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(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

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

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(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}$

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