Showing papers by "Ephraim M Sparrow published in 1971"

Local non- similarity thermal boundary- layer solutions

Abstract: A solution method is described and applied for treating non-similar thermal boundary layers. The solutions are locally autonomous (that is, independent of information from other streamwise locations) and are found by solving quasi-ordinary differential equations of the similarity type. All non-similar terms appearing in the conservation equations are retained without approximation, and only in derived subsidiary equations are terms selectively neglected. The accuracy of the results can be appraised from comparisons internal to the method itself. Thermal boundary-layer non-similarity arising both from velocity-field, non-similarity and from streamwise variations of surface temperature are analyzed. Numerical results for the surface heat transfer and for the boundary-layer temperature distribution are presented for various physical situations.

Methods for Determining Film Thickness and Optical Constants of Films and Substrates

Abstract: Several methods are developed for deducing optical constants and film thickness from measurements of the monochromatic specular reflectance for linearly polarized radiation at varying angles of incidence. Consideration is given both to transparent films and to slightly absorbing films on absorbing substrates. The methods for transparent films are based on the property that, at any angle of incidence, there are upper and lower bounds on the reflectance that, for given substrate properties, depend only on the index of refraction of the film. For slightly absorbing films, an additional relevant property is that the angular positions of the maxima and minima of the reflectance curve are insensitive to the extinction coefficient of the film. Utilization of the foregoing properties in conjunction with measured distributions of reflectance vs incidence angle leads to the determination of the refractive indices and extinction coefficients of films and substrates as well as the film thickness. Monochromatic reflectances measured for two film–substrate pairs and a pure metal were used to illustrate the application of the methods. A He–Ne laser served as the source of monochromatic polarized light in the experiments.

The effect of mainflow transverse velocities in linear stability theory

Abstract: In studying the stability of the boundary layer with surface mass injection, a generalized version of the Orr–Sommerfeld equation was derived which takes account of the transverse velocity component in the mainflow. The new terms in the generalized Orr–Sommerfeld equation are inversely proportional to the Reynolds number. The resulting eigenvalue problem was solved numerically for a wide range of values of the mass injection intensity. It was found that the critical Reynolds number (based on the distance from the leading edge) decreases with increasing mass injection. The deviations between the critical Reynolds numbers from the generalized and conventional Orr–Sommerfeld equations have a different sign at low injection intensities from that at high injection intensities.

Flow and heat transfer in a rotating enclosure with axial throughflow

Abstract: An analysis is made of the fluid flow and heat transfer processes in a circular cylindrical enclosure rotating about its own axis. A coolant is passed through the enclosure, entering and leaving through centrally located apertures in the end walls. This configuration is intended as a model of rotating enclosures in devices such as gas turbines and air compressors. The Navier-Stokes and energy equations were solved by a finite-difference formulation which can accommodate either steady or transient conditions. Buoyancy forces associated with the rotational body forces were included in some cases. All solutions were performed for laminar flow. For the parameter ranges investigated it was found that rotation inhibited the recirculating motion within the enclosure and thereby decreased the heat transfer relative to that for the stationary enclosure. Buoyancy further reduced the heat transfer owing to the break up of residual circulatory motions in the outer portion of the enclosure. Still stronger buoyancy brought about a slight increase in the heat transfer. The coolant flow was confined to a corridor adjacent to the axis of the enclosure, and there was no mixing between the coolant and the fluid in the enclosure proper.

Film Thickness and Refractive Indices of Dielectric Films on Dielectric Substrates

Abstract: Methods are described for determining the refractive indices of dielectric films and substrates and the thickness of the film. The determination makes use of a single measured distribution of monochromatic, specular reflectance as a function of incidence angle. The methods are based on certain properties of the reflectance maxima and minima, which properties are deduced from electromagnetic theory. Either perpendicular-polarized or parallel-polarized light may be employed; the latter has some advantage, in that it provides a cross check on one of the results and also facilitates the treatment of very thin films.