Generalized three‐dimensional flow due to a stretching sheet

Abstract

The three‐dimensional steady, laminar flow due to stretching of a sheet is considered. The governing equations of motion admit a similarity solution. By drawing an analogy with the flow due to a rotating disk it is demonstrated that the resulting boundary value problem admits a solution in terms of series of exponentially decaying functions. The solution is highly efficient and very accurate, as it eliminates the need of replacing numerical infinity in the range of integration by a finite value. Two perturbation solutions are also developed when the primary flow corresponds to the two‐dimensional case and the axisymmetric case. In each case the expansion is obtained up to the second degree term of the perturbation parameter. Finally, an approximate solution is derived, which is very simple and highly accurate.

Unsteady Three-Dimensional Flow in a Second-Grade Fluid Over a Stretching Surface

“…It is worth mentioning to point out that the present problem for A = 0 = α reduces to the problem of a viscous fluid. Exact numerical solution for this viscous fluid problem is computed by Ariel [13]. He employed the Ackroyd method for solving the arising mathematical problem.…”

“…He employed the Ackroyd method for solving the arising mathematical problem. For details of this Ackroyd method one may consult [13]. The present attempt extends the analysis of Ariel [13] from viscous to second-grade fluid.…”

“…However, very few researchers presented such flows in three dimensions. Ariel [13,14] found the exact and homo-topy perturbation solutions of a viscous fluid for the three-dimensional flow over a stretched surface. The magnetohydrodynamic three-dimensional viscous flow over a porous stretching surface has been presented by Hayat and Javed [15].…”

Flow of an Oldroyd-B Fluid past an Unsteady Bidirectional Stretching Sheet with Constant Temperature and Constant Heat Flux

“…He found an exact numerical solution of classical Navier-Stokes equations. Ariel (2003) derived approximate analytic and numerical solutions for the steady three dimensional flows over a stretching sheet. Liu and Andersson (2008) considered the heat transfer in three dimensional flow due to a non-isothermal stretching sheet.…”

Effects of partial slip on axisymmetric flow of an electrically conducting viscoelastic fluid past a stretching sheet

“…Moreover, the flow past a stretching sheet need not be necessarily two-dimensional, because the stretching of the sheet can take place in a variety of ways. If the flow is axisymmetric, an exact closed form solution does not seem to exist [7][8][9][10][11]. The analytic solution for the axisymmetric flow of a viscous fluid over a nonlinearly stretching sheet has been considered by Sajid et al [12].…”