Heat Transfer - Conduction and Convection

Question 11: easy

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

1. K1 = K4 and K2 = K3

2. K1K4 = K2K3

3. K1K2 = K3K4

4. \frac{K_{1}}{K_{4}}=\frac{K_{2}}{K_{3}}

View Answer

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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