The phase-lag concept in the wave theory of heat conduction is extended to
describe the thermal behavior of lumped systems. It is assumed that a phase
-lag exists between the convection heat flux from the lumped system and the
temperature difference between the lumped system and its surroundings. It
is found that the dimensionless delay time tau is an important parameter in
specifying the qualitative behavior of the lumped system. The phase-lag co
ncept has no significant effects on the thermal behavior of lumped systems
having tau < 1/4. In this case, the classical theory without delay can give
an accurate prediction for the system thermal behavior. On the other hand,
the phase-lag concept changes the quantitative and qualitative behavior of
systems having <tau> > 1/4 and these changes are enhanced as tau increases
. However, it is shown that the thermal behavior of systems having tau > 1/
4 violates the second law of thermodynamics. The physical reasoning for thi
s violation is explained. Also, the phase-lag concept is extended to descri
be the thermal behavior of composite system which consists of two domains e
ach is lumped at different temperature.