McGuire, J.H., 1954. THE SCALING OF DIMENSIONS IN HEAT CONDUCTION PROBLEMS. Fire Research Notes 94
This note investigates the relation between the growths of temperature in similar structures, of different sizes, heated under comparable conditions. It shows that the dimensions in which there is no component of heat flow play no part in the thermal problem and that, in the direction of heat flow, the times to attain any specified temperature at corresponding points vary as the square of the dimensional scales of the structures. The square law relation is shown to apply where the thermal properties of the component materials vary with temperature and where, with one exception, the effects of contained moisture are considered. Various other effects are also examined. The use of the B.S.476 time-temperature furnace curve in the conduct of fire-resistance tests precludes the application of the scaling relation to similar structures, since it requires time to be a scaled quantity. An empirical modification of the relation to avoid this difficulty, and the extension of the relation to similar structures of materials with different thermal constants, are described in two further notes.