Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K₁ and K₂ . The thermal conductivity of the composite rod will be : 1. 3(K₁+K₂)/2 2. K₁+K₂ 3. 2(K₁+K₂) 4. K₁+K₂/2

Topic: Heat transfer: conduction, convection, radiation· Properties of Solids and Liquids

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K_1 and K_2. The thermal conductivity of the composite rod will be :

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are \(K_1\) and \(K_2\). The thermal conductivity of the composite rod will be :

composite rod, A (K1) above B (K2), ends T1 and T2, length d

1. \(\frac{3(K_1+K_2)}{2}\)

2. \(K_1+K_2\)

3. \(2(K_1+K_2)\)

4. \(\frac{K_1+K_2}{2}\)

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Answer: 4. \(\frac{K_1+K_2}{2}\)

Key idea: the two rods are side by side, so heat flows through them in parallel, and the conductances add.

Let each rod have area \(A\). Total heat flow: \(\dfrac{K_1A\Delta T}{d}+\dfrac{K_2A\Delta T}{d}=\dfrac{K(2A)\Delta T}{d}\).

So \(K=\dfrac{K_1+K_2}{2}\) (both rods having equal cross-section, as drawn).

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K_1 and K_2. The thermal conductivity of the composite rod will be :

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