Question

........ expresses the relative importance of the thermal resistance of a body to that of the convection resistance at its surface.

• A. Nusselt Number
• B. Biot Number
• C. Prandtl Number
• D. Reynold's Number

Hint:

To avoid confusion: Biot number (\(Bi\)) uses the thermal conductivity of the solid (\(k_s\)), whereas Nusselt number (\(Nu\)) uses the thermal conductivity of the fluid (\(k_f\)).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Dimensionless numbers are widely used in heat transfer alysis to scale and simplify complex transport phenome.
When alyzing transient heat conduction within a solid body subjected to exterl convection, it is essential to determine whether the temperature inside the solid remains uniform or varies significantly with position.
Key Formula or Approach:
The Biot number (\(Bi\)) is defined mathematically as the ratio of interl thermal resistance to conduction to the exterl thermal resistance to convection:
\[ Bi = \frac{\text{Interl conductive resistance within the solid}}{\text{Exterl convective resistance at the surface}} \]
\[ Bi = \frac{\left(\frac{L_c}{k_s \cdot A}\right)}{\left(\frac{1}{h \cdot A}\right)} = \frac{h \cdot L_c}{k_s} \]
where:
- \(h\) is the convective heat transfer coefficient of the surrounding fluid.
- \(L_c\) is the characteristic length of the solid body, defined as volume divided by surface area (\(V/A_s\)).
- \(k_s\) is the thermal conductivity of the solid body itself.

Step 2: Detailed Explation:
The Biot number determines the temperature distribution profile inside a solid during heating or cooling:
- If the Biot number is very small (\(Bi < 0.1\)), the interl conductive resistance of the solid is negligible compared to the exterl convective resistance.
This indicates that heat diffuses rapidly within the solid, maintaining a nearly uniform temperature distribution.
Under this condition, the lumped parameter thermal alysis method can be applied to simplify calculations.
- If the Biot number is large (\(Bi > 0.1\)), the interl conductive resistance is significant, meaning noticeable temperature gradients exist inside the solid body.
- In contrast, the Nusselt number (\(Nu = \frac{h \cdot L}{k_f}\)) compares convective heat transfer to conductive heat transfer within the fluid phase.
- The Prandtl number represents the ratio of momentum diffusivity to thermal diffusivity.
- The Reynolds number represents the ratio of inertial forces to viscous forces in fluid flow.

Step 3: Fil Answer:
The dimensionless number representing the ratio of interl conductive resistance to exterl convective resistance is the Biot number.
Hence, the correct option is (B).