Download heated bar method

HEATED TRANFER IN A FIN
The heated bar method is based on the theory of extended surfaces (fins). This apparatus can be used to
calculate either the thermal conductivity of a material given the convection coefficient, h; or, h can be
calculated given the thermal conductivity, k.
The apparatus consists of a sample with rectangular cross-section clamped on one end by means of two
aluminum blocks. Four flexible heaters are attached to the aluminum blocks that supply heat to the base of
the sample. Heat is transferred by the sample via two pathways:
1. conduction through the solid sample
2. convection from the surface to the surroundings
The temperature profile of the sample is measured by attaching eight thermocouples on the top surface at
regular intervals. Two thermocouples are also attached to the aluminum blocks to measure the base
temperature.
This experiment can be conducted under four different tip conditions.
1. convection heat transfer
2. adiabatic
3. tip is at prescribed temperature
4. the fin is infinitely long
However, for this particular design, only two conditions can be maintained, namely: conduction heat
transfer, and maintaining the tip at a prescribed temperature. The corresponding temperature profiles for
these two conditions are as follows.
1. Convection heat transfer:
h( )   k
d
dx
xL
the temperature distribution
 h

cosh m( L  x)  
sinh m( L  x) 

 mk


h
b


cosh mL  
sinh mL 
 mk

2.
Prescribed temperature
 ( L)   L :
where the temperature distribution
 L

   b

b

 sinh mx  sinh m( L  x)

sinh mL
In all equations listed above, the following is true:
 ( x)  T ( x)  T
m2 
hP
kAc
M  hPkAc  b
h – convection coefficient
k- thermal conductivity
P- perimeter of sample (2w+2l)
Ac- cross-sectional area of sample
Once  is known at different ‘x’ values, a best fit curve can be interpolated at the various data points to get
a value of ‘m’ and ‘M’, or in other words, h/k. Thus, knowing one of the two, the other can be calculated.
where
As steady state is reached, the temperatures stabilize and data acquisition can begin.
Using Fourier’s law of heat conduction and the convection heat transfer equation, the thermal conductivity
of the sample can be determined, given the convection coefficient, h; or, the convection coefficient for the
setup can be determined, given the sample’s thermal conductivity, k.
Sample Size: 1” x 3” x 9”
Power Supply: Acopian DC Power supply, 100V, 1.5A
Heaters: Watlow flexible heaters: 125V, 25W
Dimensions: 1” x 5” (4)
Data Acquisition: National Instruments SCXI-1322
DIAGRAM OF APPARATUS
base
tip
Direction of Heat Flow
Heaters
GENERAL OPERATING PROCEDURES
 Obtain sample conforming to dimensions above.
 Measure and record the cross sectional area and perimeter of bar.
 Attach eight thermocouples along the centerline of the bar in order to obtain a temperature profile.
 Install sample between the two aluminum heater blocks.
 Install surrounding insulation and close off holding box.
 Set power supply to desired output.
 Once steady state has been reached, data acquisition can begin. The temperature of the heated bars is
determined by the average of all recorded readings.
 The temperature at each point of the temperature profile along the bar is determined by the average of
all readings.
 Recorded data should include the voltage supplied to heaters, resistance of each heater, temperature of
each thermocouple placed along the surface of the bar, and the surrounding, or ambient, temperature.
QUESTIONS
1. What are the assumptions when dealing with heat transfer through an extended surface?
2. What possible sources of error are associated with this experiment?
3. Why are the thermocouples placed along the centerline of the sample? Would the results be the same
if they where not placed along the centerline.
4. Suggest ways to improve this module.