Galerkin-Legendre spectral method for the velocity and thermal boundary layers over a non-linearly stretching sheet

F. Talay Akyildiz, Dennis A. Siginer

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

Analytical solutions for the velocity and temperature fields in a viscous fluid flowing over a nonlinearly stretching sheet are obtained via Galerkin-Legendre spectral method. The application of spectral methods to this problem is novel as well as the concept of the non-uniqueness of the solution and the efficient algorithms developed in this paper. The governing partial differential equations are converted into a nonlinear ordinary differential equation for the velocity field f and a variable coefficient linear ordinary differential equation for the temperature field θ by a similarity transformation in the semi-infinite physical domain. A coordinate transformation is introduced to map the physical state space into a bounded computational domain. It is shown that Galerkin-Legendre spectral method is the most efficient among spectral methods that lead to the analytical solution of the governing set of nonlinear differential equations in the computational domain. Computationally efficient algorithms are constructed for the velocity gradient and temperature profile computations and two distinct solutions of the field equations are presented.

Original languageEnglish
Pages (from-to)735-741
Number of pages7
JournalNonlinear Analysis: Real World Applications
Volume11
Issue number2
DOIs
Publication statusPublished - Apr 1 2010

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Stretching Sheet
Legendre
Spectral Methods
Galerkin
Stretching
Boundary Layer
Boundary layers
Hot Temperature
Ordinary differential equations
Temperature distribution
Temperature Field
Velocity Field
Temperature
Analytical Solution
Efficient Algorithms
Partial differential equations
Linear Ordinary Differential Equations
Similarity Transformation
Nonuniqueness
Coordinate Transformation

All Science Journal Classification (ASJC) codes

  • Analysis
  • Medicine(all)
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

Cite this

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