Spectral collocation approach for fractional order 2D viscous flow through expanding and contracting porous wall model

Abstract

Abstract In this paper, 2-D viscous fluid flow in a expanding or contracting wall has been studied by incorporating fractional order in the Caputo sense. The governing two dimensional equations are transformed to a highly nonlinear fractional differential equations with associated initial and boundary conditions. The paper focuses on dual approach. Firstly, to apply a new and efficient numerical technique called spectral collocation to the governing model. The acquired results are validated by comparing with other numerical methods. The novelty of the present method lies when absolute/residual error converges as collocation points increases. These structures are captured in the form of figures. Secondly, the paper analyses the impact of various parameters such as seepage rate (Re), wall dilation rate ( $$\gamma $$ ), and fractional order ( $$\alpha $$ ) on the axial velocity. Additionally, the normal pressure and wall shear stress for different combination of Re and $$\gamma $$ for the fractional order derivative is analysed. Furthermore, the skin friction has been determined for various combinations of parameters. The results of the investigations indicate that skin friction diminishes with an increase in seepage or dilatation rate. All these calculations are displayed through tables and figures.