Introduction
Conduction and Thermal Conductivity
Conduction can be defined as the transfer of electrons from one place to another under a potential difference or heat gradient. It is one of three modes of heat transfer between two or more bodies at different temperatures. The other two modes of heat transfer are convection and radiation. Generally, in solids conduction is due to the vibrations of molecules and motion of free electrons. Metals have high number of free electrons which explains that why they are good conductors. Thermal conductivity is the extent by which a substance can conduct heat or electricity. Solid, specifically speaking metals, have high thermal conductivity whereas gases have low value of thermal conductivity. The formula for Fourier Law of heat conduction can be given as
Q=kA dT/dx
Where,
Q = Heat flow rate, [Watt]
k = Thermal conductivity of the material, watt/km
A = Cross-sectional area of the conduction, [m2]
dT = Temperature Difference, [K]
dx = Thickness or length of the material specimen, [m]
Factors Effecting Thermal Conductivity
Thermal conductivity depends upon several parameters.
Material: It highly depends upon the material. As discussed above metals have high thermal conductivity compared to gases. Some non-metal materials can also have higher thermal conductivity compared to metals.
Length: The length of the specimen or material through which heat will flow also affects the thermal conductivity. For a material or specimen whose length is short, the heat will flow easily and faster. But in some cases, thermal conductivity may increase with the increase in length.
Temperature Difference: Thermal conductivity of a material also varies with change in temperature. In some of the cases thermal conductivity increases with increase in temperature while in some cases it decreases with increase in temperature.
Cross-Section Types: Thermal conductivity is also dependent on the shape of material. Materials. The cross-section type like hollow-shaped or C-shaped can affect the thermal conductivity as well.
Measurement of Thermal Conductivity
There are two types of techniques which are used to measure the thermal conductivity of a material. The first one is steady-state technique and the second one is non-steady or transient technique.
In the steady state technique for measuring thermal conductivity, measurement is taken when the material whose thermal conductivity is measured is in the thermal equilibrium state. The problem with this method is that it takes a lot of time to achieve the equilibrium. Moreover, this method also includes expensive equipment to take the readings correctly.
In the transient or non-steady method, readings are taken during the heating process. It records the readings of thermal conductivity using transient sensors. With this method, thermal conductivity can be found relatively quickly.
Increase and Decrease in Thermal Conductivity
For metals thermal conductivity is mainly the function of free moving electrons. With the increase in temperature, the vibrations of electron increases which decreases the passage for moving electrons. Hence, it decreases thermal conductivity. For the liquids, thermal conductivity also decreases with increase in temperature.
In the case of gases, increase in temperature will increase the amount of collisions amongst molecules. Thus it increases thermal conductivity.
Material with Highest Thermal Conductivity
Diamond is considered to have highest thermal conductivity. Solids that have crystalline structures have high thermal conductivity as compared to the solids that have amorphous structures. Due to the same reason, thermal conductivity of gases is lower because atoms are arranged in any shape. The irregularity in solids can also cause thermal conductivity to decrease. As diamond is a highly crystalline material so this characteristic of diamond makes it possible to conduct heat more easily than metals.
Experimental Procedure
Make it sure that the main switch is initially off. Then insert the specimen whose thermal conductivity is to be measured. Then insert the intermediate section into the linear module and clamp it together.
Install the temperature sensors T1 until T4 to the test module and connect the sensor leads to the panel.
Connect the heater supply lead for the linear conduction module to the power supply socket on the control panel.
Turn on the water supply and ensure that water is flowing from the free end of the water pipe to drain. This should be checked at intervals.
Turn the heater power through control knob on control panel to the fully anticlockwise position.
Turn on the power supply and the main switch; the digital readings will be displayed.
Switch on the heater and turn the heater power control and allow sufficient time to achieve steady state condition before recording the temperature at all temperature points as well as the input power reading on the wattmeter (Q). This procedure can be repeated for other power inputs. After each change, sufficient time must be allowed to achieve steady state conditions again.
Use the formula given above to calculate the value of thermal conductivity for all sets of recorded data.
Experimental Data
Water Volume |
Time |
Tin |
Tout |
T1 |
T2 |
T3 |
T4 |
740 ml |
6 min 38 seconds |
14 |
19 |
143.4 |
138.9 |
124.5 |
29.7 |
14.5 |
19.2 |
143.5 |
139 |
124.4 |
29.6 |
||
14.5 |
18.7 |
143.2 |
138.8 |
124.5 |
29.7 |
||
14.5 |
18.7 |
143 |
138.8 |
124.4 |
29.7 |
Calculated Results: Results calculated above are given in the table
below
Mass
Flow Rate (kg/sec) |
Tin (K) |
Tout (K) |
T1 (K) |
T2 (K) |
T3 (K) |
T4 (K) |
K Watt/m.k |
Percentage Error |
0.001859
|
287 |
292 |
416.4 |
411.9 |
397.5 |
302.7 |
17.6653 |
8% |
287.5 |
292.2 |
416.5 |
412 |
397.4 |
302.6 |
16.5762 |
2% |
|
287.5 |
291.7 |
416.2 |
411.8 |
397.5 |
302.7 |
15.4645 |
5% |
|
287.5 |
291.7 |
416 |
411.8 |
397.4 |
302.7 |
15.4645 |
5% |
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