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 :\(\boxed{Q = -354.55 \, \text{W}}\)