Stagnation‐point Flow towards a Stretching Surface

Abstract

An exact similarity solution of the Navier‐Stokes equations is obtained. The solution represents steady axisymmetric stagnation‐point flow towards a stretching surface. It is shown that the flow displays a boundary‐layer structure when the stretching velocity of the surface is less than the free stream velocity. On the other hand, an inverted boundary layer is formed when the surface stretching velocity exceeds the free stream velocity. Temperature distribution in the flow is found when the surface is held at a constant temperature. It turns out that when the surface temperature exceeds the ambient temperature, heat flows from the surface to the fluid near the stagnation point but further away from the stagnation point, heat flows from the fluid to the stretching surface.

Stability analysis of stagnation-point flow over a stretching/shrinking sheet

“…It is worth mentioning that the flow over a stretching sheet was studied recently by Ahmed et al, 7 Khan and Khan, 8 Mustafa et al 9 and Khan and Rahman, 10 among others. The combination of both stagnation flow and stretching surface was considered by Mahapatra and Gupta, 11,12 Nazar et al 13 and Ishak et al 14 Wang 15 considered the stagnation flow over both stretching and shrinking sheets, and found that the solutions for the shrinking case are not unique. This problem was then extended by Ishak et al 16 to a micropolar fluid.…”

Stagnation-point flows with stretching surfaces: A unified formulation and new results

“…This system was found by Mahapatra and Gupta (2003) and solved for selected positive values of σ. Wang (2008) extended this work to shrinking surfaces.…”

“…Also, Mahapatra and Gupta (2003) considered radial stretching parallel to flow streamlines for the Homann stagnation-point flow. In the following we consider other orientations of wall stretching beneath these two stagnation-point flows.…”

Brinkman Flow Past a Stretching Sheet

“…The velocity field in cylindrical form is given byV = (ū, 0,w) whereū,w are the velocity components alongx,z directions, respectively, withp(x,z) is the pressure field, ν, ρ, K , ν eff and ϕ are as in Sect. 2.1, the Navier-Stokes equations of rotational symmetry with Brinkman correction for porous medium can be written as (see, Mahapatra and Gupta 2003),…”

“…Ariel (2003) derived the perturbation solutions when the primary flow corresponds to the two-dimensional and axisymmetric cases in his threedimensional flow past a stretching sheet problem. Mahapatra and Gupta (2003) also analysed the steady axisymmetric stagnation point flow towards a stretching surface along with the heat transfer. Using homotopy analysis method, the steady laminar axisymmetric flow and heat transfer of a second grade fluid over a radially stretching sheet is considered by Hayat and Sajid (2007).…”