Convection instability of linear Oldroyd-B fluids in a vertical channel with non-Fourier heat flux model.

This article investigates the convective instability of linear Oldroyd-B viscoelastic fluids in a vertical channel incorporating a non-Fourier heat flux model, specifically the Cattaneo–Christov formulation that accounts for thermal relaxation time. Using linear stability analysis and the Chebyshev collocation method, the study examines how relaxation time (Λ1), retardation time (Λ2), and the Cattaneo number (C) influence the onset and nature of convection. Results indicate that both the non-Fourier effect (represented by C) and the fluid’s relaxation time promote instability and oscillatory convection, causing the neutral stability curve to split into stationary and oscillatory branches; conversely, increasing retardation time inhibits instability. The study reveals a novel phenomenon where, under the combined effects of viscoelasticity and non-Fourier heat flux, the neutral stability curve transitions from a single branch to two branches and back to a single branch as relaxation time increases.