Parabolic PDE and FEM Analysis of Layer Resolved Moisture Diffusion in Wheat Kernels
Ismailov K. Ismailov B. Urinboev A.
December 2025Pleiades Publishing
Mathematical Models and Computer Simulations
2025#17Issue Suppl 1S32 - S47 pp.
Abstract: A multilayer diffusion framework is formulated and numerically analyzed to simulate moisture transport in heterogeneous biological media using the example of wheat kernels. The process is modeled by a system of parabolic partial differential equations (PDEs) with continuity of concentration and flux across bran, endosperm, and germ interfaces. Each subdomain is characterized by a distinct effective diffusivity, forming a three-domain composite model solved with the finite element method (FEM). The computational domain was implemented in COMSOL Multiphysics under isothermal conditions with prescribed boundary concentration. Numerical results yield spatial temporal concentration fields, layer-resolved uptake curves, and characteristic diffusion times (). The model demonstrates the dominance of endosperm diffusivity in determining overall moisture equilibration and reveals scaling relations between kernel geometry and hydration kinetics. The proposed PDE-FEM framework transforms an empirical technological operation into a quantitative predictive tool, providing a reproducible methodology for simulating coupled mass transfer processes in multiphase porous structures. The formulation and solution strategy are general and applicable to a wide class of diffusion-driven phenomena in materials and process engineering.
finite element method , heterogeneous media , moisture transport , multilayer diffusion , parabolic partial differential equations , wheat kernel modeling
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M. Auezov South Kazakhstan University, Faculty of Information Technologies and Energy, Department of Information Systems and Modelling, Shymkent, Kazakhstan
Fergana State Technical University, Faculty of Energy Engineering and Technology, Department of Electronics and Instrumentation, Fergana, Uzbekistan
M. Auezov South Kazakhstan University
Fergana State Technical University
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