Heat Transfer Rate (\( Q_k \)):

\[ Q_k = \frac{2 \pi k L (T_i - T_o)}{\ln \left( \frac{r_o}{r_i} \right)} \]

Where:

• \( Q_k \) is the heat transfer rate, in watts (W).
• \( k \) is the thermal conductivity, in watts per kelvin-meter (W/°K-m).
• \( L \) is the length of the cylinder, in meters (m).
• \( T_i \) is the inside wall temperature, in kelvin (°K).
• \( T_o \) is the outside wall temperature, in kelvin (°K).
• \( r_i \) is the inside radius, in meters (m).
• \( r_o \) is the outside radius, in meters (m).