Viscous heating effects on the linear stability of Poiseuille flow of an inelastic fluid

In this paper, the effect of viscous heating on the stability of a non-Newtonian fluid flowing between two parallel plates under the effect of a constant pressure gradient is investigated. The viscosity of the fluid depends on both temperature and shear rate. Exponential dependence of viscosity on temperature is modeled through Arrhenius law. Non-Newtonian behavior of the fluid is modeled according to the Carreau rheological model. Motion and energy balance equations that govern the base flow and the stability of the flow are coupled and the solution to the problem is found iteratively using a pseudospectral method based on the Chebyshev polynomials. In the presence of viscous heating, the effect of activation energy parameter, Prandtl and Brinkman numbers, material time and power-law constants on the stability of the flow is presented in terms of neutral stability curves.