Numerical solution of the Jeffery–Hamel flow through the wavelet technique

Abstract

AbstractThe theory of viscous fluid flow through convergent and divergent channels has many applications in chemical, aerospace, civil, biomechanical, mechanical, and environmental engineering. It also plays a role in sympathetic rivers and canals and in human anatomy, in how capillaries and arteries are linked. In this study, we developed a new operational matrix of integration with the Hermite wavelet. We proposed a new method called the Hermite wavelet method (HWM) to solve the highly nonlinear Jeffery–Hamel flow problem. The proposed technique is beneficial and appropriate for solving nonlinear differential equations. Furthermore, the outcomes are compared with other techniques such as differential transformation method, homotopy perturbation method, variational iteration method, and Runge–Kutta method in the literature, revealing that the current method's solution is better than those of other methods. The obtained results show that HWM is more satisfactory and precise than the other known techniques in the literature. Also, the property of Reynolds number, convergent, and divergent replica of the channel on applications of the Jeffery–Hamel flow is discussed.