Question
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
The correct answer is
\(\frac{{2{k_1}{k_2}}}{{{k_1} + {k_2}}}\)
Thermal resistances add in series: \(\frac{2L}{k_{\rm eff}A}=\frac{L}{k_1A}+\frac{L}{k_2A}\). Thus \(k_{\rm eff}=\frac{2k_1k_2}{k_1+k_2}\), the harmonic mean of k₁ and k₂.
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Important Questions from Fourier Law and Thermal Conductivity
Which of the following substances has the minimum value of thermal conductivity ?
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The SI unit of Thermal Conductivity is
Which of the following has max. value of thermal conductivity?
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