Question

In transient heat conduction, the lumped capacitance method is valid only when:

• A. Internal conduction resistance is greater than surface convection resistance
• B. Biot number is less than 0.1
• C. Fourier number is less than 1
• D. Thermal diffusivity is very high

Hint:

If Bi < 0.1, object can be treated as thermally lumped (no internal gradient).

Answer 1

The Correct Option is B

Concept: Lumped capacitance method assumes: \[ \text{temperature inside object is uniform} \] This is valid only when internal resistance is negligible.

Step 1: Define Biot number.
\[ Bi = \frac{hL_c}{k} \] Where: - $h$ = convection coefficient - $L_c$ = characteristic length - $k$ = thermal conductivity

Step 2: Apply condition.
For lumped system: \[ Bi < 0.1 \]

Step 3: Physical meaning.
\[ \text{Internal resistance } \ll \text{ external resistance} \] So temperature remains uniform. Final Answer: \[ \text{Biot number < 0.1} \]