NDLI: Shifted Legendre Collocation Method for the Flow and Heat Transfer due to a Stretching Sheet Embedded in a Porous Medium with Variable Thickness, Variable Thermal Conductivity and Thermal Radiation

Content Provider	Springer Nature Link
Author	Khader, M. M.
Copyright Year	2015
Abstract	This paper is devoted to introduce a numerical simulation with a theoretical study for flow of a Newtonian fluid over an impermeable stretching sheet which embedded in a porous medium with a power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by a non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing PDEs are transformed into a system of coupled non-linear ODEs which are using appropriate boundary conditions for various physical parameters. The proposed method is based on replacement of the unknown function by truncated series of well known shifted Legendre expansion of functions. An approximate formula of the integer derivative is introduced. Special attention is given to study the convergence analysis and derive an upper bound of the error of the presented approximate formula. The introduced method converts the proposed equation by means of collocation points to a system of algebraic equations with shifted Legendre coefficients. Thus, by solving this system of equations, the shifted Legendre coefficients are obtained. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, thermal conductivity parameter and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and Nusselt numbers are presented. Comparison of obtained numerical results is made with previously published results in some special cases, and excellent agreement is noted. The results attained in this paper confirm the idea that proposed method is powerful mathematical tool and it can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.
Ending Page	2336
Page Count	18
Starting Page	2319
File Format	PDF
ISSN	16605446
e-ISSN	16605454
Journal	Mediterranean Journal of Mathematics
Issue Number	4
Volume Number	13
Language	English
Publisher	Springer International Publishing
Publisher Date	2015-06-17
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Ill-posed problems convergence analysis Mathematics Newtonian fluid variable thermal conductivity Legendre collocation method variable thickness stretching sheet thermal radiation
Content Type	Text
Resource Type	Article
Subject	Mathematics

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