The impact of second order velocity slip with zero mass flux over a malting radially surface is deliberated in the present study to explore solution boundary layer flow for MHD Casson nano-fluid heat and transfer utilizing nonlinear thermal radiation, source temperature jumping effect. equation effect cross-diffusion set. Scheme R.K. using shooting method, fourth used derive correct transformat...

Abstract. This note concerns a nonlinear ill-posedness of the Prandtl equation and an invalidity of asymptotic boundary-layer expansions of incompressible fluid flows near a solid boundary. Our analysis is built upon recent remarkable linear ill-posedness results established by Gérard-Varet and Dormy [2], and an analysis in Guo and Tice [5]. We show that the asymptotic boundary-layer expansion ...

Magnetic flux tubes or flux ropes in plasmas are important in nature and the laboratory. Axial boundary conditions strongly affect flux rope behavior, but this has never been systematically investigated. We experimentally demonstrate for the first time axial boundary conditions that are continuously varied between ideal magnetohydrodynamic (MHD) line-tied (fixed) and non-line-tied (free). In co...

We develop an improved lattice-Boltzmann numerical scheme to solve magnetohydrodynamic (MHD) equations in the regime of low magnetic Reynolds numbers, grounded on central-moment (CM) and multi-relaxation-time (MRT) collision models. The simulation induction equation within approach MHD has been usually devised along lines simplest phenomenological description—the single relaxation time (SRT) mo...

Designing a robust tracking control for a non-linear MIMO system with uncertainty is one of the most complicated control problems. In this paper, sliding mode changed to non-linear controllable canonical form by input-output linearization. This, sliding surfaces can be defined in a way that we can de-couple equations and indicate the sliding conditions of multi-variable controller system. The u...

Shock waves generated at different parts of vehicle interact with the boundary layer over the surface at high Mach flows. The adverse pressure gradient across strong shock wave causes the flow to separate and peak loads are generated at separation and reattachment points. The size of separation bubble in the shock boundary layer interaction flows depends on various parameters. Reynolds-averaged...

We reveal the basic mechanism of instability of the two-layer conductive fluid system carrying a normal current and exposed to a uniform external magnetic field. This process is a reflection of a MHD-modified interfacial gravity wave from the boundary. Due to special boundary conditions, the reflection coefficient turns out to be greater than 1 for some directions of the wave propagation. We co...

The generalized equation of Blasius arises in the boundary layer problems of hydrodynamics. We consider the decomposition solutions [10] of the Blasius equation u + auu = 0 and compare them to our numerical solutions.

We derive a perfectly matched layer-like damping layer for the nonlinear wave equation. In the layer only two auxiliary variables are needed. In the linear case the layer is perfectly matched, but in the nonlinear case it is not. Well-posedness is established for the linear case. We also prove various energy estimates which can be used as a starting point for establishing stability of more gene...