Question

In unsteady heat transfer,.......... number is defined as internal resistance to heat transfer by conduction divided by the surface resistance to heat transfer.

• A. Biot
• B. Fourier
• C. Prandtl
• D. Reynold

Hint:

Low Biot ($<$ 0.1) means the body is a "good conductor" compared to its surroundings, allowing you to use simple Lumped Analysis. High Biot means the core stays hot/cold longer than the surface.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks to identify the dimensionless number that represents the ratio of internal conductive resistance within a solid to the external convective (surface) resistance during transient (unsteady) heat transfer.
Key Formula or Approach: The Biot number (\(Bi\)) is calculated as: \[ Bi = \frac{h L_c}{k_s} \] Where \(h\) is the surface heat transfer coefficient, \(L_c\) is characteristic length, and \(k_s\) is the thermal conductivity of the solid.

Step 2: Detailed Explanation:

• Unsteady state heat transfer occurs when the temperature at any point within a system changes with time, such as during the cooling of a hot fruit or the freezing of a meat patty.

• To determine how temperature profiles develop, we analyze two types of resistance: internal resistance offered by the solid itself (conductive) and external resistance offered by the surrounding fluid (convective).

• The Biot number quantifies this relationship. If \(Bi < 0.1\), the internal resistance is negligible, and we can assume the temperature inside the solid is uniform at any instant (Lumped Heat Capacity analysis).

• If \(Bi > 0.1\), there are significant temperature gradients within the solid, and more complex methods (like Heisler charts) must be used.

• Other numbers: Fourier number (\(Fo\)) represents dimensionless time. Prandtl number (\(Pr\)) relates momentum diffusivity to thermal diffusivity in fluids. Reynold number (\(Re\)) relates to fluid flow regimes.

• Thus, the Biot number is the correct dimensionless group representing the ratio of internal to surface resistance.

Step 3: Final Answer:
The Biot number defines the ratio of internal conductive resistance to surface convective resistance.