2006-1488: LABORATORY DEMONSTRATIONS/EXPERIMENTS IN FREE ANDFORCED CONVECTION HEAT TRANSFER

Edgar Clausen, University of ArkansasEDGAR C. CLAUSEN Dr. Clausen currently serves as Adam Professor of Chemical Engineeringat the University of Arkansas. His research interests include bioprocess engineering(fermentations, kinetics, reactor design, bioseparations, process scale-up and design), gas phasefermentations, and the production of energy and chemicals from biomass and waste. Dr. Clausenis a registered professional engineer in the state of Arkansas.

William Penney, University of ArkansasW. ROY PENNEY Dr. Penney currently serves as Professor of Chemical Engineering at theUniversity of Arkansas. His research interests include fluid mixing and process design. ProfessorPenney is a registered professional engineer in the state of Arkansas.

© American Society for Engineering Education, 2006

Page 11.857.1

Laboratory Demonstrations/Experiments in Free

and Forced Convection Heat Transfer

Introduction

A number of papers have been written recently on methods for improving or supplementing the

teaching of heat transfer including the use of spreadsheets to solve two-dimensional heat transfer

problems1, a new transport approach to teaching turbulent thermal convection

2, the use of

computers to evaluate view factors in thermal radiation3, and a new computational method for

teaching free convection4. Supplemental experiments for use in the laboratory or classroom have

also been presented including rather novel experiments such as the drying of a towel5 and the

cooking of French fry-shaped potatoes6. Hunkeler and Sharp

7 found that 42% of students in

senior laboratory over a four year period were Type 3 learners, that is, action-oriented “hands-

on” common sense learners. Thus, an excellent method for reinforcing course content is to

actively involve students in laboratory exercises or demonstrations which are designed to

compare their experimental data with data or correlations from the literature.

As part of the combined requirements for CHEG 3143, Heat Transport, and CHEG 3232,

Laboratory II, junior level chemical engineering students at the University of Arkansas were

required to perform simple heat transfer experiments or demonstrations using inexpensive

materials that are readily available in most engineering departments. During the first offering in

the Fall semester of 2004, the students were required to design, implement and analyze the

results from basic experiments. During the second offering in the Fall semester of 2005, the

students were asked to suggest and implement improvements in the basic experimental design

which could lead to better agreement between their experimental results and results from

literature correlations. This exercise has several benefits:

• It provides an opportunity for students to have additional “hands-on” experience;

• It demonstrates a physical application of correlations found in the textbook; and,

• It helps students develop an appreciation for the limitations of literature correlations.

Results from three of these experiments (free convection cooling of an upward-facing plate,

forced convection cooling by flowing air over an upward facing horizontal plate, and forced

convection heating of a rod by flowing air through an annulus) are described below. In addition,

survey and test results are presented which help to demonstrate whether the

experiments/demonstrations improved or enhanced the students’ understanding of the

appropriateness and limitations of heat transfer correlations found in the literature.

Free Convection Heat Transfer from an Upward Facing Horizontal Plate

Free convection heat transfer is encountered in many practical applications, including heat

transfer from pipes, transmission lines, baseboard heaters and steam radiators. Correlations are

available for predicting free convection heat transfer coefficients for many different geometries.

One of the important geometries is the upward facing horizontal heated surface or plate, the

subject of this investigation. The overall objectives of this experiment were to:

1. Determine the experimental free convection heat transfer coefficient for the top surface of

a horizontal hot plate exposed to air, and

Page 11.857.2

2. Compare these results with results generated from the appropriate correlation of

Churchill and Chu8:

7441

1010 540 <<= RaRaNu . (1)

11741

1010 15.0 <<= RaRaNu (2)

Figures 1 and 2 show schematics of the experimental apparatus, and Figures 3-5 show

photographs of the actual equipment used in the experiment. A list of equipment and detailed

safe experimental procedures was presented by Clausen et al.9, and may also be obtained from

the corresponding author. Briefly, an aluminum plate was heated to ~65°C by setting it on a

wooden platform in an insulated box, closing the lid and heating the surrounding air in the box

with an ordinary hair dryer inserted in the top of the box. After heating the plate, it was set on an

insulated surface in a still room and wrapped with insulation so that only the black painted

surface was exposed (see Figures 2 and 4). A photograph of the second year modification of the

experiment is shown in Figure 5, where a drop cloth curtain was used to better isolate the

apparatus from air disturbances. A thermocouple was inserted into the plate, and temperature

was measured as a function of time while observing the slow cooling of the plate due to free

convection.

Figure 1. Insulated Wooden Box for Heating the Aluminum Plate

Page 11.857.3

Figure 2. Experimental Setup for Cooling the Horizontal Insulated Plate

Figure 3. Photograph of Wooden Box Figure 4. Photograph of Apparatus for

Used to Heat the Aluminum Plate Cooling the Insulated Horizontal Plate

Page 11.857.4

Figure 5. Photograph of Drop Cloth used to Isolate the Environment

Surrounding the Aluminum Plate

It was desired to compare an experimentally determined heat transfer coefficient with

correlations found in the literature. A heat balance on the plate, with no heat generation, yields:

( ) ( )dt

dTCVTTATThA PSURFACESSURFACES ρεσ =−+−− ∞∞ )()(

44 (3)

Although small, the heat balance was also corrected for the heat flow by conduction from the

aluminum plate through the insulation to the table. Experimental data of temperature vs. time

were thus used to determine the “best fit” experimental heat transfer coefficient by integrating

Equation 3 numerically using a TK Solver 4th order Runga-Kutta integration. The heat transfer

coefficient from the literature was determined using Equations 1 and 2, where the Rayleigh

number is calculated as:

( )

Pr2

3

ν

β LTTgRa SURFACE ∞−

= (4)

In Equation 4, the length of the plate is the characteristic length in free convection and, for a

horizontal flat plate, L = AS/P. Assuming that the surrounding air is an ideal gas, the volumetric

expansion coefficient may be calculated as:

T

1=β (5)

Finally, the heat transfer coefficient, hCORR, may be calculated from the Nusselt number as:

L

kNuhCORR = (6)

Page 11.857.5

Figure 6 shows a plot of the experimental temperature with no drop cloth as a function of time,

as well as a curve showing a numerical integration of Equation 3 using the “best fit”

experimental heat transfer coefficient. The emissivity (ε) of the black painted surface was

assumed to be 0.98. The experimental heat transfer coefficient was 8 W/m2K at a surface

temperature of 352 K, while the coefficient based on the Churchill/Chu relationship was 5.6

W/m2K. Thus, a correction factor (hEXP/hCORR) of 1.4 was needed in order to match the

experimental data with the correlation. When the drop cloth was added, the correction factor fell

to 1.2, indicating that the addition of the drop cloth was significant in eliminating air currents.

Figure 6. Temperature vs. Time Experimental Data (+) and Predicted by Equation 4

Multiplied by a Factor of 1.4 (hEXP = 8 W/m2K at TSURFACE = 352 K)

Forced Convection Heat Transfer from an Upward Facing Horizontal Plate

Forced convection heat transfer occurs when the fluid surrounding a surface is set in motion by

an external means such as a fan, pump or atmospheric disturbances. This study was concerned

with forced convection heat transfer from a fluid (air) flowing parallel to a flat plate at varying

velocities. The objectives of this experiment were to:

1. Determine the experimental forced convection heat transfer coefficient for parallel flow

over a flat plate.

0 500 1000 1500 2000 2500 3000 3500 4000

325

330

335

340

345

350

355

360

Time (s)

Temperature (K)

+++++++++++

++

++

++

++

++

++

++

++

+

+++++++++++

++

++

++

++

++

++

++

++

+

Page 11.857.6

2. Compare the experiment heat transfer coefficient with the coefficient calculated from the

correlations presented by Cengel8, who gives the following correlations for local heat

transfer coefficients for forced convection flow over a horizontal plate:

3/15.0PrRe332.0/ xxx kxhNu == for laminar conditions, i.e., Re < 500,000

(7)

3/18.0 PrRe0296.0/ == kxhNu xx for turbulent conditions, i.e., 5x105 < Re < 10

7 (8)

The integrated average coefficients are given by

3/15.0

PrRe332.0/ xkhxNu == for laminar conditions, i.e., Re < 500,000 (9)

3/18.0 Pr)871Re037.0(/ −== khxNu turbulent conditions, 5x105 < Re < 10

7 (10)

The experimental set up and procedures were essentially the same as shown in Figures 1-4,

except that multiple plates were used along with a three speed fan. Thus, forced convection heat

transfer was measured for horizontal plates at two selected distances from the fan and at three

different air speeds. An anemometer was used to measure the air velocity over the plate at five

different lateral positions to determine the average air velocity. A schematic of the experimental

set up is shown in Figure 7 and photographs of the apparatus are shown in Figures 8 and 9. As is

shown in Figure 9, a series of cardboard honey comb diffusers was used during year 2 in an

attempt to minimize air turbulence. The diffusers were located just after the fan (connected to the

fan outlet by a plastic “garbage bag” channel) and immediately in front of the aluminum plates.

Once again, a list of equipment and detailed safe experimental procedures was presented by

Clausen et al.10, and may also be obtained from the corresponding author.

Figure 7. Location of Fan and Plates for the Horizontal Plate Heat Transfer Experiment

Page 11.857.7

Figure 8. Photograph of Experimental Horizontal Plate Heat Transfer Experiment

Figure 9. Photograph of Diffuser and Connection between Fan and Diffuser

Page 11.857.8

Figure 10 shows a plot of the experimental temperature for the first plate, without the air

diffuser, as a function of time at an air velocity of 4.82 m/s. The procedure for obtaining the

experimental heat transfer coefficient was essentially the same as in the previous experiment.

The ratio of the experimental heat transfer coefficient to the correlation heat transfer coefficient

ranged from 2.7-3.3 (average of 3.0) for the first plate at three different fan velocities, and ranged

from 1.7-2.4 (average of 2.1) for the fourth plate. When the air diffuser was added, the ratio was

1.8-1.9 for the first plate and ranged from 2.8-5.0 (average of 3.9) for the fourth plate. Thus, the

diffuser only marginally affected the effects of air turbulence on temperature measurement.

Perhaps the addition of a drop cloth in combination with the diffuser would have improved the

ratio.

Figure 10. Temperature vs. Time Experimental Data from the First Plate

at an Air Velocity of 4.82 m/s

Forced Convection Heat Transfer from Hot Air in an Annulus to the Inner Cylinder

Another important geometry for forced convection heat transfer is the heating or cooling of a

fluid flowing through an annulus between an outer pipe and an inner cylinder. The objectives of

this experiment were to:

1. Determine the experimental forced convection heat transfer coefficient for the heating of

a brass rod, contained in an annulus, as air flows through the annulus, and

0 50 100 150 200 250 300

64

64.5

65

65.5

66

66.5

67

67.5

68

68.5

69

69.5

Time (s)

Plate Temperature (C)

+

+

++

+

+

+

+

+

+

Page 11.857.9

2. Compare these results with the heat transfer coefficient from the Dittus-Boelter

equation8:

Nu = 0.023 Re0.8

Pr 0.4 (11)

where the hydraulic diameter of the annulus (DH = DPIPE – DROD) is used as the

characteristic length in both the Reynolds and Prandtl numbers.

Figure 11 shows a schematic of the experimental apparatus, and Figures 12 and 13 show

photographs of the equipment used in the experiment. A list of equipment and detailed safe

experimental procedures was presented by Clausen et al.10, and may also be obtained from the

corresponding author. Ice was used to cool a brass rod to a temperature of 10-12°C. The wood

and brass rods were then inserted into the PVC tube as shown in Figure 11, and a thermocouple

was inserted into the brass rod. The wood rod was used to provide an inside cylinder which is

much longer than the brass rod, so that fully established turbulent flow existed prior to the hot air

reaching the brass rod. The hair dryer was then inserted into the bottom of the PVC tube, and

temperature inside the brass rod was monitored with time. After the air flow had reached steady

state, the velocity and ambient air temperature of the air exiting the annulus were recorded. The

procedure was repeated for different hair dryer speeds. The cylinder is shown in the center of

Figure 12. A photograph of the air diffuser, used during the second year modification of the

experiment, is shown in Figure 13. The diffuser was connected to the bottom of the PVC tube in

an attempt to minimize air turbulence, much like the diffuser in the horizontal plate experiments.

Figure 11. Schematic of Annulus Heating Apparatus

Page 11.857.10

Figure 12. Schematic of Annulus Heating Apparatus

Figure 13. Two Views of Diffuser Used in Annulus Heating Apparatus

Figure 14 shows a plot of the experimental temperature for the rod, without the air diffuser, as a

function of time at an air velocity of 4.22 m/s. The procedure for obtaining the experimental

heat transfer coefficient was much the same as in the previous experiment. The ratio of the

experimental heat transfer coefficient to the correlation heat transfer coefficient ranged from 1.6-

2.2 for the range of air velocities, with an average of 1.8. When the air diffuser was added, the

ratio held at 1.0 (hEXP = hCORR) for all air velocities, showing that this air diffuser was effective in

minimizing turbulence in this system that was unaffected by outside air currents.

Page 11.857.11

Figure 14. Temperature vs. Time for Experiment # 1 with the 1 in Diameter x 8.1 in Long Brass

Rod Heated by a 62°C, 4.22 m/s Air Stream in a 3 in Pipe

Assessment of Educational Value

After the second offering of this experimental program during the Fall, 2005, semester, the

participating students were asked to evaluate the effectiveness of the program as an educational

tool, and were also given a short competency quiz to also evaluate effectiveness. Results from

the survey of the18 participating students are shown in Table 1. Perhaps most importantly, the

students felt that the experiments/demonstrations helped to increase their understanding of heat

transfer (Statement 1), and gave them a better understanding of the applicability and limitations

heat transfer correlations and data (Statement 2). The students also felt that

experiments/demonstrations should be developed in conjunction with other courses besides heat

transfer (Statement 3), and preferred the use of group reports (as used in this exercise) in place of

individual reports (as used in most of the other assignments) (Statement 7). The students were

less enthusiastic about including the experiments/demonstrations as a regular part of Lab 2

(Statement 4), using the experiments/demonstrations in place of more traditional laboratory

experiments (Statement 5), and in working in the smaller groups of 2-3 people (used in this

exercise), as compared to the groups of 3-5 people used in other experiments (Statement 6).

Most of the experiments in this exercise actually required a longer time commitment than

traditional laboratory experiments, and the students were not particularly fond of TKSolver as a

computational tool. Finally, as expected, the students disliked the method of grading used on the

experiments/demonstrations (a maximum of two submissions to get it correct; receive an ‘A’ or

‘F’) (Statement 7), and instead preferred the usual method of grading a single laboratory report

submission.

-25 0 25 50 75 100 125 150 175 200 225

10

12

14

16

18

20

22

24

26

28

Time (s)

Rod Temperature (C)

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

Page 11.857.12

Table 1. Results from the Heat Transfer Experiments/Demonstrations Survey

Fall, 2005

% of Students Surveyed Survey Statement

5 4 3 2 1

1. The heat transfer experiments/demonstrations helped to

increase my understanding of heat transfer

11 67 17 0 5

2. The heat transfer experiments/demonstrations gave me a

better understanding of heat transfer correlations and data,

their applicability and limitations

5 78 11 5 0

3. Experiments/demonstrations should be developed in

conjunction with other courses besides heat transfer

5 72 17 5 0

4. Heat transfer experiments/demonstrations should be

included as a regular part of Lab 2

0 44 44 5 5

5. I prefer the experiments/demonstrations to more

traditional laboratory experiments

5 44 33 17 0

6. I prefer working in groups of 2-3 people, instead of 3-5

people

11 22 50 11 5

7. I prefer group reports in place of individual reports 33 39 11 17 0

8. I prefer the method of grading used on the heat transfer

experiments/demonstrations to traditional grading in Lab 2

0 5 28 44 22

5—strongly agree

4—agree

3—no opinion

2—disagree

1—strongly disagree

The students were also given competency quizzes to demonstrate whether the experiments

accomplished the stated objectives of the exercise. Each student was given a different

competency quiz, depending upon which experiment the student ran. The questions which

pertain to this paper are:

1. In layman’s terms, what is the difference between free and forced convection?

2. What was the diffuser (or curtain) supposed to do to improve your results? Did it help?

Why or why not?

3. What correlation was used in predicting the forced (or free) convection heat transfer

coefficient for your experiment? A name or description is sufficient. What are its

limitations?

Each student was given three questions pertaining to his or her experiment, and was expected to

give a short answer to each of the questions. The quiz was not announced, and notes and

textbooks could not be used during the quiz. The quizzes were graded on a 0-6 point basis (2

points per question). Four of the 15 students taking the quiz scored 6/6, 8 of the students scored

5/6, and 4 of the students scored 4/6. These results demonstrate competency, and show that the

objectives of the exercise had indeed been met.

Page 11.857.13

Nomenclature

AS heat transfer area, m

2

Cp specific heat, J/kg K

DH hydraulic diameter of the annulus, m

DPIPE diameter of outer pipe, m

DROD diameter of rod (inner cylinder), m

g gravitational constant, m/s2

h area average convection heat transfer coefficient, W/m2 K

hCORR heat transfer coefficient from literature correlations, W/m2 K

hEXP heat transfer coefficient from experimental data, W/m2 K

hx local heat transfer coefficient at length x along a flat plate, W/m2 K

k fluid thermal conductivity, W/Mk

L characteristic length in free convection, As/P, m

Nu area average Nusselt number, hx/k or hD/k

Nux local Nusselt number at location x along flat plate, hx/k

P perimeter, m

Pr Prandtl number of the fluid

Ra Rayleigh number

Re Reynolds number, = VDρ/µ for cylinder or Vxρ/µ for a flat plate

Rex local Reynolds number at location x along flat plate, Vxρ/µ

t time, s

T temperature, K

Tω ambient temperature of surroundings, K

TSURFACE surface temperature, K

v fluid velocity, m/s

V volume of plate or cylinder, m3

x length along flat plate in flow direction, m

β volumetric expansion coefficient, = 1/T, K-1

ε surface emissivity

ρ fluid density, kg/m3

σ Stefan-Boltzmann constant, W/m2K

4

Bibliography

1. Besser, R.S., 2002, “Spreadsheet Solutions to Two-Dimensional Heat Transfer Problems.” Chemical

Engineering Education, Vol. 36, No. 2, pp. 160-165.

2. Churchill, S.W., 2002, “A New Approach to Teaching Turbulent Thermal Convection,” Chemical

Engineering Education, Vol. 36, No. 4, pp. 264-270.

3. Henda, R., 2004, “Computer Evaluation of Exchange Factors in Thermal Radiation,” Chemical

Engineering Education, Vol. 38, No. 2, pp. 126-131.

4. Goldstein, A.S., 2004, “A Computational Model for Teaching Free Convection,” Chemical Engineering

Education, Vol. 38, No. 4, pp. 272-278.

5. Nollert, M.U., 2002, “An Easy Heat and Mass Transfer Experiment for Transport Phenomena,” Chemical

Engineering Education, Vol. 36, No. 1, pp. 56-59.

6. Smart, J.L., 2003, “Optimum Cooking of French Fry-Shaped Potatoes: A Classroom Study of Heat and

Mass Transfer,” Chemical Engineering Education, Vol. 37, No. 2, pp. 142-147, 153.

7. Hunkeler, D., Sharp, J.E., 1997, “Assigning Functional Groups: The Influence of Group Size, Academic

Record, Practical Experience, and Learning Style,” Journal of Engineering Education, Vol. 86, No. 4, pp.

321-332.

Page 11.857.14

8. Cengel, Y.A., 2003, Heat Transfer: A Practical Approach, McGraw-Hill Book Company, New York.

9. Clausen, E.C., Penney, W.R., Colville, C.E., Dunn, A.N., El Qatto, N.M., Hall, C.D., Schulte,

W.B., von der Mehden, C.A., 2005, “Laboratory/Demonstration Experiments in Heat Transfer:

Free Convection,” Proceedings of the 2005 American Society of Engineering Education-Midwest

Section Annual Conference.

10. Clausen, E.C., Penney, W.R., Dunn, A.N., Gray, J.M., Hollingsworth, J.C., Hsu, P.T., McLelland,

B.K., Sweeney, P.M., Tran, T.D., von der Mehden C.A., Wang, J.Y., 2005,

“Laboratory/Demonstration Experiments in Heat Transfer: Forced Convection,” Proceedings of

the 2005 American Society of Engineering Education-Midwest Section Annual Conference.

Page 11.857.15