Question:

Biot number is associated with

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  • Biot Number (Bi) = \(\frac{\text{Internal Conductive Resistance}}{\text{External Convective Resistance}} = \frac{hL_c}{k_s}\).
  • Used in transient heat conduction analysis.
  • \(Bi<0.1\) often indicates that lumped capacitance method can be used (uniform temperature within the object).
  • Analogous Biot numbers exist for mass transfer.
Updated On: Jun 12, 2025
  • Rheology of fluids
  • Mass transfer
  • Conduction
  • Heat transfer
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The Correct Option is D

Solution and Explanation

The Biot number is a dimensionless parameter in the field of heat transfer. It is used to compare the rate of heat conduction within an object to the rate of heat transfer across the object's boundary to its surroundings. The Biot number is significant because it helps determine whether the temperature distribution within an object can be assumed uniform, which simplifies analysis substantially.

The Biot number (\( Bi \)) is formulated as:

\( Bi = \frac{hL_c}{k} \)

where:

  • \( h \) is the convective heat transfer coefficient (W/m²·K).
  • \( L_c \) is the characteristic length, typically the volume of the object divided by its surface area (m).
  • \( k \) is the thermal conductivity of the object (W/m·K).

A Biot number much less than 1 indicates that the object is thermally thin relative to the resistance to heat flow in the surrounding fluid, and its temperature can be considered uniform. Conversely, a Biot number much greater than 1 indicates non-uniform temperature distribution, requiring detailed temperature analysis within the object.

Therefore, the Biot number is primarily associated with Heat Transfer.

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