Numerical simulation by using the spectral collocation optimization method associated with Vieta-Lucas polynomials for a fractional model of non-Newtonian fluid

Abstract

The present study is made to develop the fractional model of non-Newtonian Casson and Williamson boundary layer flow in the fluid flow taking into account the heat flux and the slip velocity. The temperature and the velocity fields, of the steady boundary layer flow, are generated by a stretched sheet with a non-uniform thickness. The governing non-linear system of PDEs is transformed into a non-linear set of coupled ODEs and then solved by using the Vieta-Lucas polynomials that will be used to implement the spectral collocation method. We used a more accurate formula for the fractional derivative (Caputo sense) which is derived in a previous work. The resulting system of ODEs is transformed using the suggested method into a non-linear system of algebraic equations. The system is built as a constrained optimization problem, then optimized to obtain the series solution’s unidentified coefficients. The results show that the skin-friction coefficient increases with increasing magnetic number, whereas the Casson and the local Williamson parameters exhibit reverse behavior. In addition, the effectiveness and accuracy of the proposed method are satisfied by computing the residual error function. The estimated solutions produced by using the given method were physically acceptable and accurate.

Keywords

• Non-Newtonian fluid
• Non-uniform stretching sheet
• Slip velocity
• Caputo fractional derivative
• Spectral collocation method
• Vieta-Lucas polynomials