Existence and non-uniqueness of similarity solutions of a boundary layer problem
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National Aeronautics and Space Administration, Langley Research Center , Hampton, Va
|Statement||M.Y. Hussaini, W.D. Lakin.|
|Series||ICASE report -- no. 84-60., NASA contractor report -- 172503., NASA contractor report -- NASA CR-172503.|
|Contributions||Lakin, William D., Langley Research Center., Institute for Computer Applications in Science and Engineering.|
|The Physical Object|
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The existence and uniqueness of Blasius' boundary layer solution to (), () with λ = 0 was rigorously proved by Weyl . The properties of similarity solutions to the boundary layer.
Get this from a library. Existence and non-uniqueness of similarity solutions of a boundary layer problem. [M Yousuff Hussaini; William D Lakin; Langley Research Center.; Institute for Computer Applications in Science and Engineering.].
Similarity solutions of the boundary-layer equations describing mixed convection flow along a vertical plate exist if the difference between the temperature of the plate and the temperature of the. Abstract. In this paper we reconsider the problem of steady mixed con-vection boundary-layer ﬂow over a vertical ﬂat plate studied in , and .
Under favorable assumptions, we prove existence of multiple similar-ity solutions, we study also their asymptotic behavior. Numerical solutions are carried out using a shooting integration.
Timol and Kalthia () also studied theoretically the existence of three-dimensional boundary layer similarity solutions for power law non-Newtonian fluids under normal conditions. Howell et al. () studied the approximate solution of the boundary layer problem over horizontal moving plate.
M.Y. Hussaini, W.D. Lakin, Existence and Non-uniqueness of similarity solutions of a boundary-layer problem. Mech. Appl. Math. 39, 17–24 () MathSciNet Author: Chunqing Lu.
Similarity solutions of degenerate boundary layer equations 1. Introduction 2. Similarity reduction 3. A shooting method and preliminary results 4.
The effects of deceleration of the surface velocity 5. Global behavior of solutions 6. Conclusion Chapter Cited by: 4. The analysis deals with existence, non-uniqueness and large t behavior of solutions to the above equation under certain conditions.
We also consider the case where the solutions are singular and give the asymptotic behavior at the singular point, for −1 ≤ α Cited by: 1. The revised Buongiorno’s nanofluid model with the effect of induced magnetic field on steady magnetohydrodynamics (MHD) stagnation-point flow of nanofluid over a stretching or shrinking sheet is investigated.
The effects of zero mass flux and suction are taken into account. A similarity transformation with symmetry variables are introduced in order to alter from the governing nonlinear Cited by: 1. The present work studies the unsteady, viscous, and incompressible laminar flow and heat transfer over a shrinking permeable cylinder.
The unsteady nonlinear Navier–Stokes and energy equations are reduced, using similarity transformations, to a Cited by: 3. The effect of transpiration on self-similar boundary layer flow over moving surfaces. Int. Eng. Sci.44, – [Google Scholar] Harris, S.D.; Ingham, D.B.; Pop, I.
Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transp. Porous Med.77, –Author: Anuar Jamaludin, Kohilavani Naganthran, Roslinda Nazar, Ioan Pop.
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Summary. In this article, axisymmetric solutions of the Navier–Stokes equations governing the flow induced by a half-line source when the fluid domain is bound.
One may naturally ask if such non-uniqueness holds for Leray-Hopf weak solutions. This problem remains open. Non-uniqueness of Leray-Hopf solutions were famously conjectured by Ladyzenskaja [ˇ ].
More recently, Sverˇ ak and Jia proved the non-uniqueness of Leray-Hopf weak solutions assuming that´ a certain spectral assumption holds . Singular Perturbation Theory R.S. Johnson. The theory of singular perturbations has evolved as a response to the need to find approximate solutions (in an analytical form) to complex problems.
Typically, such problems are expressed in terms of differential equations which contain at least one small parameter, and they can arise in many fields.
Following that, 3 more chapters cover a number of more advanced topics: free boundary conditions, non quasi linear equations, and miscellaneous topics.
The book is written by applied mathematicians for applied mathematics students. Micro-Electromechanical Systems (MEMS) combine electronics with micro-size mechanical devices in the process of designing various types of microscopic machinery, especially those involved in conceiving and building modern sensors.
Since their initial development in the s, MEMS has revolutionized numerous branches of science and industry. Indeed, MEMS-based devices are now essential Author: Yujin Guo. Another qualitative feature of boundary layer flow that plays an important role in fluid dynamics is that it can reverse directions.
In such a scenario, the near field flow around the object is pointing in the opposite direction as the far field flow associated with the object/flow, and so the flow needs to “turn around” somewhere in the boundary layer—this was the case for the sphere.
Boundary Layers Part 4. Hydrodynamic Stability Theory The series is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field.
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Basic concepts of forward and inverse problems, Ill-posedness of inverse problems, condition number, non-uniqueness and stability of solutions; L1, L2 and Lp norms, overdetermined, underdetermined and mixed determined inverse problems, quasi-linear and non-linear methods including Tikhonov’s regularization method, Singular Value Decomposion.
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Description Existence and non-uniqueness of similarity solutions of a boundary layer problem PDF
We prove the existence of solutions of the corresponding system of PDEs and then study the behavior of such solutions when the data of the problem vary slowly. We prove that a rescaled version of the dynamic evolutions converge to a “local” quasistatic evolution, which is an evolution satisfying an energy inequality and a momentum balance.
Collapse of n-point vortices in self-similar motion. It is well-known that under very little regularity of the initial vorticity it can prove the existence of the global, regular solutions of the Euler equation in 2D Kudela H and Malecha Z Eruption of a boundary layer induced by a 2D vortex patch Fluid Dyn.
Res. 41 1–Cited by: 6. Existence and Uniqueness of Solutions The fundamental result in the theory of differential equations is the existence and uniqueness theorem for systems of first order equations. The size of the gap, in conceptual space, that separates different learning exemplars of a given learn a homophone, language learners are exposed to a discrete set of learning exemplars.
For instance, for the word bat, they would observe several animal-bats and several baseball r if the underlying true concept were the broad category that encompasses animal-bats, baseball Cited by: 7.
Interestingly, he solutions of the Vlasov equation, for systems with external periodic driving, are aperiodic for most initial conditions [Physics of Plas ()]. However, solutions of the Fokker- Planck equation for such systems seem to be periodic asymptotically for most initial conditions [Physics of Plas ()].Inverse theory, non-uniqueness of solution.- Inverse theory, Singular Value.- Isostasy.- Length of day.- Lithosphere – Asthenosphere boundary.- Solutions to providing long term, stable and economical energy is a complex problem, which links social, economical, technical and environmental issues.
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