186,217 research outputs found
Analysis of a Hyperbolic Heat Transfer Model in Blood-perfused Biological Tissues with Laser Heating
No full textThis paper proposes a hyperbolic heat transport model for a homogeneously perfused biological tissue irradiated by a laser beam. In particular, involving two local energy equations, one for the blood vessel and the other for the tissue, a non-Fourier-like heat equation is introduced and solved analytically using the Laplace transform method. The generalized hyperbolic model obtained is reduced to Pennes' heat transport equation in case the thermal delay time is zero and the solution obtained is in accordance with the numerical and experimental data existing in the literature. In addition, the achieved results also show that the effects of thermal relaxation and blood perfusion on temperature distribution are similar; indeed the highest temperature is expected when the delay time IR increases during tissue cooling. Finally, the consequences of the change in the values of the physical parameters characterizing the model are described and the effect of thermal relaxation on the temperature profile in the tissue during and after laser application is investigated
The Role of the Second Law of Thermodynamics in Continuum Physics: A Muschik and Ehrentraut Theorem Revisited
No full textIn continuum physics, constitutive equations model the material properties of physical systems. In those equations, material symmetry is taken into account by applying suitable representation theorems for symmetric and/or isotropic functions. Such mathematical representations must be in accordance with the second law of thermodynamics, which imposes that, in any thermodynamic process, the entropy production must be nonnegative. This requirement is fulfilled by assigning the constitutive equations in a form that guaranties that second law of thermodynamics is satisfied along arbitrary processes. Such an approach, in practice regards the second law of thermodynamics as a restriction on the constitutive equations, which must guarantee that any solution of the balance laws also satisfy the entropy inequality. This is a useful operative assumption, but not a consequence of general physical laws. Indeed, a different point of view, which regards the second law of thermodynamics as a restriction on the thermodynamic processes, i.e., on the solutions of the system of balance laws, is possible. This is tantamount to assuming that there are solutions of the balance laws that satisfy the entropy inequality, and solutions that do not satisfy it. In order to decide what is the correct approach, Muschik and Ehrentraut in 1996, postulated an amendment to the second law, which makes explicit the evident (but rather hidden) assumption that, in any point of the body, the entropy production is zero if, and only if, this point is a thermodynamic equilibrium. Then they proved that, given the amendment, the second law of thermodynamics is necessarily a restriction on the constitutive equations and not on the thermodynamic processes. In the present paper, we revisit their proof, lighting up some geometric aspects that were hidden in therein. Moreover, we propose an alternative formulation of the second law of thermodynamics, which incorporates the amendment. In this way we make this important result more intuitive and easily accessible to a wider audience
Thermal conductivity and enhanced thermoelectric efficiency of composition-graded Si cGe 1-c alloys
No full textWe explore the efficiency of a thermoelectric energy converter constituted by a Si/Ge nanowire of length L. A constitutive equation of thermal conductivity as function of composition and temperature is derived in accordance with experimental data obtained at the constant temperatures T=300K, T=400K, and T=500K by a nonlinear regression method. A thermodynamic model of thermoelectric energy converter is developed in accordance with second law of thermodynamics. Then, we investigate the thermoelectric efficiency of such system as function of the composition, and of both composition and temperature gradients applied at its ends. For each temperature, we calculate the values of composition and heat conductivity giving the optimal efficiency of the thermoelectric energy conversion. A series of constraints on the material functions entering the model equations, which are necessary and sufficient to guarantee the optimal efficiency of the system, are determined and discussed
Thermoelectric efficiency of silicon–germanium alloys in finite-time thermodynamics
No full textWe analyze the efficiency in terms of a thermoelectric system of a one-dimensional Silicon–Germanium alloy. The dependency of thermal conductivity on the stoichiometry is pointed out, and the best fit of the experimental data is determined by a nonlinear regression method (NLRM). The thermoelectric efficiency of that system as function of the composition and of the effective temperature gradient is calculated as well. For three different temperatures (T = 300K, T = 400K, T = 500K), we determine the values of composition and thermal conductivity corresponding to the optimal thermoelectric energy conversion. The relationship of our approach with Finite-Time Thermodynamics is pointed out
A domain of influence theorem in linear thermoelasticity with thermal relaxation and internal variable
No full textA domain of influence theorem is proved for a linear thermoelastic solid with a Cattaneo's type heat conduction law and a scalar internal variable.
The obtained result is applied to prove the hyperbolicity of a semiempirical heat conduction theory, describing the propagation of thermal waves in crystals at low temperature
On the Mathematical Structure of Thermodynamics with Internal Variables
No full textThe mathematical properties of thermodynamics with internal variables are investigated
in a general framework, both for the local and gradient theory. The consequences
of the Second Law of Thermodynamics on the constitutive equations, together with
some peculiar properties of the equilibrium states, are proved. The evolution equations
of the internal variables are derived as a system of Hamilton equations resulting from a
suitable Legendre's transformation
A nonlinear model of thermoelectricity with two temperatures: Application to quasicrystalline nanowires
No full textA general two temperatures nonlinear thermodynamic model to describe thermoelectric effects is introduced. Its compatibility with second law of thermodynamics is investigated. We specialize the model in the framework of thermomass theory, and estimate the maximum efficiency of a one-dimensional thermoelectric generator
Nonlinear thermal analysis of two-dimensional materials with memory
No full textA nonlinear hyperbolic heat transport equation has been proposed based on the Cattaneo model without mechanical effects. We analyze the two-dimensional Maxwell-Cattaneo-Vernotte heat equation in a medium subjected to homogeneous and non-homogeneous boundary conditions and with thermal conductivity and relaxation time linearly dependent on temperature. Since these nonlinearities are essential from an experimental point of view, it is necessary to establish an effective and reliable way to solve the system of partial differential equations and study the behavior of temperature evolution. A numerical scheme of finite differences for the solution of the two-dimensional non-Fourier heat transfer equation is introduced and studied. We also investigate the attributes of the numerical method from the aspects of stability, dissipation and dispersive errors
Influence of the electron and phonon temperature and of the electric-charge density on the optimal efficiency of thermoelectric nanowires
No full textIn this paper we study the thermodynamic efficiency of thermoelectric generators in which the heat transport is driven by phonons and electrons. It is assumed that the phonon temperature and the electron temperature are different, and that the electric-charge density is nonuniform. The mean temperature is defined by observing that the internal energy of the system is the same either in the presence of two temperatures, or of one temperature. In steady states, we determine the influence of the gradients of the mean temperature and of the electric-charge density on the theoretical values of the thermoelectric efficiency. The physical conditions under which such efficiency is optimal are determined as well
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