An Analytical Solution Method for Composite Layer Diffusion Problems with an Application in Metallurgy

Abstract

An analytical solution method for composite layer diffusion in cylindrical geometry is studied, relying on local analytical solutions for the single material layers combined with a numerical solution scheme for the material boundary states. The one-layer submodel was formulated for one-dimensional geometry and constant material properties. An efficient algorithm for the arising local Sturm-Liouville eigenvalue problems is developed on the basis of the calculus of variations and the JWKB-technique known from quantum mechanics. Two example heat conduction calculations of the temperature profile over a composite solid were carried out. The results of the examples were in satisfactory agreement with those of previously published calculations using alternative methods. This, together with the computational benefits of obtaining the eigenvalue spectrum for the composite medium one layer at a time, demonstrates the feasibility of the adopted technique for situations requiring an analytical solution. The method was applied to thermal state computation for the lining of a metallurgical ladle, the results showing good consistency with thermocouple measurements.