Final answer:
The Biot number is important in determining the mode of transient heat conduction, indicating the relationship between conductive resistance within an object and convective resistance on its surface.
Step-by-step explanation:
The Biot number is important in the mode of transient heat conduction. This dimensionless number helps in analyzing heat transfer problems where there is a combination of conduction within an object and convection (or radiation) on its surface. The Biot number is defined as the ratio of conductive resistance within an object to convective resistance across the object's boundary. A small Biot number indicates that the temperature gradient within the object is small compared to the temperature difference between the object's surface and its surroundings, which simplifies the analysis by treating the object's temperature as uniform. Conversely, a large Biot number suggests that temperature gradients within the object cannot be ignored.