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A numerical method was developed for calculating thermal stresses in irregular cylinders cooled by one or more internal passages. The use of relaxation methods and elementary methods of finite differences was found to give approximations to the correct values when compared with previously known solutions for concentric circular cylinders possessing symmetrical and asymmetrical temperature distributions.
Includes the Committee's Technical reports no. 1-1058, reprinted in v. 1-37.

Report

United States. National Advisory Committee for Aeronautics

Published: 1952

Total Pages: 38


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Highly regarded text presents detailed discussion of fundamental aspects of theory, background, problems with detailed solutions. Basics of thermoelasticity, heat transfer theory, thermal stress analysis, more. 1985 edition.
An analytical solution is presented to the steady-state heat-conduction equation for a heat-generating circular region which is cooled by a ring of equal holes spaced uniformly on a circle concentric with the boundary of the cylinder. The solution is based upon a class of harmonic functions previously defined by Howland. Numerical results are presented in the form of dimensionless curves for the particular examples of (a) uniform heat generation within the region with cooling at the holes and insulated outer boundary, and (b) the shape factor or conductance for this geometry.
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