Stability of Plane Channel Flow With Viscous Heating

The linear stability analysis of pressure-driven flow undergoing viscous heating through a channel is considered. The walls of the channel are maintained at different constant temperatures and Nahme's law is applied to model the temperature dependence of the fluid viscosity. A modified Orr-Sommerfeld equation coupled with a linearized energy equation is derived and solved using an efficient spectral collocation method. Our results indicate that increasing the influence of viscous heating is destabilizing. It is also shown that the critical Reynolds number decreases by one order of magnitude with increase in the Nahme number. An energy analysis is conducted to understand the underlying physical mechanism of the instability.