scholarly journals Application of Successive Linearisation Method to Squeezing Flow with Bifurcation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
S. S. Motsa ◽  
O. D. Makinde ◽  
S. Shateyi
Keyword(s):  
Wall Motion ◽  
Transient Flow ◽  
Nonlinear Differential Equations ◽  
Linearization Method ◽  
Squeezing Flow ◽  
Parallel Plates ◽  
Equation Modelling ◽  
Highly Nonlinear ◽  
Successive Linearization Method ◽  
Successive Linearisation Method

This paper employs the computational approach known as successive linearization method (SLM) to tackle a fourth order nonlinear differential equation modelling the transient flow of an incompressible viscous fluid between two parallel plates produced by a simple wall motion. Numerical and graphical results obtained show excellent agreement with the earlier results reported in the literature. We obtain solution branches as well as a turning point in the flow field accurately. A comparison with numerical results generated using the inbuilt MATLAB boundary value solver,bvp4c, demonstrates that the SLM approach is a very efficient technique for tackling highly nonlinear differential equations of the type discussed in this paper.

Double Dispersion Effects on MHD Squeezing Flow of UCM Fluid through a Porous Medium

2019 ◽  
Vol 392 ◽  
pp. 10-28
Author(s):  
N. Naresh Kumar ◽  
Pravin Kashyap Kambhatla ◽  
Odelu Ojjela
Keyword(s):  
Skin Friction ◽  
Wall Motion ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Squeezing Flow ◽  
Ucm Fluid ◽  
Highly Nonlinear ◽  
Dimensional Parameters ◽  
Double Dispersion ◽  
The Impact

The objective of the current problem is to explore the impact of wall motion on flow, heat and species concentration of a UCM fluid in a magnetohydrodynamic Darcian channel. The flow is confined between two moving walls. The effects of the wall motion on the physical quantities for expanding and contracting cases are studied through non-dimensional numbers and variables. Numerical solutions for the highly nonlinear differential equations are obtained by reducing the governing PDE to ODE using well-established similarity variables. The variation of skin friction, Nusselt and Sherwood numbers has been investigated with the help of surface plots so that the influence of the squeezing number on the other non-dimensional parameters can be deeply understood. The results suggest that the squeezing channel intensifies the mass transfer and skin friction at the walls and it also increases the velocity, temperature and concentration of the fluid across the channel.

scholarly journals On the Successive Linearisation Approach to the Flow of Reactive Third-Grade Liquid in a Channel with Isothermal Walls

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
S. S. Motsa ◽  
O. D. Makinde ◽  
S. Shateyi
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Linearization Method ◽  
Third Grade ◽  
Efficient Technique ◽  
Analytical Scheme ◽  
Highly Nonlinear ◽  
Successive Linearization Method ◽  
Modeling Flow

The nonlinear differential equations modeling flow of a reactive third-grade liquid between two parallel isothermal plates is investigated using a novel hybrid of numerical-analytical scheme known as the successive linearization method (SLM). Numerical and graphical results obtained show excellence in agreement with the earlier results reported in the literature. A comparison with numerical results generated using the inbuilt MATLAB boundary value solverbvp4cdemonstrates that the new SLM approach is a very efficient technique for tackling highly nonlinear differential equations of the type discussed in this paper.

scholarly journals Successive Linearization Analysis of the Effects of Partial Slip, Thermal Diffusion, and Diffusion-Thermo on Steady MHD Convective Flow due to a Rotating Disk

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
S. S. Motsa ◽  
S. Shateyi
Keyword(s):  
Thermal Diffusion ◽  
Nonlinear Boundary ◽  
Rotating Disk ◽  
Linearization Method ◽  
Partial Slip ◽  
Similarity Transformations ◽  
Highly Nonlinear ◽  
Successive Linearization Method ◽  
And Diffusion ◽  
The Magnetic Field

We proposed a general formulation of the successive linearization method for solving highly nonlinear boundary value problem arising in rotating disk flow. The problem was studied under the effects of partial slip, thermal diffusion, and diffusion-thermo. The governing fundamental conservation equations of mass, momentum, angular momentum, energy, and concentration are transformed into a system of ordinary differential equations by means of similarity transformations. A parametric study illustrating the influence of the magnetic field, slip factor, Eckert number, Dufour and Soret numbers was carried out.

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

2020 ◽  
pp. 1-14
Author(s):  
A. Shahid ◽  
M. Ali Abbas ◽  
H.L. Huang ◽  
S.R. Mishra ◽  
M.M. Bhatti
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Linearization Method ◽  
Surface Drag ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Dissipative Effects ◽  
Successive Linearization Method

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.

scholarly journals A generalized perspective of Fourier and Fick’s laws: Magnetized effects of Cattaneo-Christov models on transient nanofluid flow between two parallel plates with Brownian motion and thermophoresis

2020 ◽  
Vol 9 (1) ◽  
pp. 201-222 ◽  
Author(s):  
Usha Shankar ◽  
Neminath B. Naduvinamani ◽  
Hussain Basha
Keyword(s):  
Brownian Motion ◽  
Joule Heating ◽  
Concentration Field ◽  
Double Diffusion ◽  
Diffusion Models ◽  
Time Dependent ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Casson Nanofluid ◽  
Highly Nonlinear

AbstractPresent research article reports the magnetized impacts of Cattaneo-Christov double diffusion models on heat and mass transfer behaviour of viscous incompressible, time-dependent, two-dimensional Casson nanofluid flow through the channel with Joule heating and viscous dissipation effects numerically. The classical transport models such as Fourier and Fick’s laws of heat and mass diffusions are generalized in terms of Cattaneo-Christov double diffusion models by accounting the thermal and concentration relaxation times. The present physical problem is examined in the presence of Lorentz forces to investigate the effects of magnetic field on double diffusion process along with Joule heating. The non-Newtonian Casson nanofluid flow between two parallel plates gives the system of time-dependent, highly nonlinear, coupled partial differential equations and is solved by utilizing RK-SM and bvp4c schemes. Present results show that, the temperature and concentration distributions are fewer in case of Cattaneo-Christov heat and mass flux models when compared to the Fourier’s and Fick’s laws of heat and mass diffusions. The concentration field is a diminishing function of thermophoresis parameter and it is an increasing function of Brownian motion parameter. Finally, an excellent comparison between the present solutions and previously published results show the accuracy of the results and methods used to achieve the objective of the present work.

scholarly journals Homotopy Analysis of Carreau Fluid Flow Over a Stretching Cylinder

2021 ◽  
Vol 88 (2) ◽  
pp. 80-92
Author(s):  
Lim Yeou Jiann ◽  
Sharidan Shafie ◽  
Ahmad Qushairi Mohamad ◽  
Noraihan Afiqah Rawi
Keyword(s):  
Nonlinear Differential Equations ◽  
Velocity Profiles ◽  
Weissenberg Number ◽  
Stretching Cylinder ◽  
Series Solutions ◽  
Carreau Fluid ◽  
Keller Box Method ◽  
Highly Nonlinear ◽  
Homotopy Analysis ◽  
Curvature Parameter

Carreau fluid flows past a stretching cylinder is elucidated in the present study. The transformed self-similarity and dimensionless boundary layer equations are solved by using the Homotopy analysis method. A convergence study of the method is illustrated explicitly. Series solutions of the highly nonlinear differential equations are computed and it is very efficient in demonstrating the characteristic of the Carreau fluid. Validation of the series solutions is achieved via comparing with earlier published results. Those results are obtained by using the Keller-Box method. The effects of the Weissenberg number and curvature parameter on the velocity profiles are discussed by graphs and tabular. The velocity curves have shown different behavior in and for an increase of the Weissenberg number. Further, the curvature parameter K does increase the velocity profiles.

scholarly journals Application of Piecewise Successive Linearization Method for the Solutions of the Chen Chaotic System

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
S. S. Motsa ◽  
Y. Khan ◽  
S. Shateyi
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Good Accuracy ◽  
Linearization Method ◽  
Chen System ◽  
Successive Linearization Method ◽  
Runge Kutta

This paper centres on the application of the new piecewise successive linearization method (PSLM) in solving the chaotic and nonchaotic Chen system. Numerical simulations are presented graphically and comparison is made between the PSLM and Runge-Kutta-based methods. The work shows that the proposed method provides good accuracy and can be easily extended to other dynamical systems including those that are chaotic in nature.

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