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Abstract <p>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 (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({t_{50}},{t_{95}}\)</EquationSource> <!--MatModCS2570064Ismailov-m1--> </InlineEquation>). 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.</p>

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Parabolic PDE and FEM Analysis of Layer Resolved Moisture Diffusion in Wheat Kernels

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Khairulla Ismailov,
  • Bakhtiyar Ismailov,
  • Abdushukur Urinboev

摘要

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 ( \({t_{50}},{t_{95}}\) ). 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.