Answer:
Let's calculate the values step by step.
Given:
- \( k = 50 \, \text{W/mK} \)
- \( h = 30,000 \, \text{W/m}^2\text{K} \)
- \( T_{\text{in}} = 15 \, \text{°C} \)
- \( T_{\text{out}} = -10 \, \text{°C} \)
- \( D_{\text{out}} = 104 \, \text{mm} \)
- \( \text{Wall thickness} = 2 \, \text{mm} \)
First, calculate \( D_{\text{in}} \):
\[ D_{\text{in}} = D_{\text{out}} - 2 \times \text{Wall thickness} \]
\[ D_{\text{in}} = 104 \, \text{mm} - 2 \times 2 \, \text{mm} = 100 \, \text{mm} \]
Convert \( D_{\text{in}} \) to meters: \( D_{\text{in}} = 0.1 \, \text{m} \)
Now, calculate \( Q_{\text{cond}} \):
\[ Q_{\text{cond}} = \frac{2\pi k L (T_{\text{in}} - T_{\text{out}})}{\ln\left(\frac{D_{\text{out}}}{D_{\text{in}}}\right)} \]
\[ Q_{\text{cond}} = \frac{2 \times \pi \times 50 \times L \times (15 - (-10))}{\ln\left(\frac{0.104}{0.1}\right)} \]
Now, calculate \( Q_{\text{conv}} \):
\[ Q_{\text{conv}} = h \times 2\pi L (T_{\text{in}} - T_{\text{out}}) \]
\[ Q_{\text{conv}} = 30,000 \times 2 \times \pi \times L \times (15 - (-10)) \]
Please provide the length (\( L \)) of the pipe so that we can calculate the numerical values.
