Flow past a porous plate of a new class of fluids with limiting stress: Analytical results and linear stability analysis

We study the linearized stability of the flow of a non-Newtonian fluid that is capable of describing the response of a large class of fluids that seemingly mimic the response of viscoplastic materials like paints, food products, solutions, etc. The flow takes place over a porous solid plate subject to suction at the plate. Not surprisingly, we find that suction decreases the boundary layer thickness and stabilizes the flow, and outside the boundary layer, the velocity is nearly the same as the free-stream velocity. The critical Reynold’s number and marginal stability curves that demarcate the region within which perturbations are stable to linearized disturbances versus those that are unstable, as function of the Reynold’s number, are determined. We find that the flows of the fluid under consideration are more stable than the corresponding flows for the Navier-Stokes fluid. • We investigate the flow of a fluid that seemingly mimics the behavior of a viscoplastic material. • We study the steady state base flow. • We perturb the base flow and study linear stability. • We solve the perturbed eigenvalue problem. • We plot marginal stability curves and discuss the effects of the physical parameters.