Generalized Laplace-Type Transform Method for Solving Multilayer Diffusion Problems. (7th March 2022)

• Record Type: Journal Article
• Authors: Akel, Mohamed; Elshehabey, Hillal M.; Ahmed, Ragaa
• Other Names: Persson Lars E. Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-03-07
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/2304219
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Multilayer diffusion problems have found significant importance that they arise in many medical, environmental, and industrial applications of heat and mass transfer. In this article, we study the solvability of a one-dimensional nonhomogeneous multilayer diffusion problem. A new generalized Laplace-type integral transform is used, namely, the M ρ, m - transform. First, we reduce the nonhomogeneous multilayer diffusion problem into a sequence of one-layer diffusion problems including time-varying given functions, followed by solving a general nonhomogeneous one-layer diffusion problem via the M ρ, m -transform. Hence, by means of general interface conditions, a renewal equations' system is determined. Finally, the M ρ, m -transform and its analytic inverse are used to obtain an explicit solution to the renewal equations' system. Our results are of general attractiveness and comprise a number of previous works as special cases.