A common method to measure thermal conductivity of a biomaterial is to insert a long metallic probe axially into the center of a long cylindrical container of the material. The probe is maintained at some uniform temperature Ti, and the outside of the container is maintained at a temperature To. Inside the metallic probe is an electrical heater for which the electrical power is measured. If the diameter of the probe maintained at 50°C is 1 cm, the outer diameter of the container maintained at 20°C is 4 cm, the length of the cylinder container is 60 cm, and the power input is 40.8 W, calculate the thermal conductivity of this material.

The thermal conductivity of the biomaterial is approximately 1.571 watts per meter-Celsius.

Explanation:

Let suppose that thermal conduction is uniform and one-dimensional, the conduction heat transfer (), measured in watts, in the hollow cylinder is:

Where:

- Thermal conductivity, measured in watts per meter-Celsius.

- Length of the cylinder, measured in meters.

- Inner diameter, measured in meters.

- Outer diameter, measured in meters.

- Temperature at inner surface, measured in Celsius.

- Temperature at outer surface, measured in Celsius.

Now we clear the thermal conductivity in the equation:

If we know that , , , , and , the thermal conductivity of the biomaterial is:

The thermal conductivity of the biomaterial is approximately 1.571 watts per meter-Celsius.

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