Heat Conduction Experiment – Linear and Radial, Procedure and Thermal Conductivity

Aim of the Experiment

To determine the thermal conductivity of a material using linear and radial heat conduction apparatus, and to verify Fourier’s law of heat conduction.

Apparatus Required

• Linear heat conduction apparatus (brass rod with heater at one end and cooling at the other)
• Radial heat conduction disc apparatus
• Temperature sensors (thermocouples) at multiple points
• Wattmeter or power supply with ammeter and voltmeter
• Cooling water supply

Theory

Fourier’s Law of heat conduction states:

Q = −k × A × (dT/dx)

Where: Q = rate of heat transfer (W), k = thermal conductivity (W/mK), A = cross-sectional area (m²), dT/dx = temperature gradient (°C/m).

For radial conduction through a disc: Q = 2πkL(T_inner − T_outer) / ln(r_outer/r_inner)

Procedure, Linear Conduction

1. Set up the linear heat conduction apparatus. Connect the heater at one end.
2. Switch on the heater and set the power input using the rheostat.
3. Allow the system to reach steady state (30–45 minutes).
4. Record temperatures at each thermocouple position (T₁ at heater end to T_n at cooler end).
5. Measure power input Q = V × I (from wattmeter).
6. Plot temperature vs. distance along the rod and measure the slope dT/dx.
7. Calculate k = Q / (A × dT/dx).

Observation Table, Linear Conduction

Result

Thermal conductivity of the material (linear): k = _______ W/mK. Thermal conductivity (radial): k = _______ W/mK. Both values are within ±10% of the standard value, confirming Fourier’s law of heat conduction.

Internal Links

Related: Heat Transfer Lab Equipment | Convection Experiment | Shell and Tube Heat Exchanger | Engineering Lab Equipment Guide

Linear Heat Conduction, Detailed Procedure and Calculations

Fourier’s Law of Heat Conduction

Q = -kA(dT/dx)

where Q = heat transfer rate (W), k = thermal conductivity (W/m·K), A = cross-sectional area (m²), dT/dx = temperature gradient (K/m)

The negative sign indicates heat flows in the direction of decreasing temperature.

Linear Conduction Experiment, Step-by-Step

1. Set up the linear conduction bar with heater at one end and water-cooled heat sink at the other end.
2. Mount thermocouples at equally spaced positions along the bar (typically 6–9 positions at 10 mm spacing).
3. Set the heater power using the wattmeter (typically 20–50 W).
4. Allow 20–30 minutes for steady state (temperature readings become stable).
5. Record all thermocouple temperatures T₁ through T₉.
6. Measure the water flow rate through the heat sink using a measuring cylinder and stopwatch.
7. Measure inlet and outlet water temperatures.

Calculation of Thermal Conductivity

Heat flow rate from heater: Q = V × I (watts), verify with Q = mc_p(T_out – T_in) from cooling water

Temperature gradient: dT/dx = (T₁ – T_n) / L (where L = length between thermocouples 1 and n)

Thermal conductivity: k = Q / (A × dT/dx) = Q × L / (A × (T₁ – T_n)) W/m·K

Reference Thermal Conductivities

Radial Heat Conduction

For the radial conduction disc, Fourier’s law in cylindrical coordinates gives:

Q = 2πkL(T_inner – T_outer) / ln(r_outer/r_inner)

where L = disc thickness, r_inner = inner radius, r_outer = outer radius