Question

Using cylindrical samples of the same material, devise an experiment to determine the thermal contact resistance. Cylindrical samples are available at any length, and the thermal conductivity of the material is known.

Short answer

Question: Explain how to conduct an experiment to determine the thermal contact resistance between two cylindrical samples of the same material. Answer: To conduct the experiment, follow these steps: 1. Gather two cylindrical samples of the same material with known thermal conductivity and set up a heat source connected to one end of the first cylindrical sample and a heat sink connected to the other end of the second cylindrical sample. 2. Measure the initial temperatures at three points: the heat source end (T1), the contact interface between the two cylindrical samples (T2), and the heat sink end (T3). 3. Turn on the heat source to allow heat transfer through the samples and monitor the temperature changes at T1, T2, and T3. 4. Once a steady state is reached, calculate the temperature differences between T1 and T2, and T2 and T3. 5. Using the known thermal conductivity, temperatures, and dimensions of the samples, calculate the heat transfer through each sample. 6. Determine the heat transfer across the contact interface, which should be the same as the heat transfer through each sample. 7. Calculate the thermal contact resistance using the heat transfer across the contact interface and the temperature difference at the interface.

Step-by-step solution

Gather Materials and Set up the Experiment

First, gather two cylindrical samples of the same material with known thermal conductivity. Set up a heat source connected to one end of the first cylindrical sample and a heat sink or a cooling system connected to the other end of the second cylindrical sample.

Measure Initial Temperatures

Measure the initial temperatures at three points: the heat source end (T1), the contact interface between the two cylindrical samples (T2), and the heat sink end (T3).

Apply Heat and Record Temperature Change

Turn on the heat source to allow heat to transfer through the first cylindrical sample to the second one and eventually to the heat sink. Monitor and record the temperature change over time at all three points (T1, T2, and T3).

Calculate Temperature Drops Across the Cylindrical Samples

After reaching a steady state (constant temperature values), calculate the difference in temperature between the heat source end (T1) and the contact interface (T2) as well as between the contact interface (T2) and the heat sink end (T3).

Calculate Heat Transfer Through Cylindrical Samples

Using the known thermal conductivity (k), the temperatures calculated in Step 4, and the dimensions of the cylindrical samples (length, L, and cross-sectional area, A), calculate the heat transfer through each cylindrical sample using the formula: q = k * A * (temperature difference) / L

Determine the Heat Transfer across the Contact Interface

The heat transfer across the contact interface should be the same as the heat transfer through the first and second samples individually. Calculate the heat transfer across the contact interface: q_interface = q_sample1 = q_sample2

Calculate the Thermal Contact Resistance

Using the heat transfer across the contact interface and the temperature difference between the two samples at the interface, calculate the thermal contact resistance (R_contact) using the following formula: R_contact = (T2 - T1) / q_interface This value represents the thermal contact resistance between the two cylindrical samples. Modify the experiment with different contact pressure levels, materials, or surface treatments to study the effect of these factors on thermal contact resistance.