4. Composite Wall - Flat Wall


\[Q = \frac{T_{\infty,1}-T_{s,1}}{R_1} = \frac{T_{s,1}-T_{2}}{R_2} = \frac{T_{2}-T_{s,2}}{R_3} = \frac{T_{s,2}-T_{\infty,2}}{R_4}\] where \[R_1 = \frac{1}{h_1A} \qquad R_2 = \frac{L_1}{k_1A} \qquad R_3=\frac{L_2}{k_2A} \qquad R_4 = \frac{1}{h_2A}\]

Adding the numerators and denominators separately, we get \[Q = \frac{T_{\infty_1}-T_{\infty,2}}{R_1+R_2+R_3+R_4}\]

From the rule of proportions, \[\frac{a}{b} = \frac{c}{d} \qquad \Longrightarrow \quad \frac{a}{b}=\frac{a+c}{b+d} = \frac{a-c}{b-d}\]