Díaz Díaz, Jesús IldefonsoStraughan, Brian2023-06-202023-06-202004-051432-095910.1007/s00161-003-0158-9https://hdl.handle.net/20.500.14352/49549Until now, an unconditional nonlinear energy stability analysis for thermal convection according to Navier–Stokes theory had not been developed for the case in which the viscosity depends on the temperature in a quadratic manner such that the viscosity has a maximum. We analyse here a model of non-Newtonian fluid behaviour that allows us to develop an unconditional analysis directly when the quadratic viscosity relation is allowed. By unconditional, we mean that the nonlinear stability so obtained holds for arbitrarily large perturbations of the initial data. The nonlinear stability boundaries derived herein are sharp when compared with the linear instability thresholds.engjournal articlehttp://www.springerlink.com/content/0935-1175/open access517.956.4Thermal convectionNonlinear stabilityEnergy methodAnálisis numérico1206 Análisis Numérico