Subtopic: Transient heat transfer in simple geometry
Question Statement:
In the transient cooling of solid food items, the lumped capacitance analysis method is physically valid and introduces less than $5\%$ error only when the Biot number ($Bi = h L_c / k$) satisfies:
Options:
(A) $Bi < 0.10$
(B) $Bi > 10.0$
(C) $0.50 < Bi < 1.0$
(D) $Bi = \infty$
Answer Key:
A
Step-by-Step Solution & Explanation
The Biot number $Bi = \frac{h L_c}{k}$ represents the ratio of conductive resistance within the solid to convective boundary layer resistance at the surface. When $Bi < 0.10$, internal resistance is negligible, spatial temperature gradients inside the body are virtually flat, and the lumped system approximation holds.