Ans: The lumped system analysis is valid when there is uniform temperature distribution throughout the body. To have uniform temperature distribution throughout the body the thermal resistance of the body to conduct heat must be negligible so that the heat is distributed evenly throughout the body.

To quantify this a non-dimensional number called Biot number is used which is a ratio of internal conductive resistance to convection resistance at the surface of the body. This number should be as small as possible.(close to zero preferred).

Biot Number, Bi = Conduction resistance within the body/ Convection resistance at the surface of the body

Bi = h.Lc/Ksolid

Hence, the lumped system analysis is exact when the Bi = 0 and approximate when Bi >0. The Bi = 0 when the thermal conductivity is infinite which is impossible in practical sense. Hence the Bi is always greater than 0 in reality and the lumped system analysis model gives more accurate results when the Biot number is close to zero or negligible.

Generally, lumped system analysis is applicable when Bi ≤ 0.1