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

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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:

2/10 Pre-Lab Report 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.

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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.

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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)

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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.

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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.

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6. EXPERIMENTAL DATA SHEET

Composite Bar (Aluminum/Stainless Steel) Test

Time

0 min. 2 min. 4 min. 6 min.

Water Temp. In

Water Temp. Out

T1

T2

T3

T4

Mass of Empty Container:

Mass of water collected:

Collection time:

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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 two-dimensional 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.

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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)

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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).

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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.

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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:

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∑ 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.

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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.

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3. THEORY

For external forced convection problems, experimental heat transfer data has been found fit a relationship of the following form:

𝑁𝑢����𝐷 = ℎ�𝐷𝑘

= 𝐶𝑅𝑒𝐷𝑚𝑃𝑟1/3 (1)

where 𝑁𝑢����𝐷is the average Nusselt Number 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 C m 0.4 - 4 0.989 0.330 4 - 40 0.911 0.385

40 - 4,000 0.683 0.466 4,000 - 40,000 0.193 0.618

40,000 - 400,000 0.027 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.

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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.

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6. DATA ANALYSIS

(a) Using a lumped capacitance analysis, the temperature variation of the cylinder with time (t) can be shown to be:

𝜃𝜃𝑖

= 𝑇−𝑇∞𝑇𝑖−𝑇∞

= 𝑒−� ℎ

�𝐴𝑠𝜌𝑉𝑐𝑝

�𝑡 (2)

where 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:

𝑙𝑛 �𝜃𝜃𝑖� = −� ℎ�𝐴𝑠

𝜌𝑉𝑐𝑝� t (3)

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.

(c) Plot ln(𝑁𝑢����𝐷) versus ln(ReD). Fit a straight line to the data and use the slope and y-axis intercept to 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.

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7. RAW EXPERIMENTAL DATA

Barometric Pressure: ______________ mmHg

Test #1

Air Temp: Manometer:

Test #2

Air Temp: Manometer:

Test #3

Air Temp: Manometer:

Test #4

Air Temp: Manometer:

Test #5

Air Temp: Manometer:

Test #6 (repro. test)

Air Temp: Manometer:

Time (s)

Temp. (oC)

Time (s)

Temp. (oC)

Time (s)

Temp. (oC)

Time (s)

Temp. (oC)

Time (s)

Temp. (oC)

Time (s)

Temp. (oC)

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Ryerson UniversityDepartment 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 horizontalcylinder and a vertical flat plate. Measurements will be made in air using a transient cooling techniqueand 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’sgravitational 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 velocitiesassociated with free convection are usually smaller than those associated with forced convection. Forthis reason, the heat transfer coefficient for free convection is generally much lower than for forcedconvection. Although the heat transfer coefficient is low, free convection has the advantage of beingreliable, 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 providesthe 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 attemperature T4. Most fluids expand when heated. So, the heated fluid near the surface of the object willbe less dense than the surrounding fluid. This fluid will rise, producing a thermal boundary layer on thesurface, and thermal plume above the object.

Figure 1: Free convection from an isothermal horizontal cylinder and an isothermal vertical plate.

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It has been found that the free convective heat transfer can be predicted by the following empiricalrelationship:

(1)

where is the average Nusselt Number and Ra is the Rayleigh number. In Eq. (1), C and n areempirical constants, determined from experiments or analysis. The fluid properties in Eq. (1) shouldbe evaluated at the film temperature, (TS+T4)/2.

The characteristic dimension used in the Nusselt number and Rayleigh number depends on thegeometry of the problem. For free convective heat transfer the dimension that has the biggest effect onthe convective heat transfer rate is the overall height of the object. So, for a horizontal cylinder, thecharacteristic length is the diameter D. Similarly, for a vertical plate, the characteristic length is theheight, 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 differentfor 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 onplastic threaded rods. A single thermocouple is embedded in each specimen in order to measure thetemperature of the object as it cools. Note that both the plate and the cylinder have been polished togive 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 verticalplate should be done first. Note that the room air must be relatively still (quiescent) in order to get goodresults. So, it is important that the apparatus is not be set up near any sources of air disturbance, suchas the ventilation diffuser. For the same reason, you should avoid moving about the room during theexperiment.

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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 Cylinder

Material: Aluminum Alloy2024-T6

Material: Aluminum Alloy2024-T6

Orientation withrespect to gravity: Vertical

Orientation withrespect to gravity: Horizontal

Mass: 0.8002 kg Mass: 0.4505 kg

Height: 15.24 cm Diameter: 2.46 cm

Width: 15.24 cm Length: 35.6 cm

Depth: 1.27 cm Emissivity: 0.04

Emissivity: 0.04

6. DATA ANALYSIS PROCEDURE

This experiment is based on the “lumped capacitance” assumption. The experiment has been designedsuch that the resistance to heat conduction inside each specimen is much smaller than the externalconvective 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 heattransfer 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 thespecimen. The specimen cools by convection and radiation. Thus, in Eq. (4) the total heat transfer ratefrom 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, :

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(5)

In this experiment, the cooling rate will be estimated from the temperature of the specimen taken at 120second intervals ()t=120 seconds). Over each time interval, the cylinder cools from temperature Ti totemperature Ti+1. Using the measured temperature at these time intervals, the cooling rate can beapproximated 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 coefficientcan 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 horizontalcylinder, H=D. For the vertical plate H=L. Note that the air properties are evaluated at the average filmtemperature 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 numberat each time step for both test specimens. Be sure to interpolate for the properties of air at the mean filmtemperature, , 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 byempirical correlations. Consult your textbook. Calculate the percentage difference between the

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measured and predicted values. Discuss the most likely reason for the difference between the measuredand predicted values.

For each geometry, present a summary of your experimental data and the empirical correlation valuesin a table, as shown below.

Table 2: Summary of Results

Time Step

i

Measured AverageHeat Transfer

Coeff., (W/m2K)

PredictedAverage

Heat Transfer

Coeff., (W/m2K)

DifferenceBetween

Measured &

Predicted (%)

ExperimentalRayleighNumber,

Ra

MeasuredAverage 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. Youcan expect a substantial amount of scatter in the data. So, you should plot both sets of data (horizontalcylinder 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 themeasured average heat transfer coefficient, calculate the Biot number. Do this calculation for both theplate and the cylinder. Is the lumped capacitance method valid? Comment on whether or not it isacceptable 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 cylinderand plate polished?

Use of an Excel spreadsheet is recommended for these repetitive calculations. If you use Excel, be sureto include an electronic copy on CD with your report (as well as a full sample calculation for eachgeometry).

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8. RAW EXPERIMENTAL DATA

(i) Cylinder Experiment

Cylinder Orientation: Horizontal Barometric Pressure: mmHgInitial Room Temperature: °F

Index i

Timet

(s)

InstantaneousCylinder Temp.

Ti (°F)

1 0

2

3

4

5

6

7

8

9

ii) Plate Experiment

Plate Orientation: Vertical Barometric Pressure: mmHgInitial Room Temperature: °F

Index i

Timet

(s)

InstantaneousPlate Temp.

Ti (°F)

1 0

2

3

4

5

6

7

8

9

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Ryerson UniversityDepartment 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 heatexchanger in counter flow mode. The measured overall U-value will be compared to the U-valuepredicted 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 pipeand cold water flows in the outer annulus. The hot water enters via the upper tube and exits via thelower tube. The direction of the cold water flow can be switched, so that either parallel or counterflow 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: Di =14.3 mmOutside Diameter of the Inner Pipe: Do =15.9 mm Inside Diameter of the Outer Shell (Annulus): DS = 25.4 mmTotal Length of Both Pipes: 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 theinner tube, Ao.

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Figure 1: Schematic diagram of the concentric tube heat exchanger in counter flow mode.

Figure 2: Cross section of the concentric tube heat exchanger.

27

The log mean temperature difference ()Tlm) depends on the temperature difference between thefluid streams at each end of the heat exchanger. For counter flow, the log mean temperaturedifference 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 tothe cold stream. However, because of errors in the measurement of the mass flow rates and fluidtemperatures (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 heatof 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 associatedwith the flow in the inner pipe and in the annulus of the heat exchanger. Using a thermal resistornetwork, 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 innerpipe and the annulus will exceed -2300. So, the flow is expected to be turbulent.

28

The average heat transfer coefficients in the pipe and in the annulus can be calculated based on fullydeveloped turbulent flow. The following correlation (by Gnielinski (1976)) is recommended:

(7)

where ReD is the Reynolds number of the flowPr is the fluid Prandtl numberf 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. Whencalculating heat transfer in a non-circular pipe, the characteristic dimension that should be used inthe Reynolds number and the Nusselt number is the hydraulic diameter (Dh). The hydraulic diameteris 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 insidediameter 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)

29

Important!

• The supply of hot water is limited to the amount stored in a local hot water tank. It will run out in about20 minutes once the hot water is turned on. So, the hot water should be turned on last, once you are readyto start the experiments.

• Be sure to check that the small (thumb-operated) drain valve at the bottom of the heat exchanger iscompletely closed. If this valve is accidentally left open, the experiment will give an extremely poor heatbalance, i.e. extremely poor results.

• Be sure to check that the large valves on both drain lines are completely open. If these valves are notfully open, the head loss for the water stream that is diverted through the flow meter will be muchdifferent than the head loss for the stream that is sent directly to drain. As a result, the flow rates willchange when the flow is diverted through the flow meter, giving an inaccurate flow measurement.

4. EXPERIMENTAL PROCEDURE

i) Turn on the computer data acquisition system. Check that the computer is readingthermocouples #6, #9, #7 and #11 as shown in Figure 1. While the system is at thermalequilibrium 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 temperaturebecomes steady. Set the flow rate of the cold water to approximately 0.3 CFM (cubic feet perminute).

v) Turn on the hot water and set the flow rate to approximately 0.24 CFM. This flow rate shouldbe kept approximately fixed throughout the experiment.

vi) When the temperatures are steady, record the flow rates and inlet/outlet temperature of the hotand 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 and0.8 CFM. Leave the hot water flow rates at approximately 0.24 CFM.

30

5. CALCULATIONS AND INTERPRETATION OF RESULTS

i) Convert all the fluid temperatures and flow rates into metric units. All results must be given in theappropriate metric units.

ii) Calculate the total heat transfer rates for the hot and cold water streams using the measuredinlet/outlet temperatures and volume flow rates. Use Eq. (3) and (4). Be sure to evaluate fluidproperties of each stream at the mean bulk temperature. For each case calculate the percentagedifference 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 thetheoretical value of Uo using Eq. (6). Again, be sure to evaluate fluid properties of each stream atthe mean bulk temperature. Include a table in your report that summarizes the experimental andtheoretical 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 measuredvalues? What is the typical percentage difference. Is the level of error reasonable for this typeof calculation?

Does the large change in the flow rate of the cold water stream have an strong or weak effecton 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 samplecalculation for one case in the Appendix of your report.

31

6. RAW EXPERIMENTAL DATA

Table 1: Experimental Data

Mode of Operation: COUNTER FLOW

Case#

Cold WaterFlow Rate

(ft3/min)

Hot WaterFlow Rate

(ft3/min)

Hot WaterInlet Temp

T.C.#6(°F)

Hot WaterOutlet Temp

T.C.#9(°F)

Cold WaterInlet Temp

T.C.#11(°F)

Cold Water Outlet Temp

T.C.#7(°F)

1

2

3

4

32

7. S

UM

MA

RY

OF

CA

LC

UL

AT

ION

S

Cas

e#

Hot

Sid

eC

old

Sid

e

(W)

Mea

sure

dU

o

(W/m

2 K)

The

oret

ical

Uo

(W/m

2 K)

% diff

.

Re D

(W)

h i(W

/m2 K

)R

e D

,h

(W)

h o(W

/m2 K

)

1

2 3 4

33

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.

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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.

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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.