Topic: Heat Transfer
A hot metal sphere is suddenly immersed in a liquid bath at a much lower temperature than the hot metal sphere. Under which of the following conditions, the temperature gradients in the metal sphere can be assumed to be neglected during the cooling of the sphere?
- A. Nusselt number >> 1
- B. Biot number >> 1
- C. Biot number << 1
- D. Nusselt number << 1
Answer: C. Biot number << 1
Explanation: The assumption of negligible internal temperature gradients characterizes lumped system analysis. This is valid when the internal conductive resistance is much smaller than the external convective resistance, which implies that the Biot number ($Bi = \frac{hL_c}{k}$) is very small, typically $Bi < 0.1$ ($Bi \ll 1$).