A pseudosimilarity approach to a steady free convection flow

In this communication we deal with the exact solutions called "pseudosimilarity" of a steady free convection problem studied by by Kumaran and Pop (2006). They showed that there is no similarity solution for the case of a wall temperature as $T_{w}(x)\sim x^{-\frac{1}{2}}$ (resp. a wall heat flux as $q_{w}(x)\sim x^{-\frac{3}{2}},$ and a dimensionless heat transfer coefficient $h_{w}(x)\sim x^{-1}$). We shall present some results about existence and asymptotic behaviour of new exact solutions of the resulting boundary value problem for each case

Multiple solutions of steady MHD flow of dilatant fluids

International audienceIn this paper we consider the problem of a steady MHD flow of a non-Newtonian power-law and electrically conducting fluid in presence of an applied magnetic field. The boundary layer equations are solved in similarity form via the Lyapunov energy method, we show that this problem has an infinite number of positive global solutions

On similarity and pseudo-similarity solutions of Falkner-Skan boundary layers

15 pagesInternational audienceThe present work deals with the two-dimensional incompressible,laminar, steady-state boundary layer equations. First, we determinea family of velocity distributions outside the boundary layer suchthat these problems may have similarity solutions. Then, we examenin detail new exact solutions, called Pseudo--similarity, where the external velocity varies inversely-linear with the distance along the surface $ (U_e(x) = U_\infty x^{-1}). The present work deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations. First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity solutions. Then, we examenin detail new exact solutions. The analysis shows that solutions exist only for a lateral suction. For specified conditions, we establish the existence of an infinite number of solutions, including monotonic solutions and solutions which oscillate an infinite number of times and tend to a certain limit. The properties of solutions depend onthe suction parameter. Furthermore, making use of the fourth--order Runge--Kutta scheme together with the shooting method, numerical solutions are obtained

Chaos synchronization of a fractional nonautonomous system

In this paper we investigate the dynamic behavior of a nonautonomous fractional-order biological system.With the stability criterion of active nonlinear fractional systems, the synchronization of the studied chaotic system is obtained. On the other hand, using a Phase-Locked-Loop (PLL) analogy we synchronize the same system. The numerical results demonstrate the efiectiveness of the proposed method