Backstepping stabilization of an underactuated 3 × 3 linear hyperbolic system of fluid flow equations

2012 ◽  
Author(s):  
F. Di Meglio ◽  
R. Vazquez ◽  
M. Krstic ◽  
N. Petit
Keyword(s):  
Fluid Flow ◽  
Hyperbolic System ◽  
Flow Equations ◽  
Linear Hyperbolic System

scholarly journals Effect of magnetized variable thermal conductivity on flow and heat transfer characteristics of unsteady Williamson fluid

2020 ◽  
Vol 9 (1) ◽  
pp. 338-351
Author(s):  
Usha Shankar ◽  
N. B. Naduvinamani ◽  
Hussain Basha
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Fluid Flow ◽  
Velocity Profile ◽  
Variable Thermal Conductivity ◽  
Flow Index ◽  
Williamson Fluid ◽  
Flow Equations ◽  
Velocity Parameter ◽  
Squeezed Flow

AbstractA two-dimensional mathematical model of magnetized unsteady incompressible Williamson fluid flow over a sensor surface with variable thermal conductivity and exterior squeezing with viscous dissipation effect is investigated, numerically. Present flow model is developed based on the considered flow geometry. Effect of Lorentz forces on flow behaviour is described in terms of magnetic field and which is accounted in momentum equation. Influence of variable thermal conductivity on heat transfer is considered in the energy equation. Present investigated problem gives the highly complicated nonlinear, unsteady governing flow equations and which are coupled in nature. Owing to the failure of analytical/direct techniques, the considered physical problem is solved by using Runge-Kutta scheme (RK-4) via similarity transformations approach. Graphs and tables are presented to describe the physical behaviour of various control parameters on flow phenomenon. Temperature boundary layer thickens for the amplifying value of Weissenberg parameter and permeable velocity parameter. Velocity profile decreased for the increasing squeezed flow index and permeable velocity parameter. Increasing magnetic number increases the velocity profile. Magnifying squeezed flow index magnifies the magnitude of Nusselt number. Also, RK-4 efficiently solves the highly complicated nonlinear complex equations that are arising in the fluid flow problems. The present results in this article are significantly matching with the published results in the literature.

Polygonal Approximation Method in the Hodograph Plane

1949 ◽  
Vol 16 (2) ◽  
pp. 123-133
Author(s):  
H. Poritsky
Keyword(s):  
Fluid Flow ◽  
Approximation Method ◽  
Applied Mechanics ◽  
Polygonal Approximation ◽  
Physical Plane ◽  
Flow Equations ◽  
Hodograph Plane ◽  
Superposition Of Solutions ◽  
Sixth International

Abstract This paper extends the discussion of the approximate method of integrating the equations of compressible fluid flow in the hodograph plane first presented by the author before the Sixth International Congress of Applied Mechanics, Paris, France, September, 1948. As an introduction to the discussion of the polygonal approximation method, fundamental fluid-flow equations are reviewed briefly. Determination of the flow function ψ by the “Method of Reflections” is described and an application of the method illustrated. How flow in the physical plane can be determined by superposition of solutions discussed is shown for the simpler incompressible case.

Riesz basis of exponential family for a hyperbolic system

2019 ◽  
Vol 25 (1) ◽  
pp. 13-23
Author(s):  
Abdelkader Intissar ◽  
Aref Jeribi ◽  
Ines Walha
Keyword(s):  
Hilbert Space ◽  
Linear System ◽  
Hyperbolic System ◽  
Riesz Basis ◽  
Infinitesimal Generator ◽  
Exponential Family ◽  
Analysis Method ◽  
Spectral Analysis Method ◽  
Weaker Conditions ◽  
Linear Hyperbolic System

Abstract This paper studies a linear hyperbolic system with boundary conditions that was first studied under some weaker conditions in [8, 11]. Problems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper. It is shown that the associated linear system is the infinitesimal generator of a {C_{0}} -semigroup; its spectrum consists of zeros of a sine-type function, and its exponential system {\{e^{\lambda_{n}t}\}_{n\geq 1}} constitutes a Riesz basis in {L^{2}[0,T]} . Furthermore, by the spectral analysis method, it is also shown that the linear system has a sequence of eigenvectors, which form a Riesz basis in Hilbert space, and hence the spectrum-determined growth condition is deduced.

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