Stages in the transient cooling of a slab

The classical solutions to the one dimensional transient heat flow situation are examined and criteria are set up to map stages in the cooling process in a parallel sided slab following step changes at the exposed surface. The temperature [theta], at a point within the slab, undergoes a perceptible deviation from the undisturbed state, and from the state determined by cooling from the nearer side alone, at times [zeta]0 (the Fourier number) found from a relation of type in the appropriate progressive wave solution. Cooling becomes virtually exponential at a time [zeta]0 when for the first term in the standing wave solution equals the sum of the higher terms. The response times are conveniently expressed in terms of [zeta]0, [zeta]0B or [zeta]0B2 (B is the Biot number) according to the model involved. Examples are given illustrating these results in a building context.