On an equation arising in the boundary-layer flow of stretching/shrinking permeable surfaces

• Published in: Journal of engineering mathematics 2020-04, Vol.121 (1), p.1-17
• Main Authors: Merkin, J. H., Pop, I.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Asymptotic methods; Boundary layer flow; Computational Mathematics and Numerical Analysis; Elastic sheets; Fluid injection; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Permeability; Stone; Stretching; Theoretical and Applied Mechanics; Viscous fluids
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-020-10036-9

In a recent paper, Al-Housseiny and Stone (J Fluid Mech 706:597–606, 2012) considered the dynamics of a stretching surface and how this interacts with the boundary-layer flow it generates. These authors discussed the cases c = - 3 for an elastic sheet and c = - 1 for the viscous fluid, c being representative for the stretching velocity of the sheet. The aim of the present paper is to extend the analysis of Al-Housseiny and Stone (2012) to the general values of c , to allow for both a stretching and a shrinking sheet and for the surface to be permeable through the parameter S , where S > 0 for the fluid withdrawal and S < 0 for fluid injection. Both the cases S = 0 (impermeable surface) and S ≠ 0 (permeable surface) are considered for both stretching surfaces and shrinking surfaces. In all these cases, asymptotic solutions are presented for large values c and S (both withdrawal and injection).