Super-transport of energy in ultra-short processes: implications to heat transfer, fluid dynamics and quantum mechanics

Abstract

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 transfer. 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 our Universe.