Question:easy

For heat transfer calculation in fins, if the Biot number is very small (\(\text{Bi} \lt 0.1\)) it implies

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Biot Number physical interpretation: - \(Bi \lt 0.1\): Conductive resistance is negligible. Temperature inside the cross-section is uniform. This justifies using the Lumped Parameter Capacity analysis for transient problems. - \(Bi \gt 0.1\): Internal temperature gradients are significant and cannot be ignored; spatial variations must be accounted for using Fourier equations.
Updated On: Jul 4, 2026
  • Higher convective resistance
  • High temperature gradient in the fin
  • Fin is infinitely long
  • Negligible internal conductive resistance
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The Correct Option is D

Solution and Explanation

A solid conducts heat within itself and also loses heat to the surrounding fluid at its surface, and the Biot number is simply a way of comparing which of these two steps is the bottleneck. Written as a resistance ratio, it is the internal conduction resistance divided by the external convection resistance. When this number works out to be less than 0.1, it tells us the conduction path inside the solid offers almost no resistance compared to how hard it is for heat to actually leave through the surface film. In practical terms, heat spreads through the solid almost instantly, and the slow step controlling the whole process is convection at the outer surface, not conduction inside. So a small Biot number simply means the internal conductive resistance can be treated as negligible, which is option 4.
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