On three-dimensional flow and heat transfer over a non-linearly stretching sheet: analytical and numerical solutions.

Junaid Ahmad Khan,Meraj Mustafa,Ahmed Alsaedi,Tasawar Hayat,Zhonghao Rao

doi:10.1371/journal.pone.0107287

Abstract

This article studies the viscous flow and heat transfer over a plane horizontal surface stretched non-linearly in two lateral directions. Appropriate wall conditions characterizing the non-linear variation in the velocity and temperature of the sheet are employed for the first time. A new set of similarity variables is introduced to reduce the boundary layer equations into self-similar forms. The velocity and temperature distributions are determined by two methods, namely (i) optimal homotopy analysis method (OHAM) and (ii) fourth-fifth-order Runge-Kutta integration based shooting technique. The analytic and numerical solutions are compared and these are found in excellent agreement. Influences of embedded parameters on momentum and thermal boundary layers are sketched and discussed.

Highlights

The fundamental problem of two-dimensional flow due to stretching plane surface, initially discussed by Crane [1], is involved in various industrial processes such as metal and polymer extrusion, drawing of plastic films, paper production etc
The unsteady three-dimensional flow of elasticoviscous fluid and mass transfer due to unsteady stretching sheet with constant wall concentration was studied by Hayat et al [7]
The steady boundary layer flow of micropolar fluid over non-linearly stretching sheet was discussed by Bhargava et al [14]

Summary

Introduction

The fundamental problem of two-dimensional flow due to stretching plane surface, initially discussed by Crane [1], is involved in various industrial processes such as metal and polymer extrusion, drawing of plastic films, paper production etc. The three-dimensional flow due to plane bi-directional linearly stretching sheet was first discussed by Wang [2]. Ariel [4] derived approximate analytic and numeric solutions for steady three-dimensional flow over a stretching sheet.

Results

Conclusion