In order to use the lumped capacitance model to evaluate transient heat transfer, the Biot number must be:

The lumped capacitance model is a simplified method used in heat transfer analysis, particularly for transient conditions. This model assumes that the temperature within the object is uniform, which is a valid assumption only when the temperature gradient within the object is negligible compared to the convection heat transfer at its surface.

The Biot number (Bi) is a dimensionless quantity defined as the ratio of the thermal resistance within a body to the thermal resistance at its surface. For the lumped capacitance model to be applicable, the Biot number must be less than 0.1. This criterion ensures that the conductive resistance within the object is small compared to the convective resistance at its surface, thus allowing the assumption of uniform temperature to hold true.

When the Biot number is less than 0.1, it indicates that heat can be conducted through the object quickly enough that the entire volume can be assumed to respond uniformly to heat transfer operations. This results in accurate transient temperature predictions across the entire body. If the Biot number were to exceed 0.1, the temperature gradient within the object may become significant, leading to inaccuracies in the lumped capacitance model since it would no longer be reasonable to assume a uniform temperature throughout the body.