Space average and interference in heat conductivity equations

Plane waves' interference and space averages play a significant role in the derivation of some vibration conductivity equations that are becoming more and more popular in modeling vibroacoustic problems. Particularly the thermal approach and the modified heat conductivity equations are here considered with the aim of establishing similarities and/or differences between them and stating relevant consequences. It is shown by formal developments that the thermal equation is obtained under the double assumption of performing appropriate space averages and neglecting the waves' interference while the modified heat equation does not need, in principle, any of these conditions. It is discussed, however, that in practical applications the conditions of validity of both approaches are quite similar.