Steady flow of Johnson-Segalman fluid through porous medium over an inclined plate

Abstract

A mathematical model is presented for the thin-film flow of Johnson-Segalman fluid through porous medium down an inclined plate under steady-state flow. The developed model is based on modified Darcy's law for viscoelastic fluid. The nonlinear equation derived from the model is solved using the Adomian decomposition method to obtain an approximate analytical solution. The results of the proposed model are compared with the numerical solution that is obtained using Mathematica solver NDSolve. Graphically, it is shown that both solutions have almost the same behavior. Sensitivity analysis is conducted to highlight the importance of the inclination angle, ratio of viscosity, slip parameter, and Wissenberg number on the fluid velocity. The results reveal that the velocity is increased by raising the inclination angle or the Wissenberg number. Moreover, the velocity decreases by increasing the slip parameter or the ratio of viscosity.