Mathematical method to characterize the inward solid state diffusion in cylindrical parts

• Published in: REM - International Engineering Journal Vol. 69; no. 3; pp. 341 - 347
• Main Authors: Barros, André dos Santos, Ferreira, Ivaldo Leão, Moreira, Antonio Luciano Seabra
• Format: Journal Article
• Language: English
• Published: Fundação Gorceix 01-09-2016
• Subjects: analytical method; ENGINEERING, MECHANICAL; GEOLOGY; MECHANICS; METALLURGY & METALLURGICAL ENGINEERING; numerical method; phase change; Solid state diffusion; phase change; analytical method; Solid state diffusion; numerical method
• ISSN: 2448-167X; 2448-167X
• DOI: 10.1590/0370-44672014690044

Abstract This work presents an analytical method for the study of the solid state diffusion process in binary systems of two phases with cylindrical radial atomic flux. The method is developed from the differential equation that describes Fick's second law that is modified by geometric function and suitable changes of variables. The modified differential equation is solved by using a well-known closed form solution based on the error function, and then analytical equations are obtained to analyze the diffusion interface position as a function of time, and the concentration profiles as a function of time and position. The predictions provided by the analytical method are compared with numerical results.