Question

Biot number is associated with

• A. Rheology of fluids
• B. Mass transfer
• C. Conduction
• D. Heat transfer

Hint:

• 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.

Answer 1

The Correct Option is D

The Biot number (Bi) is a dimensionless number used in heat transfer calculations. It represents the ratio of the internal thermal resistance of a solid body to its external thermal resistance (convective resistance at the surface). \[ Bi = \frac{hL_c}{k_s} \] where:

• \(h\) is the convective heat transfer coefficient (W/m\(^2\)K) between the solid surface and the surrounding fluid.
• \(L_c\) is a characteristic length of the solid body (e.g., Volume/Surface Area).
• \(k_s\) is the thermal conductivity of the solid material (W/mK).

The Biot number is used to determine if the temperature within a solid body will vary significantly in space during transient heat conduction processes (lumped capacitance analysis).

• If \(Bi \ll 0.1\), internal resistance is negligible compared to surface resistance, and the temperature within the body can be considered uniform (lumped system analysis is valid).
• If \(Bi \gg 0.1\), internal temperature gradients are significant.

Therefore, the Biot number is associated with heat transfer, specifically transient conduction within a solid coupled with convection at its surface. (a) Rheology of fluids: Deals with flow and deformation (e.g., Reynolds number, Deborah number). (b) Mass transfer: Analogous dimensionless numbers exist in mass transfer (e.g., Sherwood number, mass transfer Biot number), but the "Biot number" unqualified usually refers to heat transfer. (c) Conduction: Biot number involves both conduction (within the solid, related to \(k_s\)) and convection (at the surface, related to \(h\)), but it characterizes the relative importance of these in transient heat transfer. Thus, Biot number is primarily associated with heat transfer. \[ \boxed{\text{Heat transfer}} \]