Objective
The aim of the experiment is to determine the thermal conductivity of a metal specimen. This will be achieved using Fourier’s Law of conduction, which allows us to calculate the flow of heat through a specimen, by measuring the temperature difference, as is displayed below (eq. 1)
Eq. 1
Where Q = Heat flow rate k = Thermal conductivity of specimen A = Surface area of the specimen T = Temperature Δx = Thickness of the specimen Procedure
The experiment was set up as show below, in figure 1. It has been equipped with thermocouples to take the temperature of the hot surface and cold surface of the material. The heat is provided by an electrical coil up the top, and is cooled by a water cooling loop to remove heat from the opposite end of the specimen, to create a constant, non varying situation to measure the temperatures. The specimen is held between the heated and cooled section.
A voltage of 6V was applied to the heated section, and left for 25 minutes to adjust to a constant rate. The thermocouples were arranged 15mm apart, and named T1-T8, as shown in figure 2. The temperature was then taken from each thermocouple, and recorded. This procedure was then repeated, but with a voltage of 12V.
Results + Calculations
The specimen was recorded to be a length of 0.030m, and have a diameter of 0.025m.
The collected data is shown below, in figure 3.
V (Volts)
I (amp)
T1 °C
T2 °C
T3 °C
T4 °C
T5 °C
T6 °C
T7 °C
T8 °C
6
0.63
17.3
16.1
15.2
13.0
11.7
10.3
9.1
7.7
12
1.16
52.6
48.9
44.9
32.8
28.5
19.1
14.7
11.5
Heat flow rate can be found by (eq.2)
(Eq. 2) Q (6v)=6 x 0.63 = 3.78W Q (12v)=12 x 1.16 = 13.92W
The surface area of the specimen was calculated as below (eq. 3)
(Eq. 3) A = = 4.91x
To determine the thermal conductivity (k) of the specimen, the difference between T4, the hot face, and T5, the cold face, was calculated. Rearranging Eq. 1 allows k to be found for both 6V, and 12V, as shown below (eq. 1.1)
(Eq. 1.1) k (6v) = 177.6 W/m°C K (12v) = 197.8 W/m°C
Analysis
If we then plot all of the temperatures into a graph of x/°C (Distance between thermocouples/temperature at each thermocouple), we can determine the gradient, and therefore find the average conductivity of the specimen.
The metal used in the experiment was Brass, which has a given value of thermal conductivity of 109W/m°C (http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html), Which is not what was achieved through calculation. This could be due to a number of reasons, including the fact that the thermocouples were 7.5mm away from the surface of the material, meaning that Δx is inaccurate. However, to compensate for this, the graphs above are used to determine the gradient, and get a more accurate average thermal conductivity value.
For 12v, the points used were (0.02, 50.92) and (0.07, 30.55), which gives a gradient of -407.4
For 6V, the points used were (0.02, 17.01) and (0.07, 12.32), which gives a gradient of -93.8
These gradients can be used to calculate K using the equation below (eq. 1.2)
Eq. 1.2 k (6v) = 82.07 W/m°C K (12v) = 69.59 W/m°C
Discussion
Overall, the procedure seemed reliable, no flaws were seen or located, everything went as expected, and no problems occurred. However, the experiment did not seem to be the most accurate, with the closest value being found from the gradient of the 6v, and
