The stability of Falkner-Skan flows with several inflection points

Abstract

Non-unique solutions to the Falkner-Skan equation with multiple inflection points have been investigated with respect to stability properties. A temporal stability analysis based on the Orr-Sommerfeld equation has been performed. Attention has been paid to the effect of the number of inflection points in these solutions on the stability properties. While the standard Falkner-Skan flow does not have any inflection points in a favourable pressure gradient, the first non-unique solution branch has two such points. The presence of these two inflection points implies a dramatic reduction of the critical Reynolds number by four orders of magnitude. Moreover, in base flows with more than two inflection points additional neutral waves occur with the same Reynolds number but with different wave numbers. Mathematics Subject Classification (1991).Stability of parallel flows, 76E05.

Boundary Layer Flow Past a Wedge Moving in a Nanofluid

“…This equation includes nonuniform flow, that is, outer flows which, when evaluated at the wall, takes the form , where is the coordinate measured along the wedge wall and (>0), and are constants. There is a large body of literature on the solutions of Falkner-Skan equation, see Hartree [2], Stewartson [3], Chen and Libby [4], Rajagopal et al [5], Botta et al [6], Brodie and Banks [7], Heeg et al [8], Zaturska and Banks [9], Kuo [10], Pantokratoras [11], and so forth. Liao [12] has developed an analytical technique, named homotopy analysis method (HAM), and presented a uniformly valid analytic solution of Falkner-Skan equation for the wedge parameter in the range −0.19884 ≤ ≤ 2.…”