Paper presented at the 6th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 30 June - 2 July, 2008.
The paradox of instantaneous propagation of energy is
intrinsic to the classical models of energy transport. This
paradox becomes well-pronounced during ultra-short processes.
To remove the paradox, phase-lagged models of energy transport
have been proposed. The analysis of the solutions to the phaselagged
energy equations suggests that when the characteristic
time of the process is much less than the lag time, the wave
mode of transport becomes the main mechanism of energy
In ultra-short heat transfer processes, the wave transport is
manifested by an apparent increase (three-four orders of
magnitude) of the thermal conductivity of the transporting
medium. In viscous fluid flow, in addition, an apparent decrease
of viscosity occurs, so that the liquid behaves as superfluid even
at high temperatures.
It has been demonstrated that the lag time is inversely
proportional to the temperature. Thus the life span of the supertransport
phenomena should significantly increase at low
temperatures, which is consistent with observing superfluids at
lower temperatures for long periods of time.
From the quantum physics standpoint, the energy
transporting waves can be viewed as narrow wave packets,
whose wave functions describe the superfluid state of the liquid.
This may provide an alternative explanation of the phenomenon
of superfluidity: the Bose-Einstein condensation may not be
needed for superfluidity to occur.
From the phase-lagged model of energy transport, it follows
that the Schrödinger equation is but a zero-time-lag
approximation. Hence, the phase-lagged Schrödinger equation
must be used to describe ultra-short quantum interactions. It is
suggested that the finiteness of Planck’s constant and the
finiteness of the speed of energy propagation are not
independent. This circumstance may shed some light on the
understanding of processes that took place in the beginning of