On the Use of Normal Coordinates for the Solution of Lumped Parameter Transient Heat-Transfer Problems

Abstract

T USE of normal coordinates in solving lumped parameter forced vibration problems has been a valuable asset to the vibration analyst. The same method may be applied to the lumped parameter transient heat-transfer problem. Standard digital computer programs are available which will solve the matrix eigenvalue problem. Using a method such as the serial Jacobi method,' 2 the eigenvalues and eigenvectors of a 45 X 45 matrix can be obtained in about 6 minutes on an IBM 704 computer. This report shows how the matrix eigenvalue problem for heat transfer is set up and how the eigenvalues and eigenvectors are used to construct the transient solution.