Abstract
The non-symmetric flow over a stretching/shrinking surface in an other-wise quiescent fluid is considered under the assumption that the surface can stretch orshrink in one direction and stretch in a direction perpendicular to this. The problem is reduced to similarity form, being described by two dimensionless parameters, γ the relative stretching/shrinking rate and S characterizing the fluid transfer throughthe boundary. Numerical solutions are obtained for representative values of γ and S, a feature of which are the existence of critical values γc of γ dependent on S, these being determined numerically. Asymptotic forms for large γ and S, for both fluid withdrawal, S > 0 and injection S < 0 are obtained and compared with the corresponding numerical results.
Highlights
Over recent years the analysis of the boundary-layer flows of viscous fluids resulting from continuously moving or stretching/shrinking surfaces has many important applications in both engineering processes and the polymer industry
We have considered the non-symmetric flow over a stretching/shrinking surface in an otherwise quiescent fluid
We assumed that the surface could stretch or shrink in one direction and stretch in a direction perpendicular to this
Summary
Over recent years the analysis of the boundary-layer flows of viscous fluids resulting from continuously moving or stretching/shrinking surfaces has many important applications in both engineering processes and the polymer industry. Gupta and Gupta [13] discussed the heat and mass transfer due to a permeable stretching sheet They presented the analysis for both the suction and blowing cases. The three-dimensional flow due to the bi-axial stretching of a flat surface, including an axisymmetric stretching surface, was studied by Wang [28] in a quiescent fluid, and by Wang [30] in a fluid with uniform outer flow These problems lead to the exact solutions of the Navier-Stokes equations. Miklavcic and Wang [24] have investigated the two-dimensional flow towards a shrinking sheet with constant velocity in a viscous fluid and obtained the exact solutions of the full Navier-Stokes equations. We start by considering the equations that describe our model
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