A cylinder of radius R is surrounded by a cyl | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) When heat flows along the length of the cylinders,the two cylinders act as parallel conductors of heat.For parallel combination,the equivalent the

Vedclass · Accepted Answer

$\frac{K_1 + 3K_2}{4}$

Vedclass · Answer

(D) When heat flows along the length of the cylinders,the two cylinders act as parallel conductors of heat.For parallel combination,the equivalent thermal conductance is the sum of individual thermal conductances.The thermal conductance is given by $C = \frac{KA}{L}$,where $K$ is thermal conductivity,$A$ is the cross-sectional area,and $L$ is the length.For the inner cylinder,area $A_1 = \pi R^2$.For the outer cylindrical shell,area $A_2 = \pi (2R)^2 - \pi R^2 = 3\pi R^2$.The total area of the system is $A = A_1 + A_2 = 4\pi R^2$.Equating the total conductance to the sum of individual conductances:$\frac{K_{eff} A}{L} = \frac{K_1 A_1}{L} + \frac{K_2 A_2}{L}$$K_{eff} (4\pi R^2) = K_1 (\pi R^2) + K_2 (3\pi R^2)$$4 K_{eff} = K_1 + 3 K_2$$K_{eff} = \frac{K_1 + 3 K_2}{4}$

Similar Questions

Two rods of same length and material transfer a given amount of heat in $12 \ s$,when they are joined end to end. But when they are joined along their lengths (parallel combination),then they will transfer the same amount of heat under the same conditions in time $t = \dots \ s$.

Two walls have thicknesses $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$,respectively. In the steady state,the temperatures of the outer surfaces are $T_1$ and $T_2$. What is the temperature at the interface of the two walls?

Five wires each of cross-sectional area $A$ and length $l$ are combined as shown. The thermal conductivity of copper and steel are $k_1$ and $k_2$ respectively. The equivalent thermal resistance between $A$ and $C$ is

Two identical square metal rods are welded end-to-end as shown in figure $(a)$. $20 \text{ calories}$ of heat flows through them in $4 \text{ minutes}$. If they are joined as shown in figure $(b)$,the same amount of heat will flow in ...... minutes.

Vedclass Test Series

Exam Paper Generator

Online Exam Module