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.
Highlights
The multilayer diffusion problems are typical models for a variety of solute transport phenomena in layered permeable media, such as advection, dispersion, and reaction diffusions [1–10]
We focus on analytic solutions of certain nonhomogeneous diffusion problems in multilayer permeable media
The obtained solutions are applicable to more general linear nonhomogeneous diffusion equations, finite media consisting of arbitrary many layers, continuity and dispersive flow at the contact interfaces between sequal layers, and transitory boundary conditions of the arbitrary type at the inlet and outlet
Summary
The multilayer diffusion problems are typical models for a variety of solute transport phenomena in layered permeable media, such as advection, dispersion, and reaction diffusions [1–10]. The models estimate a qualitative harmony between the simulated prediction of the local spatiotemporal spread of a pandemic and the epidemiological collected datum (see [22, 23]) These data-driven emulations can essentially inform the respective authorities to purpose efficient pandemicarresting measures and foresee the geographical distribution of vital medical resources. The obtained solutions are applicable to more general linear nonhomogeneous diffusion equations, finite media consisting of arbitrary many layers, continuity and dispersive flow at the contact interfaces between sequal layers, and transitory boundary conditions of the arbitrary type at the inlet and outlet.
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