HEAT TRANSFER EXPERIMENT
Freshman Engineering Clinic II
Prepared by Drs. Kauser Jahan and Robert P. Hesketh
Spring 2009
Introduction to Heat Transfer: Natural and Forced Convection
There are many examples of natural and forced convection:
Forced Convection:
Radiator fan in car blowing air by radiator.
Fan cooling Pentium chip on personal computer.
Natural Convection
Heat loss from a road surface on a hot day: notice the density gradients in the air. (Remember seeing
the density difference?)
Heat loss from a computer monitor.
Heat loss from a hot plate.
What is the difference between the above two examples? In both cases energy is lost from a solid
surface to a fluid that is moving. In Forced Convection the fluid is moving by some outside force such
as a fan. In Natural convection the fluid motion is caused by a density difference between the hot fluid
next to the hot surface and the cold fluid far from the surface. The hot, low density fluid flows upward
causing the cold high density fluid to flow downward.
To obtain simple expressions for the transfer of heat from a solid surface to a fluid engineers use the
empirical relation:
 Rate of   " Proportionality  Area of  Temperature 
(1)

 


 Heat Transfer  Constant"   the Surface  Difference 
or
Rate of Heat Transfer = UoA(Tsurface-Tair)
(2)
The proportionality constant, Uo, is commonly referred to as an overall heat transfer coefficient. This
heat transfer coefficient is a function of the properties of the insulating material (thermal conductivity),
physical properties of the fluids, and velocity of the fluids.
All heat transfer coefficients have been obtained from carefully conducted experiments. The data from
these experiments are correlated using an appropriate equation. The results of these experiments are
first published in journal articles and then they are summarized in textbooks.
Water Cooling Experiment:
This experiment will demonstrate natural convection. In this experiment you will fill two cups with
hot water. You will measure the temperature as a function of time using the data acquisition system.
Your data will be analyzed to determine the overall heat transfer coefficient for each cup.
In this experiment you will need to know the external surface area of your cups and lids. Below is an
example of a derivation of the external surface area of your paper and Styrofoam cups using second
semester calculus:
Surface area of the side of the conical cup:
 External


 z L
z L
 Surface Area  2r dz  2 equation of the slanted line dz


 
 of Side of 
z0
z0


 Conical cup 

 z d top
z  0 2  2

z L
1.
2.


z dtop  dbottom
d
 bottom
2
L
2
 dbottom
dbottom 

dz
L
2 
eq. of slanted line: r 

(3)
(4)
(5)
 External surface area 


 d top  dbottom 
(6)

 of the side of the
  L
2




 conical cup

Sample Preparation
Top Outside Diameter
1.1. Record in your laboratory notebook a
dimensioned drawing of each of your cups and
mugs. Calculate the external surface area of
the walls and top surface of your cups and
mug.
1.2. Boil a pot of water using the electric kettle next
Cup Vertical
Height, L
to your machine. Make sure that you will have
enough water.
1.3. Weigh each empty cup and lid.
1.4. Fill the cups to the top with cold water and
weigh the combined mass of water, cup and
lid. Make sure that you do not leave an air gap
between the liquid surface and the plastic top
Bottom Outside
Diameter
of your cup. Calculate the mass of water in
each cup.
1.5. Record the room temperature.
1.6. Carefully place the thermometer through the hole in the plastic lids. Since water
evaporation will effect your results a lid is required. Make sure that the water level is as
close to the top of the plastic lid as possible.
1.7. Locate the tip of the thermometer roughly half way in the cup.
1.8. Adjust ring stand arms and to achieve this requirement.
Experimental Run
2.1. Using a team of 4 people, have one person pour water into each of the cups. Have the
second person follow by placing lids on the cup. The third person will insert the
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thermocouple into the cup. The fourth person will record the data (Time and
Temperature).
Data Analysis
3.1. On a single graph, plot the temperature as a function of time for each of the cups.
 Tliquid  Troom 
 vs t. Fit an exponential
3.2. Using the theory given below make a plot of 

T

T
 initial room 
trendline through this data.
 Tliquid  Troom 
 vs t. Fit a best fit line and obtain equation. Use slope to
3.3. Plot ln 

T

T
 initial room 
determine Uo, for each of your cups. Use the measured mass of water, heat capacity of
water = 4,184 J/(kg ºC), and your calculated external surface area.
3.
Energy Balance:
Control Volume is the hot liquid within the cup or mug
 Accumulation 

  Rate of energy additon to  Rate of energy removal 
 

 of energy in the   
  from the control volume.

  the control volume.
 control volume 
d
mC p Tliquid   0 J  Rate of Heat Loss from Coffee   U o Ao Tliquid  Troom 
1.
dt
s
T
t
 U o Ao 
dTliquid





Tliquid  Troom  t 0  mC p dt
Tin itia l
 U A
 Tliquid  Troom 

  exp   o o
T

 mC
p
 initial  Troom 


t


(7)
(8)
(9)
The appropriateness of the above equation can be checked by evaluating it at its limits. At the initial
time the temperature of the liquid is the initial temperature. At the time of infinity the liquid
temperature is equal to the room temperature.
References:
Bejan, A. (2004) Convection Heat Transfer, Publisher: Wiley, John & Sons, Incorporated.
TEAM LABORATORY REPORT
a)
b)
c)
d)
e)
f)
A letter of transmittal (should state what you did and what were your findings?)
Include typed raw data in tabular form along with values of all variables
Include calculations of surface area
Include the two plots mentioned in 3.2 and 3.3.
Show calculations indicating how you obtained the values of U0 for your cups.
Interpret your results – Compare the values of Uo for each cup. Which one has the higher
value? Why?
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SAMPLE PLOTS mentioned in 3.2 and 3.3
1
0.9
0.8
0.7
Insulated Row an Cup
0.6
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
80
100
120
140
160
180
Tim e (Minutes)
0
-0.2
0
20
40
60
80
100
120
140
160
180
-0.4
Insulated Row an Cup
-0.6
-0.8
ln
-1
-1.2
y = -0.0117x
R2 = 0.9968
-1.4
-1.6
-1.8
-2
Tim e (Minutes)
Use slope of line to determine value of Uo
U A 
Slope =  o o 
 mC p 
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