 Lumped thermal model

A lumped thermal model assigns one representative temperature and heat capacity to each region of an apparatus. For a single body of heat capacity $C$ connected to a bath by thermal conductance $G$, with supplied power $P$, an elementary balance isThe model stores internal energy in the body and treats exchange through a thermal resistance, leaving internal spatial temperature gradients unresolved.

A small solid specimen with rapid internal equilibration can approximate this behavior. A constant heating step gives a final rise $P/G$ and a thermal time constant $C/G$ when $C$ and $G$ are constant. Comparing thermometers at different positions tests the assumption of nearly uniform specimen temperature. If appreciable internal gradients persist, the apparatus needs several coupled thermal regions or a spatial heat equation model. Fitting a single exponential is useful only after this physical approximation has been checked.