Under which condition is the lumped solution (uniform temperature throughout the body during transient heat transfer) assumed valid?

• A. Bi < 0.1
• B. Bi > 1
• C. Bi = 0.5
• D. Bi between 0.1 and 1

Answer: (A)

Uniform temperature inside during a transient heat transfer is a good approximation when internal conduction is much faster than external convection. This is quantified by the Biot number Bi = hL/k. If Bi is well below 1, especially Bi < 0.1, internal temperature gradients are negligible and the body can be treated as a lumped capacitance with a single temperature that changes exponentially toward the ambient. The lumped model then simplifies the energy balance to a straightforward form using the body's total heat capacity, without solving the full conduction equation inside.

So Bi < 0.1 is the condition that makes the lumped solution valid. Larger Bi values (Bi > 1 or around 0.5, or even between 0.1 and 1) indicate significant internal temperature gradients, which invalidate the lumped assumption.