Temporal stability of multiple similarity solutions for porous channel flows with expanding or contracting walls

In this paper, the temporal stability of multiple similarity solutions (flow patterns) for incompressible laminar fluid flow along a uniformly porous channel with expanding or contracting walls is analyzed. This work extends recent results perturbations Sun et al. [“Temporal analysis viscous flows in channels moving walls,” Appl. Math. Modell. 77, 738–755 (2020)] by examining general form (including and nonsimilarity forms). Based on linear theory, two-dimensional eigenvalue problems associated equations are formulated numerically solved finite difference method staggered grids. The reveals that same under within range wall expansion ratio α. [ −5≤α≤3 as al., “Temporal (2020)]. Further, it found α has great influence type I flows: case contraction ( α<0), region cross-flow Reynolds number (R) increases |α|) increases; 0<α≤1, (α) 1≤α≤3, stable all R where they exist. other types (types II III IV = 3) always unstable. As nonlinear validation analysis, original time-dependent problem an initial perturbation over those patterns directly. It consistent analysis.