Hybrid differential evolution algorithm for Falkner-Skan flow with rotation

Abstract

A hybrid differential evolution algorithm is used in this work to study the rotating transport of Falkner-Skan flow. The problem is modeled as an equivalent optimization problem by using Padé rational approximation functions. The primary model of the governing partial differential equations is imposed to subjugate the error between profiles. A hybrid evolutionary algorithm based on differential evolution and a convergent version of Nelder-Mead direct search algorithm is employed to perform global exploratory search along with an enhanced exploitation to improve the accuracy of the proposed solution scheme. The resulting scheme is named as evolutionary Padé approximation (EPA) scheme. The performance of the proposed EPA scheme on the Falkner-Skan boundary value problem is investigated by considering various values of the rotation parameters. The developed optimizer in EPA scheme was able to minimize the residuals up to${10}^{-10}$. Results are displayed graphically in order to study the effect of various types of parameters. EPA scheme determined that angular velocity increases or decreases accordingly as fluid parameter $\left(\beta \right)$ and the rotation parameter $\left(\lambda \right)$ but shows inverse behavior with respect to power law index$\left(n\right)$. Similarly, the response of velocity profile along $y-axis$ was decreasing function of $\beta$ as well as $n$ but increasing function of λ. The performance of the proposed EPA scheme has been demonstrated by comparing results with a hybrid neural network scheme and found in excellent agreement.