The rotational flow of a non-Newtonian fluid whose viscosity is simultaneously dependent upon temperature and shear rate is analyzed while viscous heating is taken into account. Exponential dependence of viscosity on temperature is modeled through Nahme law and the shear dependency is modeled according to the non-isothermal Carreau equation. The six-dimensional dynamical system, resulted from equations of the conservation of mass and momentum and energy, includes highly correlated terms a solution of which is numerically difficult to converge. Inclusion of the temperature dependence of viscosity as well as viscous heating result in arriving at more realistic simulation of the nonlinear flow. In presence of viscous heating, the effect of Nahme number on the stability of the flow is examined. Complete flow field are given for different scenarios of the flow.

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