Flow of viscoelastic fluids through a porous channel—I

Abstract

AbstractThe flow of viscoelastic fluids through a porous channel with one impermeable wall is computed. The flow is characterized by a boundary value problem in which the order of the differential equation exceeds the number of boundary conditions. Three solutions are developed: (i) an exact numerical solution, (ii) a perturbation solution for small R, the cross‐flow Reynold's number and (iii) an asymptotic solution for large R. The results from exact numerical integration reveal that the solutions for a non‐Newtonian fluid are possible only up to a critical value of the viscoelastic fluid parameter, which decreases with an increase in R. It is further demonstrated that the perturbation solution gives acceptable results only if the viscoelastic fluid parameter is also small.Two more related problems are considered: fluid dynamics of a long porous slider, and injection of fluid through one side of a long vertical porous channel. For both the problems, exact numerical and other solutions are derived and appropriate conclusions drawn.