Subtopic: Biot number validity for lumped capacity
Question Statement:
The lumped capacity (lumped thermal capacitance) assumption of spatially uniform temperature inside a solid body during transient cooling/heating is strictly valid when the Biot number satisfies:
Options:
(A) $Bi = \frac{h L_c}{k} < 0.1$
(B) $Bi > 10.0$
(C) $Bi = 1.0$
(D) $Bi \to \infty$
Answer Key:
A
Step-by-Step Solution & Explanation
The Biot number $Bi = \frac{h L_c}{k_{solid}}$ compares internal conductive thermal resistance to external convective boundary resistance. When $Bi < 0.1$, internal thermal gradients are under $5\%$, validating the lumped isothermal assumption.