Diffusion in composite layers with automatic solution of the eigenvalue problem
Abstract
The analytical treatment of transient heat conduction problems for onedimensional multilayered composites by the orthogonal expansion technique requires the solution of a corresponding eigenvalue problem if this analytical solution is to be implemented for practical purposes. Such an eigenvalue problem is not of the conventional SturmLiouville type because of the discontinuities of the coefficient functions. Its solution with conventional techniques is not guaranteed from missing eigenvalues in the course of the computation. An analytical solution of one transient heat conduction problem in onedimensional multilayered slabs, cylinders and spheres is presented, which implements a safe algorithm for the automatic computation of the eigenvalues and the eigenfunctions of the resulting SturmLiouville type system.
 Publication:

International Journal of Heat and Mass Transfer
 Pub Date:
 August 1983
 DOI:
 10.1016/S00179310(83)801677
 Bibcode:
 1983IJHMT..26.1131M
 Keywords:

 Composite Materials;
 Conductive Heat Transfer;
 Eigenvalues;
 Laminates;
 Thermal Diffusion;
 Algorithms;
 Contact Resistance;
 Cylindrical Bodies;
 Eigenvectors;
 Orthogonal Functions;
 Slabs;
 Spheres;
 SturmLiouville Theory;
 Temperature Distribution;
 Temporal Distribution;
 Fluid Mechanics and Heat Transfer