Centrifugal and Archimedean buoyancy effects on the stability of spiral Poiseuille flow with radial heating

We investigate the linear temporal stability of non-isothermal spiral Poiseuille flow between two coaxial, vertically oriented, differentially heated rotating cylinders, accounting for both centrifugal and gravitational buoyancy effects. The stability characteristics are analyzed for counter-rotating, stationary, and co-rotating configurations, corresponding to rotation rate ratios μ=Ωo/Ωi=−0.5,0, and 0.5, respectively, where Ωo and Ωi are angular velocities of the outer and inner cylinders, respectively. The analysis is carried out for a fixed radius ratio η=Ri/Ro=0.5, where Ri and Ro are the inner and outer cylinder radii, respectively, with air as the working fluid. Thermal effects are characterized by the Grashof number (Gr), with results presented for Gr=102, 103, and 104. The findings show that thermal buoyancy strongly alters the stability boundaries at higher Gr. For μ=0 and μ=−0.5, increasing thermal forcing leads to pronounced shifts in the stability boundaries, markedly different from both the isothermal case and earlier non-isothermal spiral Poiseuille flow studies that account for only centrifugal buoyancy mechanism. For μ=0.5, the stability boundary exhibits two distinct branches connected by a turning point at Gr=102 and 103, while at Gr=104 these branches become disconnected, indicating a qualitative change in the instability behavior under strong thermal forcing. For each Gr, a threshold Reynolds number is identified beyond which the instability transitions toward a Tollmien–Schlichting-type mode, rendering the flow unstable for all Taylor numbers (Ta) and accompanied by a sharp reduction in the critical azimuthal wavenumber. For all considered values of μ, the critical Taylor number decreases with increasing Grashof number, indicating a progressively destabilizing effect of thermal forcing. Flow visualizations based on helical stream functions further reveal distinct instability structures, highlighting the complex interactions among rotation, shear, and thermal buoyancy.