Boundary layer stagnation-point flow over a stretching/shrinking cylinder in a nanofluid: A stability analysis

Abu Bakar, Nor Ashikin ; Bachok, Norfifah ; Md. Arifin, Norihan

Abstract

The stability analysis of steady boundary layer stagnation-point flow over a stretching/shrinking cylinder using Buongiorno model has been numerically studied. Using similarity transformations the governing partial differential equations have been transformed into a set of nonlinear differential equations and have been solved numerically using a shooting method in Maple software and a bvp4c method in Matlab software. These nanofluid model have been used which are taking into account the effects of Brownian motion and thermophoresis. The influences of the governing parameters namely the curvature parameter γ, Prandtl number Pr, Lewis number Le, Brownian motion parameter Nb and thermophoresis parameter Nt on the flow, heat and mass transfers characteristics have been presented graphically. The numerical results obtained for the skin friction coefficient, local Nusselt number and local Sherwood number have been thoroughly determined and presented graphically for several values of the governing parameters. From our investigation, it has been found that the non-unique (dual) solutions exist for shrinking cylinder and a unique solution exist for stretching cylinder. Otherwise, it has been observed that as curvature parameter increases, the skin friction coefficient, heat and mass transfer rates increase. Moreover, the stability analysis shows that the first solution is linearly stable, while the second solution is linearly unstable.

Keyword(s)

Stagnation-point flow; Stretching/shrinking cylinder; Nanofluid;Dual solutions; Stability analysis


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