Non-classical Heat Research Articles

Transport issues in focused electron beam chemical vapor deposition

In this contribution we critically review heat and mass transfer issues in the Focused Electron Beam Chemical Vapor Deposition (FEB-CVD). In general, the transport of both the precursor molecules and the primary/secondary electrons facilitate nanostructure deposition. Depending on the operating pressure either continuous advection–diffusion mass conservation equation or the kinetic Boltzmann Transport Equation (BTE) describes the transport of precursor molecules to the substrate surface. At the surface, some of the precursor molecules are adsorbed, spatially re-distributed by surface diffusion, and, finally, a fraction of the adsorbed molecules become converted into a solid deposit. This occurs upon interaction with back-scattered primary electrons and secondary electrons, yielded by the substrate and deposit upon impingement of the high-energy primary electron beam. The interactions of the primary electrons with the substrate and nanoscale-confined deposit possibly induce significant localized heating. Such energy transfer process is complex, involves non-classical heat conduction, and may greatly influence the deposition process. The pertinent question is then what controls the FEB-CVD process, i.e., both time dependent growth of the nanostructure and its shape evolution? The answer to this question can be obtained via complimentary theoretical and experimental studies, discussed here with the main focus on transport phenomena underlying FEB-CVD.

Some qualitative properties of solutions of the system governing acoustic waves in bubbly liquids

In this note we analyze some qualitative aspects of the solutions of the system of acoustic waves in bubbly liquids. In this sense we show uniqueness and continuous dependence of solutions for the general case. We also prove the exponential decay of solutions of the one-dimensional problem and a spatial decay estimate for the general three-dimensional case. We show how to extend the arguments and results to the case of the one-dimensional non-classical heat conduction in periodic heterogeneous materials.

Theoretical and computational aspects of non-classical thermoelasticity

In our previous work [S. Bargmann, P. Steinmann, Finite element approaches to non-classical heat conduction in solids, Comput. Modeling Engrg. Sci. 9 (2) (2005) 133–150] we investigated the Green–Naghdi-approach for modeling the phenomenon of second sound. We suggested a finite element discretization of the thermal problem. The aim of the present contribution is the extension to the linear thermomechanically coupled problem. The theory of heat conduction is coupled with a linear elastic mechanical model and studied theoretically and numerically. Numerical investigations underline the performance of the proposed method.

A one-phase Stefan problem for a non-classical heat equation with a heat flux condition on the fixed face

We prove the existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material with a heat flux boundary condition at the fixed face x = 0. Here the heat source depends on the temperature at the fixed face x = 0. We use the Friedman–Rubinstein integral representation method and the Banach contraction theorem in order to solve an equivalent system of two Volterra integral equations.

Finite Element Approaches to Non-classical Heat Conduction in Solids

Finite Element Approaches to Non-classical Heat Conduction in Solids

Thermal effects in Stokes’ second problem for unsteady micropolar fluids flow

The MCF model is used to study the non-classical heat conduction effects in Stokes’ second problem of a micropolar fluid. The effects of the thermal relaxation time and the structure wave on angular velocity, velocity field and temperature are investigated. The skin friction, the displacement thickness and the rate of the heat transfer at the plate are determined.

Multiple spatial and temporal scales method for numerical simulation of non-classical heat conduction problems: one dimensional case

A multiple spatial and temporal scales method is studied to simulate numerically the phenomenon of non-Fourier heat conduction in periodic heterogeneous materials. The model developed is based on the higher-order homogenization theory with multiple spatial and temporal scales in one dimensional case. The amplified spatial scale and the reduced temporal scale are introduced respectively to account for the fluctuations of non-Fourier heat conduction due to material heterogeneity and non-local effect of the homogenized solution. By separating the governing equations into various scales, the different orders of homogenized non-Fourier heat conduction equations are obtained. The reduced time dependence is thus eliminated and the fourth-order governing differential equations are derived. To avoid the necessity of C 1 continuous finite element implementation, a C 0 continuous mixed finite element approximation scheme is put forward. Numerical results are shown to demonstrate the efficiency and validity of the proposed method.

Nonclassical Thermal Effects in Stokes’ Second Problem for Micropolar Fluids

The MCF model is used to study the nonclassical heat conduction effects in Stokes’ second problem of a micropolar fluid. The effects of the thermal relaxation time and the structure wave on angular velocity, velocity field, and temperature are investigated. The skin friction, the displacement thickness, and the rate of the heat transfer at the plate are determined.

Helium Abundance in the Corona and Solar Wind: Gyrotropic Modeling from the Chromosphere to 1 AU

We have developed a solar wind model including helium that extends from the chromosphere to 1 AU. The model is based on the gyrotropic approximation to the 16-moment set of fluid transport equations, which allows it to accommodate temperature anisotropies, as well as nonclassical heat transport. We find that, as in a pure electron-proton solar wind, the flow geometry close to the Sun also has a large impact on helium. In a radially expanding flow, downward proton heat conduction from the corona leads to a high transition region pressure and a large thermal force that pulls helium ions into the corona. In this case α-particles may easily become the dominant species in the corona, resulting in a polar wind type of solar wind in which the light protons are accelerated outward in the electric field set up by the α-particles and electrons. By contrast, applying the same form for the coronal heating in a rapidly expanding geometry intended to simulate a coronal hole, protons become collisionless closer to the Sun, and therefore the downward proton heat flux is smaller, resulting in a lower transition region pressure and a lower thermal force on helium. In this case the helium abundance is low everywhere and helium is unimportant for the acceleration of the solar wind. For the low coronal proton and α-particle densities found in the rapidly expanding flow, where asymptotic flow speeds are typically significantly higher than the gravitational escape speed at the solar surface, the solar wind helium mass flux is determined by the amount of helium available at the top of the chromosphere. In the radially expanding flow, with asymptotic flow speeds lower than the escape speed, the helium mass flux depends on the amount of energy available in the corona to lift helium out of the gravitational potential. In both cases the frictional coupling between helium and hydrogen in the chromosphere, using currently accepted elastic cross sections, is too weak to pull a sufficient number of helium atoms up to the top of the chromosphere and thus obtain a mass flux in agreement with observations. A better understanding of the chromosphere is therefore called for.

A Stefan Problem for a non-classical heat equation

A Stefan Problem for a non-classical heat equation

Asymptotic behaviour of a non-classical heat conduction problem for a semi-infinite material

The asymptotic behaviour of a heat conduction problem involving a non-linear heat source depending on the heat-flux occurring in the extremum of a semi-infinite slab is discussed. Conditions are given on the non-linearity so as to accelerate the convergence of the solution to zero.

Wave structure in Stokes' second problem for a dipolar fluid with nonclassical heat conduction

The classical heat conduction law of Fourier associates an infinite speed of propagation to a thermal disturbance in a material body. Such behavior is a violation of the causality principle. In recent years, several modifications of Fourier's heat law have been proposed. In this work, a modified form of Fourier's heat law, based on the Maxwell-Cattaneo-Fox (MCF) model, is used to analyze the heat conduction effects in Stokes' second problem for a dipolar fluid. The structure of the waves and the influence of the dipolar constants on the velocity field is investigated. These results are then compared to the viscous fluid case. In addition, the displacement thickness and skin friction at the plate are determined.

Stokes' first problem for a dipolar fluid with nonclassical heat conduction

The classical heat law of Fourier associates an infinite speed of propagation to a thermal disturbance in a material body. Such behavior is a violation of the causality principle. In recent years, several modifications of Fourier's heat law have been proposed. In this work a modification of Fourier's heat law based on the Maxwell-Cattaneo-Fox (MCF) model is used to describe the influence of heat conduction at low temperatures and/or high heat-flux conditions on Stokes' first problem for a dipolar fluid. The effects of discontinuous boundary data and a finite propagation speed of thermal waves on the velocity and stress fields are investigated. In addition, special and limiting cases of the material constants are examined. Lastly, results for the special case of equal dipolar constants are compared to the corresponding results found using Fourier's heat law.

Stokes’ First and Second Problems for Rivlin-Ericksen Fluids With Nonclassical Heat Conduction

The nonclassical heat conduction equation based on the Maxwell-Cattaneo-Fox (MCF) model is used to study the Stokes’ first and second problems for the Rivlin-Ericksen fluids. The discontinuities in velocity gradients in fluid flows induced by impulsive or sudden heating of a plate and the influence of the thermal relaxation time and elastic parameter of the fluid on the velocity field are investigated. The structure of the waves in the temperature and velocity fields is presented. An anomalous behavior of the medium is characterized by infinite or negative values of the group velocity for the wave packets as the frequency attains or exceeds a critical value. The displacement thickness and the rate of heat transfer at the plate are determined.

Discontinuities in velocity gradients and temperature in the Stokes’ first problem with nonclassical heat conduction

The nonclassical heat conduction equation based on the MCF model is used to study the discontinuities in velocity gradients and temperature in fluid flows induced by impulsive or sudden heating of a plate. The influence of the thermal relaxation time in the temperature and velocity fields is investigated.

Constraints on solar wind acceleration mechanisms from Ulysses plasma observations: The first polar pass

The mass flux density and velocity of the solar wind at polar latitudes can provide strong constraints on solar wind acceleration mechanisms. We use plasma observations from the first polar passage of the Ulysses spacecraft to investigate this question. We find that the mass flux density and velocity are too high to reconcile with acceleration of the solar wind by classical thermal conduction alone. Therefore acceleration of the high‐speed wind must involve extended deposition of energy by some other mechanism, either as heat or as a direct effective pressure, due possibly to waves and/or turbulence, or completely non‐classical heat transport.

Nonclassical thermal effects in Stokes' second problem

The MCF model is used to study the nonclassical heat conduction effects in Stoke's second problem. The structure of the waves and the influence of the thermal relaxation time on the temperature and velocity fields are investigated. The displacement thickness, skin friction and the rate of the heat transfer at the plate are determined.

Nonclassical heat conduction problem for crystal bodies with coatings heated by radiation with account for the curvature of the coating

Generalized conditions for heat transfer of thermosensitive crystal bodies with coatings are formulated that are necessary for determination of their Kirchhoff variables with account for the curvature of the coating.

The role of nonclassical electron transport in the lower solar transition region

view Abstract Citations (19) References (23) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Role of Nonclassical Electron Transport in the Lower Solar Transition Region Owocki, S. P. ; Canfield, R. C. Abstract One problem in solar physics is concerned with an understanding of the observed brightness of the quiet solar atmosphere in spectral lines which are formed in the lower solar transition region. The present paper has the objective to examine the possibility that the observed line emission results from nonclassical electron transport effects which are associated with the inherently steep temperature gradients in the solar transition region. The height variation of the electron temperature is parameterized to enable correspondence with a variety of one-dimensional constant pressure transition region models. The models include empirical models, theoretical models, and the constant classical heat fluxx model used by Shoub (1983). The electron velocity distribution function is considered along with the effect on collisional excitation and ionization rates, and effects on heat transport. Publication: The Astrophysical Journal Pub Date: January 1986 DOI: 10.1086/163816 Bibcode: 1986ApJ...300..420O Keywords: Chromosphere; Electron Acceleration; Line Spectra; Solar Atmosphere; Solar Spectra; Solar Temperature; Electron Distribution; Electron Energy; Heat Flux; Thermalization (Energy Absorption); Transport Theory; Solar Physics; LINE FORMATION; PARTICLE ACCELERATION; SUN: ATMOSPHERE; SUN: CHROMOSPHERE full text sources ADS |

Proton temperature anisotropy in the polar wind

We studied the steady state flow of a fully ionized H+‐O+‐electron plasma along geomagnetic field lines in the high‐latitude topside ionosphere. Our theoretical formulation was based on the 13‐moment system of transport equations, which allows for different species temperatures parallel and perpendicular to the geomagnetic field and nonclassical heat flows. Solutions to the plasma transport equations were obtained over the altitude range from 1500 to 12,000 km for a range of lower‐boundary conditions leading to both subsonic and supersonic H+ outflows. For both subsonic and supersonic flows an appreciable H+ temperature anisotropy occurs at all altitudes above 1500 km, and in both cases the H+ temperature anisotropy tends to be regulated at high altitudes. However, the direction of the anisotropy is opposite for the two cases. For supersonic flow, Tp∥ > Tp⊥ at high altitudes, while the reverse occurs for subsonic flow. To some extent, the direction of the temperature anisotropy is related to the direction of the H+ heat flow. For supersonic flow an upward flow of heat from the lower ionosphere is required, while for subsonic flow we were able to obtain solutions with a downward H+ heat flow. For supersonic flow, collisionless transport effects are important at altitudes as low as 1500 km while for subsonic flow H+‐H+ collisions have an important effect on the H+ stress and heat flow balance at all altitudes between 1500 and 12,000 km.