Abstract
The classical von Karman equations governing the boundary layer flow induced by a rotating disk are solved using the spectral homotopy analysis method and a novel successive linearisation method. The methods combine nonperturbation techniques with the Chebyshev spectral collocation method, and this study seeks to show the accuracy and reliability of the two methods in finding solutions of nonlinear systems of equations. The rapid convergence of the methods is determined by comparing the current results with numerical results and previous results in the literature.
Highlights
Most natural phenomena can be described by nonlinear equations that, in general, are not easy to solve in closed form
Our focus is on the original von Karman equation for the steady, laminar, axially symmetric viscous flow induced by an infinite disk rotating steadily with angular velocity Ω about the z-axis with the fluid confined to the half-space z > 0 above the disk
To check the accuracy of the successive linearisation method and the spectral homotopy analysis method, comparison is made with numerical solutions obtained using the Matlab bvp4c routine, which is an adaptive Lobatto quadrature scheme see 22
Summary
Most natural phenomena can be described by nonlinear equations that, in general, are not easy to solve in closed form. The study of the steady, laminar, and axially symmetric viscous flow induced by an infinite disk rotating steadily with constant angular velocity was pioneered by von Karman 1 He showed that the Navier-Stokes equations could be reduced to a set of ordinary differential equations and solved using an approximate integral method. Turkyilmazoglu used the homotopy analysis method to solve the equations governing the flow of a steady, laminar, incompressible, viscous, and electrically conducting fluid due to a rotating disk subjected to a uniform suction and injection through the walls in the presence of a uniform transverse magnetic field For this extended form of the von Karmam problem, the homotopy analysis method, produced secular terms in the series solution. Inter alia, that notwithstanding the fact that these two methods may involve more computations per step than the HAM, both the SHAM and SLM are efficient, robust, and converge much more rapidly compared to the standard homotopy analysis method
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
