Periodic heat transfer through inhomogeneous media part 2: Hollow cylinder
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The paper presents exact analytical solutions for periodic radial heat conduction through an inhomogeneous hollow circular cylinder for a certain class of thermal conductivity profile. The exact analytical solutions for some of these profiles (including linear and quadratic) are compared with those obtained by considering the cylindrical medium to be made up of a number of homogeneous layers with different thermal conductivities, varying from layer to layer, and using the layered-structure (or matrix-multiplication) method. The numerical results arrived at by the layered-structure method converge rapidly (with increasing number of layers considered) to the values obtained from the exact analytical solutions. This gives confidence in the application of the layered-structure method to periodic heat conduction through an inhomogeneous hollow cylinder. Assuming the inhomogeneous hollow cylinder to be made up of a number of cylindrical layers with a linear profile of thermal conductivity has also been shown to be a more effective alternative method of considering any type of inhomogeniety; it saves computation time, as the rate of converegence is much higher than for the homogeneous-layer structure method. Numerical results are presented in the form of elements of a 2 × 2 matrix, relating the sinusoidal steady-state temperature and the heat flux on the two sides of the cylinder.Keywords:
Matrix (chemical analysis)
A thermal rectifier has such nature that its thermal conductance or thermal conductivity has different values with reversed heat flux direction. This work investigates the rectification of the cross-plane thermal conductivity and interfacial thermal resistance of nanoscale bi-layered films using the nonequilibrium molecular dynamics (NEMD) method. The effects of the thickness of the single layer with the total thickness constant, the ratio of the atomic mass and temperature difference in the two ends on the thermal rectification are all considered. The results of the simulations show that the thermal conductivity and the interfacial thermal resistance are different for the heat flux with opposite directions. For the composite film with two layers of the same thicknesses, the thermal conductivity is larger when the heat flux direction is from the light layer to the heavy one. The difference becomes larger when the ratio of the atomic mass in the two layers increases. Increasing the heat flux makes the rectification of thermal conductivity larger, which means that the rectification is dependent on the temperature. For the composite film with fixed total thickness, the rectification becomes smaller when the thickness of the light layer increases. When the light layer is thick enough, the rectification is found reversed, which means that the thermal conductivity is larger with the heat flux direction from the heavy layer to the light one. The phonon density of states is also calculated to explain the phenomenon, and it is found that the overlap of the phonon density of states for the two layers is almost same even if the rectification of the thermal conductivity is reversed.
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among which are the variation of heat production throughout the sample (due to local neutron-flux perturbations) and the variation of thermal conductivity occasioned by unusually steep temperature gradients. Various assumptions, which are considered to fit most closely the conditions at hand, are made for these calculations. As no standard set of assumptions can fit all cases, four illustrative cases are presented, representing four different sets of conditions applied to the heatconduction equation. The four cases considered may be briefly described as follows: varlable thermal conductivity, nonuniform heat production; variable thermal conductivity, uniform heat production; constant thermal conductivity, nonuniform heat production; and constant thermal conductivity, uniform heat production. (auth)
Constant (computer programming)
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Basis (linear algebra)
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Classification of discontinuities
Relativistic heat conduction
Constant (computer programming)
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Two-dimensional materials are usually predicted to have ultrahigh thermal conductivity because of the numerous phonon normal scatterings, which might cause hydrodynamic heat conduction. In addition, boundary and interface are significant in the polycrystalline structure and material contacts. Therefore, this article investigates the thermal behaviors at the boundary and interface in phonon hydrodynamics. Monte Carlo simulation is adopted to study the heat conduction phenomena in Poiseuille hydrodynamics and Ziman hydrodynamics. The concept of a boundary temperature step is defined to depict the temperature decline behaviors at the boundary in steady hydrodynamic heat conduction. Interfacial thermal behaviors can be treated as a combination of the boundary effects and phonon transmission effects, where the interface properties can be described by the interface transmissivity and the specular reflectivity. Moreover, the inverse temperature difference at the interface is observed, which means that the heat is transported from low temperature to high temperature, implying that the definition of temperature in phonon hydrodynamic heat conduction ought to be further investigated. Then, two theoretical models are proposed to describe these phenomena, namely, the particle propagation model and the dual boundary flux model. The particle propagation model tries to trace the propagation and evolution of phonons with simpler rules, and it finds that the heat flux reduction originates from the backward phonons that are scattered by the normal scattering process. The dual boundary flux model divides the whole boundary heat flux into the hydrodynamic heat flux and the diffusive heat flux, and the boundary temperature step appears in the transition between these two fluxes. These two models are compared with the results obtained by Monte Carlo simulations.
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In most engineering applications related with the heat conduction phenomena, a conventional Fourier heat conduction equation has been successfully applied and it has supplied quite reasonable results. However, it is well known that the Fourier heat conduction equation is failed in the application to the extremely small space and short time, in other words, a nano-scale system and a pico-second time. In this study, non-Fourier effect was evaluated in the heat conduction by considering the concept of a phase lag model. The results show the existence of a heat wave, which means that the heat is transferred with a finite speed while an infinite speed of heat transfer is assumed in the conventional Fourier heat conduction. In addition, the copper and the gold are tested to evaluate the phase lag time between the heat flux and the temperature gradient. The results show that the gold has the heat wave speed faster than that of the copper consistent with the prediction based on an actual experiment.
Heat equation
Relativistic heat conduction
Fourier number
Phase lag
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Thermal conductivity measurement
Thermal effusivity
Volumetric heat capacity
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Anisotropic solids possess thermal conductivities ranging from among the highest found in nature, as in the in-plane thermal conductivity of graphite, to the lowest, as in the cross-plane thermal conductivity of disordered layered crystals. Though these extremes of thermal conductivity make anisotropic materials attractive for diverse applications such as thermal management and thermal insulation, the microscopic physics of heat conduction in these materials remain poorly understood. In this review article, we discuss the recent advances in our understanding of thermal phonon transport in anisotropic solids obtained using new theoretical, computational, and experimental tools.
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