Masters Theses


"The molten glass flow (temperature range 1300 to 1500°C) in the entrance region of a duct was investigated with numerical methods. The mathematical model was restricted by assuming: (1) two dimensional, steady state, (2) Newtonian fluid, variable viscosity, and (3) Rosseland approximation. In addition, appropriate use was made of the fact that the Reynolds number is small and the Eckert number is very small. The inclusion of temperature dependent viscosity and a Rosseland approximation for radiation produced from the mass, momentum, and energy equations a system of coupled, nonlinear, partial differential equations which were solved by an iterative finite difference approximation employing unequal step sizes. The computations involved calculating the velocity profiles assuming constant viscosity, calculating the temperature profiles using the velocities found in the constant viscosity flow, and iterating once by putting the nonisothermal temperature field into the momentum equation and recalculating the velocity profiles as evolved from variable viscosity. In addition to velocity and temperature results, conclusions were drawn from pressure gradients, heat transfer, and wall shear stress.

Results indicated that the finite difference method involving unequal step sizes improved efficiency as compared to equal grid spacing for a given accuracy. In addition, one iteration of the energy-momentum equation coupling gave a good indication of actual results.

Results showed that the velocity profile had only a minor influence on the temperature distribution, but the existence of convective terms was important. For the temperature distribution conduction played only a minor role. As a result of the coupling the variable viscosity almost doubled the relative magnitude of the velocity kinks found on both sides of the center axis near the entrance. The center line velocity for the variable viscosity case was found to increase and then decrease unlike the isothermal flow velocity, thereby making the variable viscosity development length greater than the isothermal development length"--Abstract, pages iii-iv.


Crosbie, A. L. (Alfred L.)

Committee Member(s)

Medrow, Robert A.
Kerr, Richard H., 1907-1980


Mechanical and Aerospace Engineering

Degree Name

M.S. in Mechanical Engineering


United States. Department of Health, Education, and Welfare


University of Missouri--Rolla

Publication Date



xii, 94 pages

Note about bibliography

Includes bibliographical references (pages 81-83).


© 1974 Russell Ralph Beckmeyer, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Heat -- Radiation and absorption
Heat -- Transmission
Glass -- Thermal properties

Thesis Number

T 2971

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