Dottorato in MODELLI MATEMATICI PER L'INGEGNERIA, ELETTROMAGNETISMO E
NANOSCIENZE

Titolo della tesi: Diffusione anisotropa e ondulatoria del calore e Effetti termomagnetici e termoelettrici oscillanti autoindotti sui conduttori rotanti.

In this work I have developed a previous model presented at the 67th Course of International School of Quantum Electronics on Progress in Photoacoustic and photo thermal Phenomena hold in Erice in September 2023 aimed to the formulation of a dynamic generalization of the Tolman effect and of the Barnett effect. I have studied in particular the influence of rotation on heat transfer and on thermomagnetic and thermoelectric effects on metals exposed to harmonic heat source generated by chopped laser, formulating a wavelike anisotropic model of heat diffusion on rotating metallic disks. I have analyzed in the first Chapter the problem of transformation of the temperature of a moving body discussed initially by Planck and Einstein, inspired by the problem of the formulation of a relativistic theory of the black body, which stimulated then the search of a relativistic thermodynamic theory. I have then compared the different proposals present in the scientific literature of relativistic transformation of temperature outlining the role of some them for their prediction of heating and cooling effect consistent with the redshift and blueshift associated to the Doppler effect. I have then deepened in the second Chapter the two general models of heat diffusion of Fourier and of Cattaneo-Vernotte, analyzing the correspondent parabolic and hyperbolic thermal fields and comparing two different thermal longitudinal Doppler shift predicted in two recent papers. I have then analyzed in the third Chapter the conventional thermomagnetic and thermoelectric effects valid on materials at rest and exposed to stationary heat source. I have discussed then in the fourth Chapter the effect of inertial forces on a rotating metal analyzing the Stewart-Tolman effect, the Barnett effect and the Schiff-Irvine Electrodynamic theory, and the Zel’dovich effect of rotational superradiance, outlining the necessity to generalize these giroelectric effects and gyromagnetic effects taking in account thermodynamic aspects. I have developed therefore in the last Chapter a dynamic generalization of the Barnett effect and of thermal Hall effect, showing that they imply an anisotropic wave like heat diffusion law based on a temperature field dependent thermal conductivity tensor . Assuming the validity of a thermal analogue of the rotational superradiance effect discovered by Zel’dovich in 1971, illustrated in the fourth Chapter, in accordance with a paper published recently by the author, we deduce a selfinduced dynamic magnetic Thomson cooling-heating effect. We showed with some simple quantitative estimates that it could be amplified by modulating the Barnett effective magnetic field, that is tuning the angular velocity of the rotating disk esxposed to the laser beam. We deduce a non linear telegraphist equation satisfied by the thermal fields generated by the laser source on the rotating disks showing that they have variable phase velocity, helicoidal wavefronts and rotational Doppler frequency shift. We outlined the relevance of this effect for enhancing the dynamic Thomson effect, suggesting that it could be used as a signature of oscillating magnetic transition induced by rotation and exploited for thermal management and spincaloritronics. Finally we analyze critically our proposal suggesting a possible way to generalize it in a relativistic way, taking in account the mathematical relation between non linear telegraph equation and Klein-Gordon equation. We hope that our new model could be applied to describe non-Fourier heat conduction in accelerated metamaterials implementing a new approach to thermal management by coupling thermal conduction to tunable infrared emission of rotating nanomaterials.