This study aims to investigate the linear and nonlinear stability characteristics of double-diffusive convection in a viscoelastic fluid layer with higher-order diffusion effects, extended by incorporating the Biot number to account for convective heat exchange at the boundaries.
The Biot number is introduced to non-dimensionalize the governing equations. The classical thermal boundary conditions are replaced by Robin-type conditions to model realistic heat transfer at the boundaries. Linear stability analysis is carried out using normal mode techniques, leading to an eigenvalue problem solved numerically via a spectral collocation method. Global stability thresholds are determined by applying the energy method to nonlinear stability.
The base temperature distribution and the system’s stability characteristics are significantly altered by the addition of the Biot number. Increasing the Biot number enhances heat transfer at the boundaries, which raises the critical thermal Rayleigh number and stabilizes the system. The boundary heat exchange mechanism influences both oscillatory and stationary instability modes, with notable changes in stability thresholds depending on the Biot number and other governing parameters.
This work extends classical double-diffusive convection studies by incorporating convective boundary effects through the Biot number, thus providing a more realistic thermal boundary framework. The study bridges the gap between perfectly conducting and thermally insulated boundaries and highlights the role of boundary heat transfer in controlling convective instability in viscoelastic fluids. The findings have engineering relevance for heat exchanger design, polymer processing and geothermal energy extraction, where controlling convection onset via boundary heat management can improve operational efficiency and stability.
