5. Composite Hollow Cylinder




\[Q = \frac{T_{\infty_1}-T_{\infty,2}}{R_1+R_2+R_3+R_4}\] where \[R_1 = \frac{1}{h_12\pi r_1H} \quad \ R_2 = \frac{\ln(r_2/r_1)}{2\pi k_1H} \quad \ R_3=\frac{\ln(r_3/r_2)}{2\pi k_2H} \quad \ R_4 = \frac{1}{h_22\pi r_2H}\]




At steady state, the temperature variation in a plane wall, made of two different solids I and II is shown below:

Then, the thermal conductivity of material I

1997-2.09

(a) is smaller than that of II
(b) is greater than that of II
(c) is equal to that of II
(d) can be greater than or smaller than that of II

(a) Explanation:  \(q = k\, \dfrac{\Delta T}{\Delta x} = k\times \text{slope} = \text{const.}\) Here, \(\text{slope}_{\text{I}} > \text{slope}_{\text{II}}\). Therefore \(k_{\text{I}} < k_{\text{II}}\).