Penetrative convection in Navier-Stokes-Voigt fluid induced by internal heat source

This study investigates the phenomenon of penetrative convection in a viscoelastic fluid described by the Navier-Stokes-Kelvin-Voigt (NSKV) model, incorporating internal heat sources and realistic rigid boundary conditions. We examine four distinct space-dependent heat source distributions: constant, linearly increasing, decreasing, and non-uniform across the fluid layer. The Kelvin-Voigt fluid layer is simultaneously heated and salted from the bottom. We employ both linear instability analysis using normal mode technique and nonlinear stability analysis through energy method. The resulting differential eigenvalue systems are treated using the Chebyshev-Spectral-QZ method. Our investigation focuses on the effects of the internal heating parameter, Kelvin-Voigt number, and solute Rayleigh number on the threshold values for convection onset. Our results reveal that internal heat sources destabilize the fluid system, while the salt Rayleigh number contributes to system stabilization. Nonlinear analysis reveals that the total energy of perturbations to the steady-state conduction solutions decays exponentially, and the decay rate is stronger for the Kelvin-Voigt fluid than for Newtonian fluid. Furthermore, the Kelvin-Voigt number acts as a stabilizing factor for the onset of convection, exerting a stabilizing effect on the system. Importantly, the thresholds obtained from linear and nonlinear theories differ in both the presence and absence of internal heat sources, suggesting the existence of a subcritical instability region (SIR). This comprehensive analysis provides new insights into the complex dynamics of penetrative convection in viscoelastic fluids with internal heating.