Doctoral Dissertations

Abstract

"The purpose of this investigation was to determine the eddy thermal diffusivity values as a function of radial position at various Reynolds numbers for a fluid flowing turbulently in a pipe. The ratios of the eddy thermal diffusivity and the eddy viscosity were also investigated.

A vertical column of copper tube two inches in diameter was constructed which consisted of an entrance section for the development of the velocity profile and a heating section for the development of the temperature distribution. The heating section was jacketed and maintained at a constant wall temperature at about 103 ° F by the circulation of hot water. The working fluid, air, was passed upward through the column at Reynolds numbers ranging from 10,100 to 41,100. The radial temperature distribution, velocity profile, and thermal flux at the wall were measured at the top end of the column where the flow was fully developed. Evaluations of the eddy thermal diffusivity were based on the appropriate energy equation which could be expressed in dimensionless form as [formula presented]...

A numerical method was developed to solve the energy equation using a digital computer for the determination of the temperature distribution from any given complex eddy function and velocity profile if so desired. Its application can be extended to solve other problems in transport phenomena of an analogous nature such as the calculation of concentration profiles when the eddy mass diffusivity function or data are known.

The velocity profiles were measured by means of a hypodermic needle impact tube. The universal constant, K, based on the Prandtl logarithmic velocity distribution equation was determined to be 0.38 from these experimental data..

A thermistor was used to measure the temperature distribution in the air stream. It was found to have favorable characteristics such as high resistance, high temperature coefficient, and a negligible self-heating effect all of which increased the sensitivity for detecting small temperature gradients.

A mathematical procedure was formulated so that eddy values could be evaluated from the experimental data on a digital computer. The eddy functions exhibited a maximum point at a dimensionless radial position of approximately 0.4. A curve fitting expression for the eddy diffusivity function was proposed as follows: [formula presented].

This expression was found to predict values of the eddy thermal diffusivity with uncertainties of approximately 15% in comparison with the experimental values.

The ratio of the eddy thermal diffusivity to the eddy viscosity, γ, was found to deviate from a mean value of γ by less than 10% in the region between the dimensionless radial positions of 0.3 and 0.7. The mean values of γ in this region were 1.27, 1.16 and 1.06 for Reynolds numbers of 10,100, 25,200 and 41,100 respectively. The ratio tended to increase near the wall and also toward the center. These values of γ, together with some previous experimental data, indicated a quantitative relationship between the eddy viscosity and the eddy thermal diffusivity which was more complex than that predicted from theoretical analysis"--Abstract, pages 2-4.

Advisor(s)

Strunk, Mailand R., 1919-2008

Department(s)

Chemical and Biochemical Engineering

Degree Name

Ph. D. in Chemical Engineering

Comments

The author is grateful for the financial assistance received from a Grant from the National Science Foundation without which this study would not have been possible.

Publisher

University of Missouri at Rolla

Publication Date

1964

Pagination

xi, 234 pages

Note about bibliography

Includes bibliographical references (pages 117-124).

Rights

© 1964 Frank Fu-Kun Tao, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Subject Headings

Heat -- Transmission

Thesis Number

T 1560

Print OCLC #

9526564

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