Electronic Theses and Dissertations

Identifier

6237

Paul Koziel

Date

2018

Document Type

Thesis

Degree Name

Master of Science

Major

Mechanical Engineering

Committee Chair

William Janna

Committee Member

Jeffrey Marchetta

Committee Member

John Hochstein

Abstract

Algorithms for determining the real eigenvalues of the confluent hypergeometric function known as the Kummer function are presented. There is a need for a large number of eigenvalues in order to describe thermally developing flow in the classic Graetz problem. Numerical approaches using the power series definition for the real portion of the Kummer function M(a; b; z) are implenented through user-friendly MATLAB functions to compute 150 eigenvalues for ducts of circular, triangular, and square cross-section. Methods of iterative rot calculation using bisection, secant method, Newton's method, and Brent's method are considered. Comparison with Graetz problem eigenvalues published in the litearture using a finite number of terms for the power series, hypergeometric function calculators, as well as asymptotic approximations is provided to predict accuracy. The length of time needed to calculate a finite number of eigenvalues is measured and compared for the algorithms presented.

Comments

Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.

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