Viscoelastic sub-diffusive channel flow in a transverse magnetic field

We report the temporal linear stability as well as the nonlinear stability, via direct numerical simulations, of the viscoelastic sub-diffusive plane Poiseuille flow subjected to an external magnetic field. The fluid is described by the fractional upper-convected Maxwell constitutive model. Linear stability analysis reveals the critical conditions under which viscoelastic sub-diffusive flow transitions from stable to unstable regimes. Direct numerical simulations are shown to quantify the transitional pathway to the formation of the stable macrostructures. The spatiotemporally stable macrostructures within this flow paradigm are shown to be relevant to the experimentally observed transition of flow instability in sub-diffusive axisymmetric channel flows.