c) A composite wall is composed of 5 sections as represented in the below diagram. The temperature at the left side is $25^{\circ} \mathrm{C}$ and at the right side is $90^{\circ} \mathrm{C}$ and $\mathrm{h}=15 \mathrm{~W} / \mathrm{m} 2 \mathrm{~K}$ on both sides. The coefficient of heat transfer are $k_{1}=k_{3}=80 \mathrm{~W} / \mathrm{mK}, k_{2}=120 \mathrm{~W} / \mathrm{mK}, \mathrm{k}_{4}=100 \mathrm{~W} / \mathrm{mK}$, and $\mathrm{k}_{\mathrm{s}}=150 \mathrm{~W} / \mathrm{mK}$. Determine:
i. The total thermal resistance,
ii. Heat transfer rate through the composite.
Answer
\(\boxed{Q = -354.55 \, \text{W}}\)
Step 1 ：Calculate the total thermal resistance: \(R_{total} = R_1 + R_2 + R_3 + R_4 + R_s + 2R_{conv} = \frac{L_1}{k_1} + \frac{L_2}{k_2} + \frac{L_3}{k_3} + \frac{L_4}{k_4} + \frac{L_s}{k_s} + \frac{2}{h}\)
Step 2 ：Plug in the given values: \(R_{total} = \frac{L_1}{80} + \frac{L_2}{120} + \frac{L_3}{80} + \frac{L_4}{100} + \frac{L_s}{150} + \frac{2}{15}\)
Step 3 ：Calculate the heat transfer rate: \(Q = \frac{T_1 - T_2}{R_{total}}\)
Step 4 ：Plug in the given temperatures: \(Q = \frac{25 - 90}{R_{total}}\)
Step 5 ：Solve for Q: \(Q = -354.55 \, \text{W}\)
Step 6 ：\(\boxed{Q = -354.55 \, \text{W}}\)
