Stability Analysis of Mass Transfer Effects on the Unsteady Stagnation-Point Flow Past a Permeable Sheet

Abstract

This study involves the problem of mass transfer effects on unsteady stagnation-point flow through a permeable stretching/shrinking sheet. Similarity transformations in the form of nonlinear partial differential equations to ordinary differential equations were used to reduce the basic governing equations. The resulting equations were then solved numerically using the bvp4c function and shooting method. The programming codes for bvp4c function were built using Matlab software, whereas the programming codes for shooting method were built using Maple software. The effects of the Schmidt number, stretching/shrinking, suction/injection, unsteadiness and the reaction rate parameter on the flow and mass transfer characteristics were numerically analysed. The boundary layer thickness and velocity gradient are also influenced by these parameters. Dual solutions were figured out for the problems involving stretching/shrinking sheet at the stagnation-point. To determine the stability of the solutions obtained, stability analysis was performed by solving the linear eigenvalue problems using the bvp4c function. The analysis showed that for the first solution, there was an initial decay of disturbance, while the second and third solutions were opposite, where an initial growth of disturbance were detected for both. This result indicated that the first solution was more stable and physically realizable compared to others.