On second sound at the critical temperature (original) (raw)

Nonlinearity and memory effects in low temperature heat propagation

Archives of Mechanics, 2000

In order to account for low temperature heat propagation phenomena in crystals of sodium fluoride and bismuth, we employ a thermodynamic model for rigid materials involving a vector-field internal state variable. The model is either wavelike or diffusive, depending on the temperature regime considered.

Nonlinearity and memory efiects in low temperature heat propagation

2000

In order to account for low temperature heat propagation phenomena in crystals of sodium ∞uoride and bismuth, we employ a thermodynamic model for rigid ma- terials involving a vector-fleld internal state variable. The model is either wavelike or difiusive, depending on the temperature regime considered.

Sources of Finite Speed Temperature Propagation

Journal of Non-Equilibrium Thermodynamics

The relation between heat flux and temperature gradient has been considered as a constitutive structure or as a balance law in different approaches. Both views may allow a description of heat conduction characterized by finite speed propagation of temperature disturbances. Such a result, which overcomes Fourier’s drawback of infinite speed propagation, can be obtained also by considering insufficient the representation of a conductor, even when it is considered to be rigid, rather than the sole relation between heat flux and temperature gradient. We comment this last view and describe the intersection with previous proposals. Eventually, we show how under Fourier’s law we can have traveling-wave-type temperature propagation when thermal microstructures are accounted for.

Second sound speed in a crystal of NaF at low temperature

Archives of Mechanics, 1997

WE DERIVE a physically justifiable model of heat conduction for rigid heat conductors based on a recent approach involving the gradient generalization of an internal state variable. The model accounts for observable phenomena in solid dielectric crystals, related to wave-like conduction of heat in certain ranges of low temperatures and a rapid decay of the speed of thermal waves close to a temperature value V λ , at which the conductivity of the material reaches a peak.

Some effects of phase transitions on heat propagation

Archives of Mechanics, 2002

We consider phase transitions in solids due to heat propagating through crystalline materials at low temperatures. These are considered in a steady state context where, at the transition temperature, the specific heat becomes singular and the heat conductivity has a maximum. Several consequences are found for the heat capacity having finite or infinite jump discontinuities.

Unphysical Behaviors of Heat Conduction

In the previous studies, the traditional thermal wave model and dual-phase-lag model had been verified that they could present unphysical behaviors due to sudden heating or cooling on the boundaries of the body and heat source within the body, respectively. Furthermore, some researchers claimed that the thermal wave model is not coincident with the theory of relativity. This thesis studied six different well-known mathematical models of heat conduction by the theory of relativity and the laws of thermodynamics. It also investigated that whether the models are valid according to the theory of relativity and the second law of thermodynamics. In addition, it examined the thermal behaviors of thermal wave model and the dual-phase-lag model in a finite slab owning to the step function effects on the boundary and heat source inside the body to see whether they exist unphysical behaviors. It was demonstrated in this study that the traditional thermal wave model and the dual-phase-lag model will violate the second law of thermodynamics under some circumstances. Even if one considers the relativistic models, they sometimes follow the laws of the thermodynamics under some circumstance. For example, if the rotational speed of virtual coordinate is greater than the speed of heat waves, the solutions of temperature and entropy production rate of the relativistic thermal wave model with instantaneous heating and cooling boundary can satisfy the laws of thermodynamics.