Doctoral Dissertations


"A finite element method is presented for solution of direct and inverse heat conduction problems in rock materials. Finite element programs for direct and inverse heat conduction problems were developed and demonstrated. Flow charts are given for the finite element programs.

The direct finite element heat conduction program changes material properties with temperature to approximate the temperature dependent properties of rock materials. An example problem was solved by the finite element method and also using Kirchoff's transformation. The finite element solution compared quite well with the Kirchoff transformation solution.

The inverse method utilizes the direct finite element heat conduction program to iterate for the inverse solution. Data to test the inverse finite element program was generated with the direct finite element program of this research. The inverse program solved these generated problems very accurately.

Internal temperature and fracture time measurements are presented on a series of hollow Dresser Basalt cylinders heated by a Kanthal wire heater. The internal temperature measurements were used in conjunction with the inverse method to obtain surface temperatures. The surface temperatures were used for thermal stress calculations to obtain time to fracture for an infinite cylinder"--Abstract, page ii.


Lehnhoff, T. F., 1939-

Committee Member(s)

Pagano, Sylvester J., 1924-2006
Johnson, R. T. (Richard T.)
Clark, George Bromley, 1912-
Keith, Harold D. (Harold Dean), 1941-


Mechanical and Aerospace Engineering

Degree Name

Ph. D. in Mechanical Engineering


University of Missouri--Rolla. Rock Mechanics & Explosives Research Center
Missouri University of Science and Technology. Department of Mechanical Engineering


University of Missouri--Rolla

Publication Date



xiv, 126 pages

Note about bibliography

Includes bibliographical references (pages 97-102).


© 1974 Vernon Dale Allen, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Heat -- Conduction
Inverse problems (Differential equations)
Finite element method

Thesis Number

T 3021

Print OCLC #


Electronic OCLC #