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 Nanoscale Research Letters , 2009, Abstract: The scale effect of heat conduction of air in nano spacing (NS) is very important for nanodevices to improve their life and efficiency. By constructing a special technique, the changes of heat conduction of air were studied by means of measuring the heat conduction with heat conduction instrument in NS between the hot plate and the cooling plate. Carbon nanotubes were used to produce the nano spacing. The results show that when the spacing is small down to nanometer scale, heat conduction plays a prominent role in NS. It was found that the thickness of air is a non-linear parameter for demarcating the heat conduction of air in NS and the rate of heat conduction in unit area could be regard as a typical parameter for the heat conduction characterization at nanometer scale.
 Physics , 2008, DOI: 10.1007/s00220-008-0691-2 Abstract: We define a deterministic scattering'' model for heat conduction which is continuous in space, and which has a Boltzmann type flavor, obtained by a closure based on memory loss between collisions. We prove that this model has, for stochastic driving forces at the boundary, close to Maxwellians, a unique non-equilibrium steady state.
 Bulletin of the Institute of Heat Engineering , 1977, Abstract: This paper discusses mathematical and physical fundamentals of heat conduction in anisotropic media dealing with Fourier's constitutive law, symmetry of conductivity tensor, mutual geometrical relations between heat flux vector and temperature gradient directions as wel l as the thermal contact resistance in anisotropic bodies. I t presents heat conduction differential equation with an appropriate coordinate axis transformation enabling to transform anisotropic problems to isotropic ones. It gives also a short survey of the experimental methods used to determine the conductivity tensor components together with the analytica l and numerical methods applied for finding solutions of anisotropic heat conduction problems.
 Beat Aebischer Mathematical Problems in Engineering , 2007, DOI: 10.1155/2007/57360 Abstract: We consider several heat conduction problems for glass lenses with different boundary conditions. The problems dealt with in Sections sec:1 to sec:3 are motivated by the problem of an airborne digital camera that is initially too cold and must be heated up to reach the required image quality. The problem is how to distribute the heat to the different lenses in the system in order to reach acceptable operating conditions as quickly as possible. The problem of Section sec:4 concerns a space borne laser altimeter for planetary exploration. Will a coating used to absorb unwanted parts of the solar spectrum lead to unacceptable heating? In this paper, we present analytic solutions for idealized cases that help in understanding the essence of the problems qualitatively and quantitatively, without having to resort to finite element computations. The use of dimensionless quantities greatly simplifies the picture by reducing the number of relevant parameters. The methods used are classical: elementary real analysis and special functions. However, the boundary conditions dictated by our applications are not usually considered in classical works on the heat equation, so that the analytic solutions given here seem to be new. We will also show how energy conservation leads to interesting sum formulae in connection with Bessel functions. The other side of the story, to determine the deterioration of image quality by given (inhomogeneous) temperature distributions in the optical system, is not dealt with here.
 Physics , 2014, Abstract: Thermal transport at short length and time scales inherently constitutes a nonlocal relation between heat flux and temperature gradient, but this is rarely addressed explicitly. Here, we present a formalism that enables detailed characterisation of the delocalisation effects in nondiffusive heat flow regimes. A convolution kernel $\kappa^{\ast}$, which we term the nonlocal thermal conductivity, fully embodies the spatiotemporal memory of the heat flux with respect to the temperature gradient. Under the relaxation time approximation, the Boltzmann transport equation formally obeys the postulated constitutive law and yields a generic expression for $\kappa^{\ast}$ in terms of the microscopic phonon properties. Subsequent synergy with stochastic frameworks captures the essential transport physics in compact models with easy to understand parameters. A fully analytical solution for $\kappa^{\ast}(x')$ in tempered L\'evy transport with fractal dimension $\alpha$ and diffusive recovery length $x_{\text{R}}$ reveals that nonlocality is physically important over distances $\sqrt{2-\alpha} \,\,x_{\text{R}}$. This is not only relevant to quasiballistic heat conduction in semiconductor alloys but also applies to similar dynamics observed in other disciplines including hydrology and chemistry. We also discuss how the previously introduced effective thermal conductivity $\kappa_{\text{eff}}$ inferred phenomenologically by transient thermal grating and time domain thermoreflectance measurements relates to $\kappa^{\ast}$. Whereas effective conductivities depend on the experimental conditions, the nonlocal thermal conductivity forms an intrinsic material property. Experimental results indicate nonlocality lengths of 400$\,$nm in Si membranes and $\simeq 1\,\mu$m in InGaAs and SiGe, in good agreement with typical median phonon mean free paths.
 International Journal of Energy and Environment , 2011, Abstract: The model of an energy selective electron (ESE) heat engine with filter heat conduction via phonons is presented in this paper. The general expressions for power output and efficiency of the ESE heat engine are derived for the maximum power operation regime and the intermediate operation regime, respectively. The optimum performance and the optimal operation regions in the two different operation regimes of the ESE heat engine are analyzed by detailed numerical calculations. The influences of filter heat conduction and the temperature of hot reservoir on the optimum performance of the ESE heat engine are analyzed in detail. Furthermore, the influence of resonance width on the performance of the ESE heat engine in intermediate operation regime is also discussed. The results obtained herein have theoretical significance for understanding and improving the performance of practical electron energy conversion systems.
 中国物理快报 , 2010, Abstract: Based on a new definition of user similarity, we introduce an improved collaborative filtering (ICF) algorithm, which could improve the algorithmic accuracy and diversity simultaneously. In the ICF, instead of the standard Pearson coefficient, the user-user similarities are obtained by integrating the heat conduction and mass diffusion processes. The simulation results on a benchmark data set indicate that the corresponding algorithmic accuracy, measured by the ranking score, is improved by 6.7% in the optimal case compared to the standard collaborative filtering (CF) algorithm. More importantly, the diversity of the recommendation lists is also improved by 63.6%. Since the user similarity is crucial for the CF algorithm, this work may shed some light on how to improve the algorithmic performance by giving accurate similarity measurement.
 Physics , 2014, DOI: 10.1103/PhysRevB.90.155459 Abstract: Short-range order in strongly disordered structures plays an important role in their heat conduction property. Using numerical and analytical methods, we show that short-range spatial correlation (with a correlation length of $\Lambda_{m}$) in the mass distribution of the one-dimensional (1D) alloy-like random binary lattice leads to a dramatic enhancement of the high-frequency phonon transmittance but also increases the low-frequency phonon opacity. High-frequency semi-extended states are formed while low-frequency modes become more localized. This results in ballistic heat conduction at finite lengths but also paradoxically higher thermal resistance that scale as $\sqrt{\Lambda_{m}}$ in the $L\rightarrow\infty$ limit. We identify an emergent crossover length ($L_{c}$) below which the onset of thermal transparency appears. The crossover length is linearly dependent on but is two orders of magnitude larger than $\Lambda_{m}$. Our results suggest that the phonon transmittance spectrum and heat conduction in a disordered 1D lattice can be controlled via statistical clustering of the constituent component atoms into domains. They also imply that the detection of ballistic heat conduction in disordered 1D structures may be a signature of the intrinsic mass correlation at a much smaller length scale.
 Mathematics , 2014, Abstract: We consider the identification of nonlinear heat conduction laws in stationary and instationary heat transfer problems. Only a single additional measurement of the temperature on a curve on the boundary is required to determine the unknown parameter function on the range of observed temperatures. We first present a new proof of Cannon's uniqueness result for the stationary case, then derive a corresponding stability estimate, and finally extend our argument to instationary problems.
 Physics , 2005, DOI: 10.1007/1-4020-3949-2_1 Abstract: In this paper we give a brief review of the relation between microscopic dynamical properties and the Fourier law of heat conduction as well as the connection between anomalous conduction and anomalous diffusion. We then discuss the possibility to control the heat flow.
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