On successive linearization method for differential equations with nonlinear conditions

This paper presents a new technique for solving linear and nonlinear boundary value problems subject to linear or nonlinear conditions. The technique is based on the blending of the Chebyshev pseudospectral method. The rapid convergence and effectiveness are verified by several linear and nonlinear examples, and results are compared with the exact solutions. Our results show a remarkable improvement in the convergence of the results when compared with exact solutions.

The Effectiveness of Mass Transfer in the MHD Upper-Convected Maxwell Fluid Flow on a Stretched Porous Sheet near Stagnation Point: A Numerical Investigation

The present inquiry studies the influence of mass transfer in magnetohydrodynamics (MHD) upper-convected Maxwell (UCM) fluid flow on a stretchable, porous subsurface. The governing partial differential equations for the flow problem are reformed to ordinary differential equations through similarity transformations. The numerical outcomes for the arising non-linear boundary value problem are determined by implementing the successive linearization method (SLM) via Matlab software. The accuracy of the SLM is confirmed through known methods, and convergence analysis is also presented. The graphical behavior for all the parametric quantities in the governing equations across the velocity and concentration magnitudes, as well as the skin friction and Sherwood number, is presented and debated in detail. A comparability inquiry of the novel proposed technique, along with the preceding explored literature, is also provided. It is expected that the current achieved results will furnish fruitful knowledge in industrious utilities and correlate with the prevailing literature.

Dissipative effects on a chemically and thermally radiative heat fluid flow past a shrinking porous sheet

The present study analyses the dissipative influence into an unsteady electrically conducting fluid flow embedded in a pervious medium over a shrinkable sheet. The behavior of thermal radiation and chemical reactions are also contemplated. The governing partial differential equations are reformed to ordinary differential equations by operating similarity transformations. The numerical outcomes for the arising non-linear boundary value problem are determined by implementing the Successive linearization method (SLM) via Matlab software. The velocity, temperature, and concentration magnitudes for distant values of the governing parametric quantities are conferred, and their conduct is debated via graphical curves. The surface drag coefficient increases, whereas the local Nusselt number and Sherwood number decreases for enhancing unsteadiness parameter across suction parameter. Moreover, the magnetic and suction parameters accelerate velocity magnitudes while by raising porosity parameter, velocity decelerates. Larger numeric of thermal radiation parameter and Eckert number accelerates the temperature profile while by enhancing Prandtl number it decelerates. Schmidt number and chemical reaction parameters slowdowns the concentration distribution, and the chemical reaction parameter influences on the point of chemical reaction that benefits the interface mass transfer. It is expected that the current achieved results will furnish fruitful knowledge in industrious utilities.

Pipe resistance coefficients identification of water networks considering solvable conditions

To make hydraulic models more accurate and realistic, this paper proposes a method to identify pipe resistance coefficients (PRCs) by using the measured heads at partial nodes. A successive linearization method is adopted to solve for the pipe flows, node heads, and PRCs. Based on the matrix analysis theory, the relationships among the number and location of measurement sites, number of hydraulic conditions (HCs), and solvable condition of PRC identification are established. The proposed method can identify all the PRCs when a solvable condition can be satisfied. In addition, the analysis process can be used as a tool to evaluate whether a given arrangement of measurement sites can meet the solvable condition of PRC identification, and to determine the minimum number of HCs. The performed case studies verified the feasibility of the proposed method, and the determined accuracy of PRC identification was noted to satisfy the actual engineering requirements.

Bioconvection of Micropolar Fluid in an Annulus

This paper deals with the bioconvection of microploar fluid in an annulus containing microorganisms in which the outer cylinder is rotating. A mathematical model, with a fully coupled system of partial differential equations presenting the velocity, total mass, momentum, thermal energy, mass diffusion, and motile microorganisms is presented. A suitable transformations is adopted to reduce the governing non-linear governing to a set of non-linear ordinary differential equations and then linearized by means of successive linearization method. The resulign linearized equaions are solved using Chebyshev collocation method. The illustrating analysis of influences of the various flow governing physical parameters such as the micropolar coupling number, the bioconvection Schmidt-number, Prandtl number, Lewis number and bioconvection Peclet-number and Reynolds number on motile microorganism distribution are studied and is presented. Also, the density number of motile microorganism is examined for various governing parameters along with slip parameter of motile microorganism.

Heat transfer on magnetohydrodynamic stagnation point flow through a porous shrinking/stretching sheet: A numerical study

This article examines the numerical study of heat transfer analysis on MHD stagnation point flow past a permeable shrinking/stretching sheet through a porous media. The governing equations have been reduced to the ODE by utilizing similarity variables. The obtained highly non-linear coupled differential equations have been solved by implementing a numerical scheme labeled as successive linearization method. The influences for the pertinent parameters on velocity profile and temperature profile is debated and demonstrated graphically. Numerical comparisons in some special cases have been brought along the prevailing literature, and it is noticed that the current outcomes are in good concord.