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<p>This study investigates natural convection in a fluid-saturated porous medium that features constant volumetric internal heating and is influenced by a gravity field that varies with distance. A key innovation of this research is analyzing four distinct configurations of gravity variation and their effects on the onset of convection in a three-dimensional rectangular enclosure. An unsteady Navier–Stokes equations and temperature equation, incorporating Boussinesq approximations, are solved numerically. A significant contribution of this work is applying Chebyshev pseudospectral method to determine critical Rayleigh numbers through linear and nonlinear stability analyses. This study uniquely explores how different boundary conditions, specifically, non-permeable and conductive, permeable and non-conductive, and other combinations, affect the system’s stability. Thus, results reveal a subcritical instability region for Rayleigh numbers influenced by internal heat, variable gravity coefficients, and wavenumbers, depending on specific boundary conditions and selected polynomial gravity functions. Additionally, findings indicate that the system exhibits enhanced stability with configuration B1 (non-permeable and conductive top and bottom boundaries) and reduced stability with configuration B3 (non-permeable and non-conductive bottom boundary with a permeable and non-conductive top boundary) across all gravity profiles.</p>

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Linear and Nonlinear Analysis of a Fluid in an Internally Heated Porous Rectangular Enclosure with Variable Gravity Field

  • 期刊论文

  • 发表日期：

    2025年8月21日

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  • Amit Mahajan,
  • Madhvi Raj

摘要

This study investigates natural convection in a fluid-saturated porous medium that features constant volumetric internal heating and is influenced by a gravity field that varies with distance. A key innovation of this research is analyzing four distinct configurations of gravity variation and their effects on the onset of convection in a three-dimensional rectangular enclosure. An unsteady Navier–Stokes equations and temperature equation, incorporating Boussinesq approximations, are solved numerically. A significant contribution of this work is applying Chebyshev pseudospectral method to determine critical Rayleigh numbers through linear and nonlinear stability analyses. This study uniquely explores how different boundary conditions, specifically, non-permeable and conductive, permeable and non-conductive, and other combinations, affect the system’s stability. Thus, results reveal a subcritical instability region for Rayleigh numbers influenced by internal heat, variable gravity coefficients, and wavenumbers, depending on specific boundary conditions and selected polynomial gravity functions. Additionally, findings indicate that the system exhibits enhanced stability with configuration B1 (non-permeable and conductive top and bottom boundaries) and reduced stability with configuration B3 (non-permeable and non-conductive bottom boundary with a permeable and non-conductive top boundary) across all gravity profiles.