Fourier's Law in a Generalized Piston Model

A simplified, but non trivial, mechanical model -- gas of $N$ particles of mass $m$ in a box partitioned by $n$ mobile adiabatic walls of mass $M$ -- interacting with two thermal baths at different temperatures, is discussed in the framework of kinetic theory. Following an approach due to Smoluchowski, from an analysis of the collisions particles/walls, we derive the values of the main thermodynamic quantities for the stationary non-equilibrium states. The results are compared with extensive numerical simulations; in the limit of large $n$, $mN/M\gg 1$ and $m/M \ll 1$, we find a good approximation of Fourier's law.Comment: 14 pages, 5 figure

Contributions to the Fourth Solar Wind Conference

Recent results in interplanetary physics are examined. These include observations of shock waves and post-shock magnetic fields made by Voyager 1, 2; observations of the electron temperature as a function of distance between 1.36 AU and 2.25 AU; and observations of the structure of sector boundaries observed by Helios 1. A theory of electron energy transport in the collisionless solar wind is presented, and compared with observations. Alfven waves and Alvenic fluctuations in the solar wind are also discussed

Thermal conductances of aligned structures and thin films with embedded carbon nanotubes

Individual carbon nanotubes (CNTs) have superior thermal conductivity than conventional materials. The applications for CNTs range from heat sinks, thin films to thermal interface materials. However, when CNTs are grouped together in macroscopic quantities and embedded in different media their thermal conductivity changes. Therefore, it is important to determine the thermal conductance changes when CNTs are embedded in different media. In my research, CNTs were embedded in thin films and as aligned structures (fins) in water. Analytical and experimental methods were used to determine the thermal conductances of these aligned structures and thin films. The primary goals of this research were to develop novel analytical methods to determine thermal conductivity and also experimental techniques to determine effectiveness of the embedded CNTs as carriers of heat by thermal conductance evaluation. It is observed that CNTs fins are effective carriers of heat and result in up to 57% decrease in thermal resistance. In the case of CNTs embedded in thin films, it is important to consider non Fourier effects and neglecting non Fourier effects would lead to an underestimation of the thermal conductivity. In addition to the thermal conductivity value, the analysis also provides a way to determine the thermal relaxation time of thin films

An introduction to acoustics

This is an extended and revised edition of IWDE 92-06

Effects of friction and heat conduction on sound propagation in ducts

The theory of sound propagation is examined in a viscous, heat-conducting fluid, initially at rest and in a uniform state, and contained in a rigid, impermeable duct with isothermal walls. Topics covered include: (1) theoretical formulation of the small amplitude fluctuating motions of a viscous, heat-conducting and compressible fluid; (2) sound propagation in a two dimensional duct; and (3) perturbation study of the inplane modes

ENTROPY CONSIDERATIONS APPLIED TO SHOCK UNSTEADINESS IN HYPERSONIC INLETS.

The stability of curved or rectangular shocks in hypersonic inlets in reponse to flow perturbations can be determined analytically from the principle of minimum entropy. Unsteady shock wave motion can have a significant effect on the flow in a hypersonic inlet or combustor. According to the principle of minimum entropy, a stable thermodynamic state is one with the lowest entropy gain. A model based on piston theory and its limits has been developed for applying the principle of minimum entropy to quasi-steady flow. Relations are derived for analyzing the time-averaged entropy gain flux across a shock for quasi-steady perturbations in atmospheric conditions and angle as a perturbation in entropy gain flux from the steady state. Initial results from sweeping a wedge at Mach 10 through several degrees in AEDC's Tunnel 9 indicates the bow shock becomes unsteady near the predicted normal Mach number. Several curved shocks of varying curvature are compared to a straight shock with the same mean normal Mach number, pressure ratio, or temperature ratio. The present work provides analysis and guidelines for designing an inlet robust to off- design flight or perturbations in flow conditions an inlet is likely to face. It also suggests that inlets with curved shocks are less robust to off-design flight than those with straight shocks such as rectangular inlets. Relations for evaluating entropy perturbations for highly unsteady flow across a shock and limits on their use were also developed. The normal Mach number at which a shock could be stable to high frequency upstream perturbations increases as the speed of the shock motion increases and slightly decreases as the perturbation size increases. The present work advances the principle of minimum entropy theory by providing additional validity for using the theory for time-varying flows and applying it to shocks, specifically those in inlets. While this analytic tool is applied in the present work for evaluating the stability of shocks in hypersonic inlets, it can be used for an arbitrary application with a shock

A bibliography /with abstracts/ on gas-lubricated bearings Interim report

Gas lubricated bearings - annotated bibliograph