Startup of Couette Flow and the Rayleigh–Stokes Problem in a Right-Angled Isosceles Triangular Channel

Exact solutions of the Navier–Stokes equations are derived for three startup flows in a right-angled isosceles triangular channel: Couette flow driven by impulsive motion of the hypotenuse, Couette flow driven by impulsive motion of one leg, and the Rayleigh–Stokes problem with all three walls set simultaneously into motion. Explicit transient series are obtained for the velocity field, the volumetric flow rate, and the net viscous momentum transfer. These solutions show how the triangular geometry modifies the transient response and the wall loading, and they provide exact benchmarks for startup flows in a non-separable domain.