Federico Vázquez

Optimization of Two-Stage Peltier Modules: Structure and Exergetic Efficiency

In this paper we undertake the theoretical analysis of a two-stage semiconductor thermoelectric module (TEM) which contains an arbitrary and different number of thermocouples, n1 and n2, in each stage (pyramid-styled TEM). The analysis is based on a dimensionless entropy balance set of equations. We study the effects of n1 and n2, the flowing electric currents through each stage, the applied temperatures and the thermoelectric properties of the semiconductor materials on the exergetic efficiency. Our main result implies that the electric currents flowing in each stage must necessarily be different with a ratio about 4.3 if the best thermal performance and the highest temperature difference possible between the cold and hot side of the device are pursued. This fact had not been pointed out before for pyramid-styled two stage TEM. The ratio n1/n2 should be about 8.

Size effects on heat transport in small systems: Dynamical phase transition from diffusive to ballistic regime

The size effects on heat conduction in small systems are analyzed by using irreversible thermodynamics and Boltzmann equation derived heat transport models. The system’s size dependent group velocity of heat waves and thermal response of the system are studied in the diffusive-ballistic transition of heat transport. A critical range of values for the Knudsen number is found which features a dynamic phase transition between the diffusive and ballistic regimes. The transition system’s sizes range from 10 to 380 μm.

Thermodynamic characterization of the diffusive transport to wave propagation transition in heat conducting thin films

In this paper, we undertake the thermodynamical analysis of the diffusive transport to wave propagation transition in heat conducting thin films. Several constitutive equations have been conceived to describe heat transport but most fail at the nanometric length scales, where size effects must be taken into account or at time scales in the order of magnitude of heat carriers relaxation time, as for example when a laser pulse is applied to the system. The analysis is based on Jeffreys model since it allows a jointed description of Fourier and Cattaneo heat conduction mechanisms. Jeffreys model is complemented with a size dependent heat conductivity derived from Boltzmann transport equation. We study the diffusive transport to wave propagation transition in terms of the group and phase velocity of propagating modes, the systems effective thermodynamic susceptibility, the statistical properties of heat flux fluctuations, and the entropy produced in a thin heat conducting film. Jeffreys model predicts a k...

Viscoelastic Effects on the Entropy Production in Oscillatory Flow between Parallel Plates with Convective Cooling

The heat transfer problem of a zero-mean oscillatory flow of a Maxwell fluid between infinite parallel plates with boundary conditions of the third kind is considered. With these conditions, the amount of heat entering or leaving the system depends on the external temperature as well as on the convective heat transfer coefficient. The local and global time-averaged entropy production are computed, and the consequences of convective cooling of the plates are also assessed. It is found that the global entropy production is a minimum for certain suitable combination of the physical parameters. For a discrete set of values of the oscillatory Reynolds number, the extracted heat from one of the plates shows maxima.

Extensive study of shape and surface structure formation in the mercury beating heart system.

A phenomenological study of the mercury beating heart system in a three electrode electrochemical cell configuration forced with a harmonic perturbation is presented. The system is controlled via a potentiostat, where the mercury drop is electrically connected to a platinum wire and acts as the working electrode. This configuration exhibits geometrical shapes and complex surface structures when a harmonic signal is superimposed to the working electrode potential. This study involves a wide range of frequencies and amplitudes of the forcing signal. Differents levels of structure complexity are observed as a function of the parameters of the applied perturbation. At certain amplitudes and frequencies, rotational behavior is also observed.

Coarse graining from coarse-grained descriptions.

We present a generalization of Zwanzigsmethod of projection operators to the case where the underlying dynamics is not deterministic. The method allows us to perform a coarse graining of an already coarse–grained level of description in which fluctuations are important. The initial level of description is described by a Fokker–Planck equation and, under suitable approximations, the final slower level of description is also described by a Fokker–Planck equation. We illustrate the method for the simple case of the diffusion of colloidal particles at two levels of descriptions.

Classical field theory and stochastic properties of hyperbolic equations of dissipative processes

The set of damped hyperbolic transport equations is one of the wide class of equations for the description of dissipative physical processes. Deeper understanding into the structure of these physical phenomena can be obtained with the help of the Hamiltonian formalism. In the present paper, we show that the Hamilton–Lagrange formalism can be constructed for these kinds of transport equations. We obtain the Hamiltonian, the canonically conjugate quantities and the Poisson-bracket expressions for them. With this formalism we analyze the statistical properties of path fluctuations in the new conjugated thermodynamic variable space. We show that for short times the stochastic behavior under this new scope obeys the Chapman–Kolmogorov relationship.

Fluctuating Hydrodynamics and Irreversible Thermodynamics

Abstract The equilibrium Rayleigh-Brillouin spectrum for a Maxwell fluid in which heat conduction is governed by the classical Fourier law is computed. This is done by using fluctuating hydrodynamics and by the alternative procedure used by Mountain. It is found that both calculations render the same results only if the fluctuation-dissipation relations in the former are the ones prescribed by Landau and Lifshitz for the case where a dispersive dissipation coefficient is present. This result brings up the question of whether extended irreversible thermodynamics is the proper underlying nonequilibrium thermodynamic framework for the Maxwell fluid. It also suggests that at least the version of fluctuating hydrodynamics based on extended irreversible thermodynamics as introduced by Jou and Casas-Vázquez many years ago [18] must be revised, since it leads to a different form for the fluctuation-dissipation relations.

Path integral approach to fluctuations in relativistic transport

In this paper we analyze the fluctuations in an approximation to relativistic heat transport theory from a path integral approach. We start with a telegraphist type equation for the heat transport derived from a Meixner–Prigogine scheme and construct a classical variational principle for it. We use Hamiltonian-like function to obtain the transition probability between two different non-equilibrium states. We show that this probability obeys the Chapman–Kolmogorov equation.

Nonlinear Heat Waves In Extended Irreversible Thermodynamics

A variational approach to nonlinear heat waves in solids within extended irreversible thermodynamics is presented. The formalism gives a nonlinear in time evolution equation for the heat flux in a rigid solid which, together with the energy balance, describes in closed form the nonequilibrium processes which occur in a time scale comparable to the relaxation time of the heat flux. Well known results of heat transport are recovered in the appropriate limits by the structure of the equation which also allows for couplings not considered up until now whose consequences remain to be assessed.