Mechanical Engineering ETDs

Publication Date



The problem of transient conduction combined with surface radiation and variable emissivities is solved numerically. The existing, but little used, multidimensional Douglas-Peaceman-Rachford alternating-direction-implicit (ADI) technique for finite differencing is chosen as the best available. It is modified and applied to the three-dimensional transient heat equation with source term. Techniques for blocking conduction in excluded directions are demonstrated. Quasi-linearization is used to combine the radiant enclosure calculations with the transient conduction calculations. That is, on an alternating basis, a time step in conduction is followed by a radiant enclosure solution. The radiant enclosure problem is solved in a novel manner, combining matrix inversion with direct-search. Specifically, matrix methods from current literature are made more efficient by forcing them to be symmetric whenever either all temperatures or all heat fluxes are given. However, the matrix methods are merely used to get initial values for a more efficient technique. These initial values are used to start the iteration in a direct-search with pattern-formation technique for function minimization from the field of operations research. This technique is a form of relaxation and unfortunately it appears to run at the same speed as the usual relaxation. A large gain had been hoped for. However, it is applicable to nonlinear equations. Analyses of re-entry vehicles with the best of current heat-transfer codes require hours, even on such advanced computers as the UNIVAC-1108 and CDC-6600. This fact prompted the search for more efficient techniques, which ended with considerable success in the conduction area but with only partial success in the radiant enclosure area.

Degree Name

Mechanical Engineering

Level of Degree


Department Name

Mechanical Engineering

First Committee Member (Chair)

Arthur Vincent Houghton III

Second Committee Member

Francis Christopher Wessling, Jr.

Third Committee Member

Charles Gilbert Richards

Document Type