Characterization of magnetized CNT-based hybrid nanofluid subjected to convective phenomenon

Hybrid nanofluid gains attention of scientists due to its dynamic properties in various fields, and thus, hybrid nanofluids can be taken as an innovative form of nanofluids. Even though analysts acquire tremendous results in the field of hybrid nanofluids but yet no study has been carried out to predict magnetohydrodynamic effects in such fluid models. In this present analysis, influence of MHD has been investigated for the micro hybrid nanofluid over a stretched surface under convective conditions. Combine boundary layer equations for the flow have been altered into a suitable form via boundary layer approximations. Further, complete nonlinear system of equations has been numerically solved via BVP-4C method. Interesting results have been demonstrated for an exponentially stretched surface and expressed in the form of shear stress and rate of heat transfer. Results have also been visualized in the form of streamlines and isotherms. This study reveals after observing the numeric values of skin friction and Nusselt number that micropolar hybrid nanofluid models have greater heat transfer rate as compared to nanofluids.

Design General Cam Profiles Based on Finite Element Method

This paper presents a general framework to design a cam profile using the finite element method from given displacements of the follower. The arbitrarily complex cam profile is described by Lagrangian finite elements, which are formed by the connectivity of nodes. In order to obtain the desired profile, a penalty-type functional that enforces the prescribed displacement of the follower is proposed. Additionally, in order to ensure convexity of the functional, a numerical stabilization scheme is used. The nodal positions are then obtained by solving a nonlinear system of equations resulting from minimizing the total functional. The geometrical accuracy of the cam profile can be controlled by the number of finite elements. A case study is considered to illustrate the flexibility, accuracy, and robustness of the proposed approach.

Newton's method for the eigenvalue problem of a symmetric matrix

Newton's method for calculating the eigenvalue and the corresponding eigenvector of a symmetric real matrix is considered. The nonlinear system of equations solved by Newton's method consists of an equation that determines the eigenvalue and eigenvector of the matrix and the normalization condition for the eigenvector. The method allows someone to simultaneously calculate the eigenvalue and the corresponding eigenvector. Initial approximations for the eigenvalue and the corresponding eigenvector can be found by the power method or by the reverse iteration with shift. A simple proof of the convergence of Newton's method in a neighborhood of a simple eigenvalue is proposed. It is shown that the method has a quadratic convergence rate. In terms of computational costs per iteration, Newton's method is comparable to the reverse iteration method with the Rayleigh ratio. Unlike reverse iteration, Newton's method allows to compute the eigenpair with better accuracy.

On semilocal convergence of three-step Kurchatov method under weak condition

The purpose of this paper to establish the semilocal convergence analysis of three-step Kurchatov method under weaker conditions in Banach spaces. We construct the recurrence relations under the assumption that involved first-order divided difference operators satisfy the $$\omega $$ ω condition. Theorems are given for the existence-uniqueness balls enclosing the unique solution. The application of the iterative method is shown by solving nonlinear system of equations and nonlinear Hammerstein-type integral equations. It illustrates the theoretical development of this study.