Temporal linear stability analysis of an entry flow in a channel with viscous heating

A non-isothermal flow in the entry region of a straight channel in the presence of viscous heating is investigated via direct numerical simulations and a temporal linear stability analysis. Initially, the system is maintained at an isothermal state. As the time progresses, the temperature near the channel walls increases, which in turn decreases the viscosity of the working fluid. This resulting viscosity-stratification in the flow gives rise to an unexpected stability behavior. From the linear stability analysis, we found that viscous heating has a destabilising influence, and the flow becomes linearly unstable to infinitesimal small disturbance near the developing region of the channel. We also found that increasing the Reynolds number and decreasing the Prandtl number enhance the instability behavior. For the parameter values considered, the Grashof number does not change the stability characteristics qualitatively. These findings may be relevant to several industrial applications, such as lubrication, tribology, food processing, instrumentation, and polymer processing, to name a few.