Topic
Similarity solution
About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.
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22 Jun 2015TL;DR: In this paper, the authors investigate both the type I and II modes of stationary instability within the boundarylayer flow over a rotating disk and find that the flow can be stabilised via the introduction of shear-thinning non-Newtonian fluids.
Abstract: We investigate both the type I and II modes of stationary instability within the boundarylayer flow over a rotating disk. Extending the work of previous studies we find that the flow can be stabilised via the introduction of shear-thinning non-Newtonian fluids. Laminar-flow profiles are determined from a generalised von Karman similarity solution. An asymptotic study is presented in the limit of large Reynolds number and a numerical investigation which includes the effects of streamline curvature and Coriolis force is also conducted. Favourable agreement is obtained between solutions from the two schemes. Results indicate that the transition process from laminar to turbulent flow can be significantly delayed, in this case at least. Such a study is presented with a view to suggesting potential control mechanisms in aerodynamically-significant flows.
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TL;DR: In this paper, the free convection heat transfer over an arbitrary hot surface in a porous medium is studied. But the authors assume that the fluid and solid phases are not in local thermal equilibrium and therefore a two-temperature model of heat transfer is applied.
Abstract: The study of the natural convection flow and heat transfer from hot surfaces in a porous medium has been of considerable interest in energy-related engineering problems. This paper is concerned with the free convection heat transfer over an arbitrary hot surface in a porous medium. It is assumed that the fluid and solid phases are not in local thermal equilibrium and therefore a two-temperature model of heat transfer is applied. The coupled momentum and energy equations are used and transformed into ODE’s. The similar equations obtained are solved numerically and the local heat flux is shown for three types of axisymmetric shapes, i.e., a vertical plate, horizontal cylinder and sphere. The results have also been validated with the available results in the literature; which show that our assumptions and numerical method are accurate. Mathematical derivation of a similarity solution for an arbitrary geometry in the heat transfer analysis is the main novelty of the present study.
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TL;DR: By using scalar similarity transformation, nonlinear model of time-fractional diffusion/Harry Dym equation is transformed to corresponding ordinary fractional differential equations, from which a travelling-wave similarity solution of time fractional diffusion equation is presented as discussed by the authors.
Abstract: By using scalar similarity transformation, nonlinear model of time-fractional diffusion/Harry Dym equation is transformed to corresponding ordinary fractional differential equations, from which a travelling-wave similarity solution of time-fractional Harry Dym equation is presented. Furthermore, numerical solutions of time-fractional diffusion equation are discussed. Again, through another similarity transformation, nonlinear model of space-fractional diffusion/Harry Dym equation is turned into corresponding ordinary differential equations, whose two similarity solutions are also worked out.
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TL;DR: In this article, an experimental study has been carried out to explore the nature of the turbulent flow in the vicinity of a highly swept swept attachment line and has revealed a quite complex, non-monotonic development of the momentum thickness in this region.
Abstract: This work is motivated by the need for low-order aerodynamic models to predict accurately the effect on profile drag of controlling attachment line transition. Head's entrainment method (1) , a rapid integral boundary layer technique used for design studies on swept wings, suffers from the governing swept-tapered turbulent integral boundary layer equations being ill-posed in the vicinity of the attachment line. This singularity has been treated using crude extrapolations of the attachment-line similarity solution for over half a century, but this approach is unlikely to deliver accurate predictions of the effect of changes in the attachment line flow on profile drag. An experimental study has been carried out to explore the nature of the turbulent flow in the vicinity of a highly swept swept attachment line and has revealed a quite complex, non-monotonic development of the momentum thickness in this region. It has also revealed lower levels of twist in the boundary layer velocity profiles than anticipated from the highly curved character of the inviscid flow streamlines. These observations have prompted an alternative approach to the modelling of the flow in this region which not only successfully eliminates the lack of robustness in the swept-tapered equations but which also matches the experimental results to within ±5%.