ASYMPTOTIC ANALYSIS OF THE LUMPED-CAPACITANCE APPROXIMATION

The lumped-capacitance (LC) approximation for solid bodies suddenly exposed to constant-property environments is analyzed. A mathematical derivation of the LC approximation is presented for bodies of an arbitrary shape. A Biot number is treated as a small parameter, and asymptotic analyses of the parabolic heat equation are developed in terms of this parameter. The LC approximation is recovered to leading order, while first-order solutions include spatial temperature variations and provide error estimates involved with using the LC approximation. It is also shown that the LC approximation may sometimes be accurate when conventionally-defined Biot numbers are of order unity or greater.