Stability of Natural Convection in a Vertical Porous Layer of Viscoelastic Navier–Stokes–Voigt Fluid
D. L. Shivaraj
Abstract
Abstract This study investigates the linear stability of natural convection in a vertical Darcy–Brinkman porous layer saturated with a viscoelastic Navier–Stokes–Voigt (NSV) fluid, which is equivalent to a zero-order Kelvin–Voigt fluid. The coupled Orr–Sommerfeld equations (OS-EQ) governing the stability of the flow are derived and solved using two prominent numerical methods: the Galerkin method (GM) and the Chebyshev collocation method (CCM). Basis functions and their derivatives are constructed through symbolic integration to enhance computational accuracy. The resulting eigenvalue problem is solved using advanced eigenvalue solvers from the International Mathematics and Statistics Library (imsl) via the python Interface for the International Mathematics and Statistics Library (pyimsl), version 2020.0.1. Additionally, high-performance computing packages such as the Portable, Extensible Toolkit for Scientific Computation (petsc), via its python bindings (petsc4py version 3.21.4), and the Scalable Library for Eigenvalue Problem Computations (slepc), via its python bindings (slepc4py version 3.21.1), were utilized. The study focuses on capturing the most unstable modes that trigger the onset of instability. The influence of the Grashof number (G), porous parameter (M), Kelvin–Voigt elasticity (Λ), and Prandtl number (Pr) on flow stability is extensively analyzed. The eigenvalue spectra, neutral stability curves, critical triplet analysis, and streamline–isotherm distributions collectively demonstrate that the porous parameter strongly stabilizes both stationary and traveling wave modes by suppressing oscillatory disturbances and enhancing flow stability. In contrast, the Kelvin–Voigt parameter exhibits a dual nature, although its influence is less significant in stationary modes compared to traveling wave modes. In this configuration, increasing the Prandtl number reduces thermal diffusion and enhances the growth of disturbances, thereby acting as a destabilizing agent. Furthermore, the non-porous medium and Newtonian fluid cases have been examined as limiting scenarios.