scholarly journals A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
S. S. Motsa
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Nonlinear Boundary ◽  
Linearization Method ◽  
Variable Boundary ◽  
Flow Problems ◽  
Local Linearization ◽  
Highly Nonlinear ◽  
Layer Flow ◽  
Local Linearization Method

We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM), is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.

scholarly journals Analysis of Boundary Layer Flow and Heat Transfer along a Stretching Cylinder in a Porous Medium

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Swati Mukhopadhyay
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Heat Equations ◽  
Stretching Cylinder ◽  
Highly Nonlinear ◽  
Layer Flow

This paper presents an axi-symmetric laminar boundary layer flow of a viscous incompressible fluid and heat transfer towards a stretching cylinder embedded in a porous medium. The partial differential equations corresponding to the momentum and heat equations are converted into highly nonlinear ordinary differential equations with the help of similarity transformations. Numerical solutions of these equations are obtained by shooting method. It is found that the velocity decreases with increasing permeability parameter. The skin friction as well as the heat transfer rate at the surface is larger for a cylinder compared to a flat plate.

scholarly journals Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
P. G. Dlamini ◽  
S. S. Motsa ◽  
M. Khumalo
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Nonlinear Partial Differential Equations ◽  
Finite Difference Schemes ◽  
Unsteady Boundary Layer ◽  
Compact Finite Difference ◽  
Flow Problems ◽  
Layer Flow

We investigate the applicability of the compact finite difference relaxation method (CFDRM) in solving unsteady boundary layer flow problems modelled by nonlinear partial differential equations. The CFDRM utilizes the Gauss-Seidel approach of decoupling algebraic equations to linearize the governing equations and solve the resulting system of ordinary differential equations using compact finite difference schemes. The CFDRM has only been used to solve ordinary differential equations modelling boundary layer problems. This work extends its applications to nonlinear partial differential equations modelling unsteady boundary layer flows. The CFDRM is validated on two examples and the results are compared to results of the Keller-box method.

A third-order accurate in time method for boundary layer flow problems

2021 ◽  
Vol 161 ◽  
pp. 13-26 ◽  
Author(s):  
Syed Ahmed Pasha ◽  
Yasir Nawaz ◽  
Muhammad Shoaib Arif
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Third Order ◽  
Flow Problems ◽  
Layer Flow

scholarly journals Mass Transpiration in Nonlinear MHD Flow Due to Porous Stretching Sheet

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Jitender Singh ◽  
U. S. Mahabaleshwar ◽  
Gabriella Bognár
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Flow Characteristics ◽  
Nonlinear Flow ◽  
Numerical Work ◽  
Highly Nonlinear ◽  
Homotopy Analysis ◽  
Layer Flow

AbstractMotivated from numerous practical applications, the present theoretical and numerical work investigates the nonlinear magnetohydrodynamic (MHD) laminar boundary layer flow of an incompressible, viscous fluid over a porous stretching sheet in the presence of suction/injection (mass transpiration). The flow characteristics are obtained by solving the underlying highly nonlinear ordinary differential equation using homotopy analysis method. The effect of parameters corresponding to suction/injection (mass transpiration), applied magnetic field, and porous stretching sheet parameters on the nonlinear flow is investigated. The asymptotic limits of the parameters regarding the flow characteristics are obtained mathematically, which compare very well with those obtained using the homotopy analysis technique. A detailed numerical study of the laminar boundary layer flow in the vicinity of the porous stretching sheet in MHD and offers a particular choice of the parametric values to be taken in order to practically model a particular type of the event among suction and injection at the sheet surface.

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