Transition to Turbulence in a Heated Non-Newtonian Pipe Flow

A simplified mono-dimensional model for investigating the transition to turbulence in nonisothermal and non-Newtonian pipe flows is proposed. The flow stability is analyzed within the framework of such a model, showing that uniformly heating the pipe wall leads to an earlier transition to turbulence, while differentially heating the pipe wall produces a stabilizing effect. For power-law fluids, we also demonstrate that an increase in the power-law index, i.e., passing from shear-thinning to shear-thickening fluids, leads to a stabilization of the system.