Investigation of the structure of non-isothermal power-law fluid flow in an $\mathrm{L}$-shaped channel

This paper is devoted to the investigation of a steady-state non-isothermal power-law fluid flow in a flat $\mathrm{L}$-shaped channel with account for viscous dissipation. Mathematical model of the flow includes the motion, continuity, and energy equations written using the dimensionless variables in a Cartesian coordinate system. The fluid rheological behavior is described by the Ostwald-de Waele power law with an exponential dependence of the consistency on temperature. The control volume method and the SIMPLE procedure are applied to solve the formulated problem numerically using the staggered computational grid. The effect of both power-law index and Reynolds and Brinkman numbers on the size of recirculation zones observed in the vicinity of internal and external angles of the $\mathrm{L}$-channel and on the size of two-dimensional flow regions is studied. It is found that the variation in the intensity of mechanical energy dissipation in a stream leads to a weak change in the flow pattern. Considering rising of the power-law index from the values providing pseudoplastic properties of the fluid to that providing dilatant properties, the size of recirculation zone in the vicinity of internal angle is found to tend to a constant value. With an increase in the power-law index, the two-dimensional flow region ahead of the stream turn increases and tends to a constant value, and after turn it decreases. The results obtained for a Newtonian fluid are in a good agreement with numerical and experimental data of other authors.