Boundary—Layer Equations in Plane Flow; Plate Boundary Layer

Schlichting, Herrmann; Gersten, Klaus

doi:10.1007/978-3-642-85829-1_6

Cited by 10 publications

(3 citation statements)

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“…From fundamental knowledge of the boundary layer theory, 29) previous works 25,26) and the present results, it can be established that there is boundary layer separation at the instant the steel flow reaches the upper internal side of the port, generating a low pressure zone with strong changes in the fluctuant velocity which are reflected in high kinetic energy dissipation, as can be seen in Figs. 10 and 11, respectively.…”

Section: Application Of the Internal Upper Port Radiussupporting

confidence: 68%

Numerical Optimization of Nozzle Ports to Improve the Fluidynamics by Controlling Backflow in a Continuous Casting Slab Mold

et al. 2013

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In order to improve the fluid flow patterns inside the mold, a better understanding of the backflow phenomenon and its controlling parameters is necessary; then a mathematical simulation of the fluidynamics in the mold and the submerge entry nozzle (SEN) are carried out considering two typical nozzle designs and different modifications applied to the outlet ports. The numerical model considers isothermal three dimensional continuity and the Navier-Stokes equations in Cartesian co-ordinates, which are solved together with the k-ε standard turbulence and the Volume of Fluid (VOF) models through the volume finite method. The results show that the backflow phenomenon emerges from an inadequate SEN port design, when a boundary layer separation is generated before the steel is delivered to the mold. This separation occurs at the upper internal side of the port inducing a low pressure zone with high levels of kinetic energy dissipation, producing the backflow phenomenon. From the analysis, it is concluded that the implementation of a radius at the internal upper side of the port avoids the separation of the boundary layer, eliminating the backflow phenomenon which allows the use of the complete effective exit area of the port; this is reflected in a velocity decrease of the jets and consequently a velocity decrement of the bulk flow. Furthermore, the size of the radius controls the penetration angle of the jets, the impact point position and the meniscus deformation; which avoids the need of the inclination angle of the port.

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Section: Application Of the Internal Upper Port Radiussupporting

confidence: 68%

Numerical Optimization of Nozzle Ports to Improve the Fluidynamics by Controlling Backflow in a Continuous Casting Slab Mold

et al. 2013

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“…The Leith equation holds for spherical particles and other non-spherical particles with small deviations from a sphere, yet it does not hold for very high or low aspect ratios. For the particles with plate shape (e.g., kaolinite), the drag force could be obtained based on the boundary theory , F normalD = c normalf 1 2 ρ normalf u normalp 2 A …”

Section: Methodsmentioning

confidence: 99%

Modeling the Breakup of Oil–Particle Aggregates in Turbulent Environments for Projectile Penetration

Liu

Lee

et al. 2023

Langmuir

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After an oil spill incident, the spilled oil slicks are observed to migrate to the shoreline area. Under the turbulent conditions, they break into small droplets and are suspended in the water column. The dispersed droplets are expected to interact with the suspended particles and form the oil–particle aggregates (OPAs), which significantly changes the transport of the oil. Instead of an earlier assumption that particles cover the oil surface, thus preventing further breakage or aggregation of OPAs, recent studies demonstrated that particles act like projectiles penetrating the oil droplets, resulting in the breakage of OPAs over a longer period of time. A model looking into the OPA breakup through two breakup mechanisms was proposed for the first time. The first method depicted the breakup of one large OPA into two daughter droplets owing to the turbulent nature, while the second method demonstrated the tear of the OPA surface layer caused by particle uprooting. The model was then calibrated by an experimental study targeting crude oil with varied viscosities, along with previous experimental investigations. Three key factors were identified accounting for the breakage of OPAs, where the increase in particle concentration in the natural environment and the increase in turbulent energy of the surrounding flows benefited the breakage of OPAs, and the increase in oil viscosity suppressed the breakage due to large resistance to shear stress. Besides these elements, the impact of the particle shape on the penetration depth was discussed. The model serves as a fundamental theory to describe the evolution of OPAs for fragmentation behavior.

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“…Nevertheless, altering the sort of nanoparticles fundamentally influences the hotness move process during maintenance. 9 The Koo-Kleinstreuer-Li (KKL) version, which addresses nanoparticle's Brownian development, is used to obtain the nanofluid sturdy heat conductivity and nanofluid consistency. It is also considered how the streamlines, isotherms, and rate of heat flow are impacted by the propensity factor of great area, Hartmann variety, Rayleigh variety, void width, and nanoparticle extent element.…”

Section: Background Surveymentioning

confidence: 99%

Thermal scrutinization of magetohydrodynamics CuO engine oil nanofluid flow across a horizontal surface via Koo–Kleinstreuer–Li modeling: A thermal case study

Hussain

Shahzad

Jamshed

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part E:

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The current investigation aims to investigate the effects of ohmic heating, heat source, and adhesive dispersion in third-grade nanofluid flowing magnetohydrodynamics (MHD) boundary layer heat transmission using the Koo–Kleinstreuer–Li (KKL) model. As a basic fluid, copper oxide nano molecules are suspended in engine oil. The controlling formulas that regulate the fields of flow and heat conduction are partial differential equations (PDEs) which are then converted into models of nonlinear ordinary differential equations (ODEs) that use the necessary similarity conversions. The resulting ODEs are numerically resolved using the Keller-Box approach. The effects of different common liquids, nano molecule sizes, magnetic parameter, Prandtl, material constant, and Eckert numbers are described using diagrams and tables for the field of motion, the field of temperature, the rate of heat transfer, and the drag force factor. The results show that the speed, drag force, and nozzle number for copper oxide engine oil nanofluids are lower than that of the basic liquid, while the addition of nanoparticles raises the temperature. The drag force factor and the rate of heat transfer are both found to increase when the material constant rises.

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Boundary—Layer Equations in Plane Flow; Plate Boundary Layer

Cited by 10 publications

References 0 publications

Numerical Optimization of Nozzle Ports to Improve the Fluidynamics by Controlling Backflow in a Continuous Casting Slab Mold

Numerical Optimization of Nozzle Ports to Improve the Fluidynamics by Controlling Backflow in a Continuous Casting Slab Mold

Modeling the Breakup of Oil–Particle Aggregates in Turbulent Environments for Projectile Penetration

Thermal scrutinization of magetohydrodynamics CuO engine oil nanofluid flow across a horizontal surface via Koo–Kleinstreuer–Li modeling: A thermal case study

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