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A composite slab is made of two materials with thermal conductivities K and 2K and thicknesses x and 4x respectively, placed in series. The outer surfaces are at temperatures T2 and T1 (T2 > T1). In steady state the heat-flow rate is written as f * A*(T2 - T1)*K / x. Find f.

1. 1
2. 1/2
3. 2/3
4. 1/3

Correct answer: 1/3

Solution

The series thermal resistance is x/(KA) + 2x/(KA) = 3x/(KA), so the heat rate equals (1/3)*A(T2-T1)K/x, giving f = 1/3.

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