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A slender rod of length L, diameter d (L >> d) and thermal conductivity k1 is joined with another rod of identical dimensions, but of thermal conductivity k2, to form a composite cylindrical rod of length 2L. The heat transfer in radial direction and contact resistance are negligible. The effective thermal conductivity of the composite rod is

1. k1 + k2
2. √(k1k2)
3. (k1k2)/(k1 + k2)
4. (2k1k2)/(k1 + k2)

Correct answer: (2k1k2)/(k1 + k2)

Solution

The effective thermal conductivity of two rods in series is determined by the formula for thermal resistances, which leads to the result of (2k1k2)/(k1 + k2). This accounts for the combined effect of both materials, reflecting how they share the thermal load.

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