from the correlation (by Petukhov (1970)):
(8)
The flow in the annulus (formed by the inner pipe and outer shell) requires special treatment. When
calculating heat transfer in a non-circular pipe, the characteristic dimension that should be used in
the Reynolds number and the Nusselt number is the hydraulic diameter (Dh). The hydraulic diameter
is defined as:
(9)
where Ac is the cross sectional area of the non-circular pipe (m2)
P is the wetted perimeter of the non-circular pipe (m).
For an annulus formed by the a pipe (with outside diameter Do) and the outer shell (with inside
diameter DS) is:
(10)
The Reynolds and Nusselt numbers for the flow in the annulus can then be calculated as:
(11)
where &
V is the average fluid velocity in the annulus.
Note that, for the annulus:
(12)
28
4. EXPERIMENTAL PROCEDURE
i)
Turn on the computer data acquisition system. Check that the computer is reading
thermocouples #6, #9, #7 and #11 as shown in Figure 1. While the system is at thermal
equilibrium check that all the thermocouples read the same temperature. Note any corrections,
if necessary.
ii)
Check that the two large valves on drain pipes are completely open.
iii)
Set the valving so that the heat exchanger is operating in counter flow mode.
iv)
Turn the on the cold water. Let the cold water run for a few minutes, so that temperature
becomes steady. Set the flow rate of the cold water to approximately 0.3 CFM (cubic feet per
minute).
v)
Turn on the hot water and set the flow rate to approximately 0.24 CFM. This flow rate should
be kept approximately fixed throughout the experiment.
vi)
When the temperatures are steady, record the flow rates and inlet/outlet temperature of the hot
and cold water streams. A table for recording the data is provided for your convenience.
vii)
Repeat steps (vi) to (vii) for cold water flow rates of approximately 0. 4 CFM, 0.6 CFM and
0.8 CFM. Leave the hot water flow rates at approximately 0.24 CFM.
Important!
• The supply of hot water is limited to the amount stored in a local hot water tank. It will run out in about
20 minutes once the hot water is turned on. So, the hot water should be turned on last, once you are ready
to start the experiments.
• Be sure to check that the small (thumb-operated) drain valve at the bottom of the heat exchanger is
completely closed. If this valve is accidentally left open, the experiment will give an extremely poor heat
balance, i.e. extremely poor results.
• Be sure to check that the large valves on both drain lines are completely open. If these valves are not
fully open, the head loss for the water stream that is diverted through the flow meter will be much
different than the head loss for the stream that is sent directly to drain. As a result, the flow rates will
change when the flow is diverted through the flow meter, giving an inaccurate flow measurement.
29
5. CALCULATIONS AND INTERPRETATION OF RESULTS
i) Convert all the fluid temperatures and flow rates into metric units. All results must be given in the
appropriate metric units.
ii) Calculate the total heat transfer rates for the hot and cold water streams using the measured
inlet/outlet temperatures and volume flow rates. Use Eq. (3) and (4). Be sure to evaluate fluid
properties of each stream at the mean bulk temperature. For each case calculate the percentage
difference between hot and cold side heat transfer rates. Comment on the results.
iii) For each case, calculate the experimental U-value (based on Ao) using Eq. (5).
iv) For each case, calculate the heat transfer coefficient inside the pipe (hi) and inside the annulus
(ho) using empirical correlations for turbulent flow in a pipe. Use these results to calculate the
theoretical value of Uo using Eq. (6). Again, be sure to evaluate fluid properties of each stream at
the mean bulk temperature. Include a table in your report that summarizes the experimental and
theoretical results for U-value and total heat transfer rates.
In your report, be sure to answer the following questions:
Is the flow turbulent in both the hot and cold streams in all cases studied?
How do the theoretically predicted Uo values compare with the experimentally measured
values? What is the typical percentage difference. Is the level of error reasonable for this type
of calculation?
Does the large change in the flow rate of the cold water stream have an strong or weak effect
on the U-value? Discuss.
Although not mandatory, it is recommended that the calculations be done on an Excel spreadsheet.
Include the spreadsheet on CD with your report. Also, be sure to include a full detailed sample
calculation for one case in the Appendix of your report.
30
6. RAW EXPERIMENTAL DATA
Table 1: Experimental Data
Mode of Operation: COUNTER FLOW
Case
#
Cold Water
Flow Rate
Hot Water
Flow Rate
(ft3/min)
(ft3/min)
Hot Water
Inlet Temp
T.C.#6
(°F)
1
2
3
4
31
Hot Water
Outlet Temp
T.C.#9
(°F)
Cold Water
Inlet Temp
T.C.#11
(°F)
Cold Water
Outlet Temp
T.C.#7
(°F)
4
3
2
1
Case
#
ReD
(W)
Hot Side
hi
(W/m2K)
7. SUMMARY OF CALCULATIONS
Re D,h
(W)
Cold Side
32
ho
(W/m2K)
(W)
Theoretical
Uo
(W/m2K)
Measured
Uo
(W/m2K)
%
diff.
Appendix
General Safety Rules and Regulations for Laboratories and Research Facilities
Campus Security: Ext. 5001/5040
Emergency: Ext. 80
Department Safety Officer: Roy Churaman, Ext. 6408
The following safety rules and regulations are to be followed in all of the Department of Mechanical and
Industrial Engineering laboratories and research facilities. These rules and regulations are to ensure that
all personnel working in these areas are protected, and that a safe working environment is maintained at
all times. Attention to these can reduce the risk of injury caused by laboratory hazards.
1. Know what you are working with and how to use it safely. Identify potential hazards involved and
determine the correct safety precautions to follow. Know how to safely shut down the equipment or
experiment before start up.
2. Perform only appropriate experiments following the instructions given by the Instructor, Teaching
Assistant or Technical Staff. Be sure you understand the procedures involved before you begin. If
anything unexpected, dangerous, threatening or unmanageable happens, immediately call your Instructor
or the Laboratory staff present.
3. Wear the proper protective clothing and equipment for each job. Required personal protective
equipment will be provided where needed, these may include safety eyewear, hearing protection, splash
shields, heat resistant gloves and aprons. Users are responsible for wearing these for the duration of the
experiment.
4. Contact lenses can be a serious problem in the lab as they can trap fumes or chemicals in spill accidents
and make it difficult to apply appropriate treatment. All users are discouraged from using contact lenses
whilst in the laboratories.
5. Students who are not appropriately attired will not be allowed to perform experimental procedures.
Clothing that unduly exposes limbs to splash or drop hazards should not be worn i.e. shorts, halter tops,
sandals and open-toed shoes. Loose clothing and or long hair should be confined to avoid contact with
hazardous materials, equipment, rotating machinery or heat sources.
6. Lifting or moving of heavy loads is prohibited except by Technical Support or under the supervision of
Technical Support. Appropriate foot protection Must be worn.
7. Be familiar with emergency procedures; know the location of, and how to use, the nearest emergency
equipment. Note the location of fire extinguishers. (These should only be used in small fires, make sure
they are rated for the type of fire) Also note the location of Fire Alarm Pull Boxes. Upon hearing the fire
alarm all persons MUST leave the building by the nearest exit. Emergency Exits are posted on all
buildings. Leave quickly making sure laboratory doors are closed. Do not use the elevators during a fire.
8. Keep work areas clean and free from obstructions. Note Emergency Exits of laboratories and keep all
aisles and doorways free from obstructions. Bags and personal belongings should be kept to a minimum
and stored against a wall without obstructing quick exit from laboratory.
9. Clean-up all work areas after completion of experiment and return all supplies to their appropriate
storage location.
33
10. All food and drink are prohibited in the laboratories; always wash hands after working and before
handling food and drink .
11. Follow prescribed waste disposal procedures; if unsure, contact Faculty, Teaching Assistant or
Technical Support.
12. Be Alert to unsafe conditions; bring such conditions to the attention of laboratory staff so corrective
action can be taken. Report any accident, unusual occurrence or injury immediately to the Instructor,
Teaching Assistant and or Technical Support Staff, most of whom are trained First Aiders. First Aid Kits
for minor injuries are located in all laboratories where the potential for injury exist. Know the location of
the First Aid Kits and their contents.
13. Students are NOT allowed to work alone in the laboratories at any time.
14. WHMIS: In June, 1987 both Federal and Ontario Governments passed legislation to implement the
Workplace Hazardous Materials Information System (WHMIS) across Canada. WHMIS is designed to
give workers the right to know about hazardous materials to which they are exposed on the job. Any
person who is required to handle any hazardous material covered under this act should first read the label
and the products materials safety data sheet (MSDS). No student shall handle any hazardous materials
unless supervised by Faculty, Technical Support or Teaching Assistant. The Laboratory Technical
Officer, Faculty and or Teaching Assistant is responsible for ensuring that all hazardous materials are
stored safely using WHMIS recommended methods and storage procedures. All MSDS must be displayed
and stored in a readily accessible place known to all users in the workplace and Laboratory.
15. Spills and leaks must be cleaned up immediately. Check with Laboratory Personnel for cleaning up
WHMIS designated ubstances.
16. Never handle broken glassware with bare hands; immediately remove from work area or floor using a
dustpan and brush. se specially marked containers for disposal of broken glass.
17. Compressed gas cylinders must be secured at all times. Appropriate safety procedures must be
followed when moving compressed gas cylinders; Valves must be capped and cylinders secured on
moving vehicle.
Compressed gas cylinders, full or empty, may not be stored in laboratories; the University provides a
storage room at 60 Gould Street, contact Technical Support staff for access.
18. Ensure that gauges used to dispense gases are rated for the particular gas in question. NEVER modify
or otherwise change gas delivery system; fittings, piping and connections etc. must be designed and rated
for the various pressures available in these cylinders.
19. Equipment that has been deemed unsafe, or equipment that is being serviced or repaired must be
tagged and locked out by Technical Support Staff; the Department Safety Officer must be notified of such
action.
ELECTRICAL SAFETY:
There is always a potential danger of electric shock or fire wherever there are outlets, plugs, wiring or
connections, as there are in all laboratories. In addition to the usual electrical hazards, some laboratories
have electrical equipment which poses an even greater potential problem. Students should be extra careful
with these equipment, and learn how to disable the power
source in an emergency.
The following are some Do’s and Don’ts for working with and around electricity.
34
20. Don’t work with electricity if your hands, feet or other body parts are wet or when standing in water
e.g., Fluid Mechanics Lab.
21. Inspect electrical equipment (with power off and unplugged) for frayed cords and damaged or loose
connections -- if any found, do not use the equipment -- report it to immediately to Laboratory Staff for
repairs.
22. Never attempt to repair electrical equipment yourself -- qualified staff must do it.
23. If you receive even a mild electrical shock from a piece of equipment, turn it in immediately for
repair.
24. Do not use or store highly flammable liquids near electrical equipment – sparks from electrical
equipment can ignite some materials.
25. Use 3-prong plugs for 3-prong receptacles - - never break off or alter a 3-prong plug to fit into an
outlet.
26. Extension cords should never be used in place of permanent wiring; their use should be temporary and
they should not be run under doorways, across isles or walkways, through windows or holes in the wall,
around pipes or near sinks.
27. Do not overload circuits by using power strips or multiple outlets on regular sockets.
28. Do not remove or alter safety features on electrical equipment -- it is there to protect you.
29. The instructions on all warning signs must be read and followed at all times in all Laboratories and
Research Facilities.
30. Good housekeeping encourages safer environments and should be practiced at all times in all areas of
the Department.
31. ALL accidents Must be reported immediately to the appropriate laboratory staff present at the time;
injured party(s) must be rendered First Aid at the scene and/or directed or escorted to the University’s
Health Center or the nearest hospital emergency room.
32. In the event of a medical or personal emergency contact Ryerson Security – Dial “80” from any
phone on Campus or press the RED “EMERGENCY” button on any pay phone on campus. To contact
Police, Fire or Ambulance Services Dial “911” for EMERGENCY only from any pay phone on Campus.
Internal office phones requires you to dial “9” for an outside line before dialing “911”. If you call
Emergency Services first, contact Ryerson Security to let them know of the location of the emergency so
they can direct Emergency Services to the scene quickly.
33. Casual visitors to the Laboratories and Research Facilities are to be discouraged. Invited guests must
adhere to the safety Rules and Regulations.
All the foregoing Rules and Regulations are in addition to the Occupational Health and Safety Act, 1987
and to Ryerson University Health and Safety Rules, Regulations and Policies.
35