## THERMAL SCIENCE

International Scientific Journal

### AN EFFICIENT SPECTRAL SOLUTION FOR UNSTEADY BOUNDARY-LAYER FLOW AND HEAT TRANSFER DUE TO A STRETCHING SHEET

**ABSTRACT**

In this paper, an efficient spectral collocation method based on the shifted Legendre polynomials is applied to study the unsteady boundary-layer flow and heat transfer due to a stretching sheet. A similarity transformation is used to reduce the governing unsteady boundary-layer equations to a system of non-linear ordinary differential equations. Then, the shifted Legendre polynomials and their operational matrix of derivative are used for producing an analytical approximate solution of this system of non-linear ordinary differential equations. The main advantage of the proposed method is that the need for guessing and correcting the initial values during the solution procedure is eliminated and a stable solution with good accuracy can be obtained by using the given boundary conditions in the problem. A very good agreement is observed between the obtained results by the proposed spectral collocation method and those of previously published ones.

**KEYWORDS**

PAPER SUBMITTED: 2015-03-29

PAPER REVISED: 2015-06-10

PAPER ACCEPTED: 2015-06-24

PUBLISHED ONLINE: 2015-07-03

**THERMAL SCIENCE** YEAR

**2017**, VOLUME

**21**, ISSUE

**Issue 5**, PAGES [2167 - 2176]

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