Linear Instability of Penetrative Double‐Diffusive Convection in a Darcy–Brinkman–Kelvin–Voigt Fluid‐Saturated Porous Medium: A Numerical Study

ABSTRACT A numerical study is performed to analyze the linear instability of penetrative double‐diffusive convection (DDC) in a Darcy–Brinkman–Kelvin–Voigt fluid‐saturated porous medium, focusing on the combined influence of viscoelastic stresses and internal heat generation on instability onset. A linear stability analysis is performed by formulating the governing equations as a generalized eigenvalue problem, which is solved numerically using the Galerkin method. Three velocity boundary configurations: rigid–rigid (RR), rigid–free, and free–free (FF) are examined, revealing two distinct instability regimes. The critical conditions for the onset of convection are determined for both stationary and oscillatory modes under various velocity boundary configurations. The stationary mode of convection is unaffected by the Voigt viscoelastic parameter, consistent with the steady conductive base state. However, the oscillatory mode is strongly modulated by viscoelasticity, internal heat generation, and double‐diffusive mechanisms. Viscoelastic stresses suppress time‐dependent disturbances, increase the oscillatory critical thermal Darcy–Rayleigh number, and significantly reduce oscillation frequency, while the internal heat source exerts a destabilizing influence by enhancing buoyancy forces and lowering critical thresholds. Solutal buoyancy, permeability, the Darcy–Prandtl number, the diffusivity ratio, and the effective heat capacity group are found to play competing stabilizing and destabilizing roles, shaping both the spatial and temporal characteristics of the instability. A consistent stability ordering of boundary conditions is observed, with FF boundaries being the least stable and RR boundaries the most stable. Excellent agreement with previously published results in limiting cases validates the accuracy and robustness of the numerical formulation. The present findings synthesize the competing thermal, solutal, elastic, and porous effects governing internally heated DDC in viscoelastic media. Future extensions of this work may address nonlinear stability, variable internal heat generation, and spatially nonuniform porous structures, thereby broadening its relevance to geophysical, energy, and industrial applications.