The phase-lag concept in the thermal behavior of lumped systems

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.