Thermal Conductivity of Metal Rod

Thermal Conductivity of Metal Rod

Aim: To determine the thermal conductivity of metal rod

Theory: Thermal conductivity is the property of the material and indicates the ease, with which a particular substance transfers thermal energy. The thermal conductivity of the material generally depends on the chemical composition of the substance or substances of which it is composed, the phase (i.e. gas, liquid or solid) in which it exists, its crystalline structure if a solid, the temperature and pressure, to which it is subjected and its homogeneity.

Table below lists the values of the thermal conductivities for some common metals:

Table: Conductivities of Materials

Material	Thermal Conductivity ( W / m K)
Silver	420
Pure Copper	386
Aluminium	220
Brass	95
Iron	70
Stainless Steel	14

                

Heat energy is conducted in solids by lattice vibrations and transport by free electrons. Since metals have free electrons in their outer orbit, they are a good conductor of heat energy. Just as these electrons transport electric charge, they also carry thermal energy from a high-temperature region to a low-temperature region.    Transfer of energy by lattice vibrations is not as large as in electron transport. For this reason, good electrical conductors are also good thermal conductors e.g. Copper, Aluminum, Silver, etc.

With the increase in temperature, however, the increased lattice vibrations obstruct the transport of heat by free electrons and hence, for most of the metals, conductivity decreases with increase in the temperature. However, aluminium is the exception.

Experimental Set Up:

The figure shows the experimental setup. It consists of the metal bar, one end of which is heated by an electric heater of band type, while the other end of the bar projects inside the cooling water jacket. The middle portion of the bar is surrounded by a cylindrical shell filled with the asbestos powder. The temperature of the bar is measured at different sections, while the temp in the radial direction is measured by separate thermocouples at two different sections in the insulating shell.

The heater is provided with a dimmerstat for controlling the heat input. Water under constant rate is circulated through the jacket and its flow rate and temperature rise are noted.

 

 Specifications of Set up:

 Material of rod = Copper

 Diameter of metal bar = 25.4 mm

 Length of the bar = 450 mm; Test length AC=300mm

 No. of the thermocouples mounted on the bar = 6

 No. of the thermocouples mounted in the insulation shell =4

 Heater coil (Band type) =Nichrome Heater

 Temperature indicator – 0 to 300⁰ C

 Thermocouple positions on the metal bar - 1 to 6

 Thermocouple positions in the shell - 7 to 10

 To measure rise in temperature of cooling water - thermocouples 11 & 12

                         Dimmerstat heater coil - 2 A /230 V

 Voltmeter -  0 to 200volts.

 Ammeter - 0 to 2 amps.

 Measuring flask for water flow rate 1000 cc

 Stop Watch

 Conductivity of insulation = 0.22 W/mK

 Radial distance of thermocouple in insulating shell

r_i = 50 mm

r_o =100 mm

Procedure:

1. Put dimmerstat to zero position and the switch on the main electric supply.

2. Give input to the heater by slowly rotating the dimmerstat and adjust it to the safe voltage

    80 - 100V.

3. Start the water supply through the jacket and adjust it about 500cc/min.

4. Check and record the temperatures at time intervals of 15 minutes and

    continue this till steady state condition is reached. For this, keep noting down the temperatures readings 1 to 12 till last 2 readings are almost the same.

5. Note the flow rate of the water in cc/min.

Safety Precautions:

1. Ensure that dimmestat is at zero position before switching on main supply

2. Switch on main supply and gradually increase it to 70 to 100 V

3. Do not exceed power input beyond 100 V

Observation Table:

Thermocouple Number/  Time (min)

T1 °C

T2 °C

T3 °C

T4 °C

T5 °C

T6 °C

T7 °C

T8 °C

T9 °C

T10 °C

T11 °C

T12 °C

15

30

45

60

75

90

105

120

Mass flow rate of water         =          cc  in        seconds                                   

Calculations: 

Mass flow rate =Vol flow rate in cc x 10^-6 x density of water =     (kg/s)

After attaining the steady state, heat flowing through section C-C of the bar;

            Q cc =  Heat gained by water

                    =  m_w C_pw ∆T

  where   m_w = mass flow rate of the cooling water (kg/s)

   C_pw = Specific heat of the water (kJ/kg K)

                                                   ∆T = (T₁₂ - T₁₁)

Thermal conductivity of bar at section C-C can now be calculated as: 

                                

 The value of

is to be found out from temp v/s distance graph to be plotted.

                             

A  is cross sectional area of bar, k_cc thermal conductivity of metal rod at section C-C                                                    

Heat conducted through the section B-B of the bar

                               

                                Q _BB     =  Q _cc + Radial heat lost between sections B-B and C-C

                                            

Similarly, thermal conductivity at B-B can be calculated as:

                    

 Heat conducted through the section A-A

and   

                               

Thus the thermal conductivity of bar at different temperatures can be calculated.

Also, Average conductivity = (k_AA + k_BB + k_CC) / 3 = …………. W/mK

Draw plots temp vs distance to find out dT/dx at different sections.

Draw plot to show that conductivity of copper decreases with increase in temp.

Results: 

1. The thermal conductivity of metal rod is --------W/mK

2. The thermal conductivity of copper decreases with an increase in temp.

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