Rankers Physics

Heat Transfer - Conduction and Convection: Practice Problem & Solution

Five rods of same dimensions are arranged as shown in the figure. They have thermal conductivities K1, K2, K3, K4 and K5. When points A and C are maintained at different temperature, no heat flows through the central rod if Heat Transfer - Conduction and Convection diagram: Five rods of same dimensions are arranged as
K1 = K4 and K2 = K3
K1K4 = K2K3
K1K2 = K3K4
\frac{K_{1}}{K_{4}}=\frac{K_{2}}{K_{3}}

Solution Explained:

To solve this problem, we apply the core principles of Heat Transfer - Conduction and Convection. Understanding the underlying formula is key to arriving at the correct answer below:

No heat flows through the central rod \(K_5\) if the system is balanced like a Wheatstone bridge. The condition for this is:

\[
\frac{K_1}{K_2} = \frac{K_3}{K_4}
\]

This ensures that the temperature difference between points B and D is zero, preventing any heat flow through \(K_5\).

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