Effect of viscosity models on the stability of a Non-Newtonian fluid in a channel with heat transfer

This study investigates the effect of temperature-dependent and shear-thinning viscosity of a non-Newtonian fluid on the stability of a channel flow. Exponential dependence of viscosity on temperature is modeled through Arrhenius law and Nahme Law. Non-Newtonian behaviour of the fluid is modeled according to the Carreau rheological equation. Channel walls are kept at constant but different temperatures. Steady base flow governing boundary value problem and stability governing eigenvalue problem are solved using a pseudospectral method based on Chebyshev polynomials. Results are presented in the form of marginal stability curves. It is found that fluids obeying the Arrhenius law are more stable than those of Nahme law if both models are used on the same temperature-sensitive viscosity, reference viscosity and temperature.