Doctoral Dissertations


"The exact formulations for the radiative flux and the emissive power are presented for a two-dimensional, finite, planar, absorbing and emitting, gray medium in radiative equilibrium. Exact expressions are obtained for the medium subjected to the following types of boundary conditions: (1) cosine varying diffuse, (2) cosine varying collimated, (3) constant temperature strip, and (4) the strip illuminated by a uniform collimated flux. The solutions for the physically unrealistic cosine varying models are used to construct the solutions for the more practical finite strip models. The two-dimensional equations are reduced to one-dimensional equations by the method of separation of variables. This simplification is made possible by the cosine form of the boundary radiation. The corresponding equations for the semi-infinite medium are obtained from the equations for the finite optical thick medium by letting the optical thickness become infinite. The reduced one-dimensional equations are then solved exactly by techniques from one-dimensional radiative theory for the emissive power and radiative flux at the boundaries for both the finite and semi-infinite models. A wide range of exact numerical data is presented. The cosine varying collimated boundary condition generates functions which are analogous to the one-dimensional X- and Y-functions of Chandrasekhar for the finite model and the H-function of Chandrasekhar for the semi-infinite model. These generalized functions represent the dimensionless emissive power at the boundaries and appear in the radiative flux and emissive power at the boundaries for the cosine varying diffuse model as well as for both finite strip models. The generalized H-, X- and Y-functions are tabulated exactly for a wide range of numerical values. In addition to the generalized H-, X- and Y-functions, a function analogous to the exponential integral function is introduced. Generalized exponential integral functions of the first, second, and third order are defined and the recurrence formulas and series expansions are developed. The generalized exponential integral functions are tabulated for a wide range of numerical values"--Abstract, pages ii-iii.


Crosbie, A. L. (Alfred L.)

Committee Member(s)

Chen, T. S.
Pagano, Sylvester J., 1924-2006
Davis, Robert L.
Faucett, T. R.
Lehnhoff, T. F., 1939-


Mechanical and Aerospace Engineering

Degree Name

Ph. D. in Mechanical Engineering


University of Missouri--Rolla. Department of Mechanical Engineering
University of Missouri--Rolla. Department of Engineering Mechanics


University of Missouri--Rolla

Publication Date



xxii, 274 pages

Note about bibliography

Includes bibliographical references (pages 185-187).


© 1972 William Francis Breig, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Radiative transfer -- Mathematical models
Heat -- Radiation and absorption -- Mathematical models
Boundary value problems -- Numerical solutions

Thesis Number

T 2754

Print OCLC #


Electronic OCLC #