Prandtl Boundary Layer Theory Research Articles

Performance of copper nanofluid on changing width of stretching sheet using thermal radiation and heat flux

The phenomenon of nanomaterial carrying fluid-flow over a non-linear elongated sheet with changing thickness is investigated in this study. The present research focuses at the flow of magnetic nanofluid over non-linear elongated sheets of dif-ferent thicknesses, with an emphasis on copper nanoparticles distributed in water. The phenomena, which is significant in many industrial applications including paper manufacturing and atomic reactors, is analysed using Prandtl boundary-layer theory and Navier-Stoke's equation. The study covers a wide range of physical features. There have been fewer works on the mathematical modelling of stretching sheets with varying widths. The main aim of investigation is to analyse the effect of EMHD, as well as other characteristics like Eckert number, Boit number, radiation effect, and absorption factor. Paper manufacturing, dye and filament extrusion, atomic reactors, and metallurgical processes all rely heavily on these sheets of varied widths. The problem employs Navier-Stokes' equation and Prandtl boundary-layer theory. The similarity transformation converts PDE into ODE. The MATLAB bvp4c programme is used to obtain numerical solutions. The present study helps to achieve desired quality of stretching sheet.

The droplet dynamics of asymmetrical impingement on moving ridged surface.

The droplet dynamics of asymmetrical impingement on moving ridged surface.

Physical Formation Mechanisms of the Southwest China Vortex

On the basis of the Prandtl boundary layer theory and an improved perturbation method, the process of laminar flow bifurcating into the Southwest China vortex (SWV) in the Hengduan Mountains is studied. The results show that the formation of SWV is mainly determined by the speed of incoming airflow in the direction of the main axis of the Hengduan Mountains. The vortex is generated in the leeward area of the Hengduan Mountains when the speed of incoming airflow is greater than the critical velocity. Moreover, it means that the laminar flow bifurcates into a vortex. The formation position of the SWV is mainly determined by the relative position of the incoming airflow in the windward area of the Hengduan Mountains and the main axis of the Hengduan Mountains. The seasonal distribution of SWVs is determined by both the velocity of the incoming airflow and the relative position of the incoming airflow to the main axis of the Hengduan Mountains. These findings are consistent with the SWV observation facts, which not only adequately explain the physical formation mechanisms and processes of SWVs, but also present the formation location and seasonal distribution of SWVs. Meanwhile, a solution from laminar to vortex in circumflow motion is also presented.

Pressure performance for a thin-walled ring and turbulent-jet orifice modeled elastic squeeze film damper

Pressure performance for a thin-walled ring and turbulent-jet orifice modeled elastic squeeze film damper

Implications of the third-grade nanomaterials lubrication problem in terms of radiative heat flux: A Keller box analysis

Implications of the third-grade nanomaterials lubrication problem in terms of radiative heat flux: A Keller box analysis

Stability of the boundary layer expansion for the 3D plane parallel MHD flow

In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flows of viscous incompressible magnetohydrodynamic flow with the no-slip boundary condition of velocity and perfectly conducting walls for magnetic fields. The convergence is shown under various Sobolev norms, including the physically important space–time uniform norm L∞(H1). In addition, similar convergence results are also obtained under the case with uniform magnetic fields. This implies the stabilizing effects of magnetic fields. Besides, the higher-order expansion is also considered.

Richard von Mises’ work for ZAMM until his emigration in 1933 and glimpses of the later history of ZAMM

Richard von Mises’ work for ZAMM until his emigration in 1933 and glimpses of the later history of ZAMM

Boundary layer for 3D plane parallel channel flows of nonhomogeneous incompressible Navier-Stokes equations

<p style='text-indent:20px;'>In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flows of nonhomogeneous incompressible Navier-Stokes equations. The convergence is shown under various Sobolev norms, including the physically important space-time uniform norm, as well as the <inline-formula><tex-math id="M1">\begin{document}$ L^\infty(H^1) $\end{document}</tex-math></inline-formula> norm. It is mentioned that the mathematical validity of the Prandtl boundary layer theory for nonlinear plane parallel flow is generalized to the nonhomogeneous case.

Symmetrical Prandtl boundary layer expansions of steady Navier-Stokes equations on bounded domain

Symmetrical Prandtl boundary layer expansions of steady Navier-Stokes equations on bounded domain

Diffusion vanishing limit of the nonlinear pipe Magnetohydrodynamic flow with fixed viscosity

Diffusion vanishing limit of the nonlinear pipe Magnetohydrodynamic flow with fixed viscosity

Prandtl Boundary Layer Expansions of Steady Navier–Stokes Flows Over a Moving Plate

This paper concerns the validity of the Prandtl boundary layer theory in the inviscid limit for steady incompressible Navier–Stokes flows. The stationary flows, with small viscosity, are considered on $$[0,L]\times \mathbb {R}_{+}$$ , with a no-slip boundary condition over a moving plate at $$y=0$$ . We establish the validity of the Prandtl boundary layer expansion and its error estimates.

Steady Prandtl Boundary Layer Expansions Over a Rotating Disk

This paper concerns the validity of the Prandtl boundary layer theory for steady, incompressible Navier-Stokes flows over a rotating disk. We prove that the Navier-Stokes flows can be decomposed into Euler and Prandtl flows in the inviscid limit. In so doing, we develop a new set of function spaces and prove several embedding theorems which capture the interaction between the Prandtl scaling and the geometry of our domain.

A hypersonic aeroheating calculation method based on inviscid outer edge of boundary layer parameters

A hypersonic aeroheating calculation method based on inviscid outer edge of boundary layer parameters

Incompressible Flow and Heat Transfer over a Plate: A Hybrid Integral Domain-Discretized Numerical Procedure

This work deals with incompressible two-dimensional viscous flow over a semi-infinite plate ac-cording to the approximations resulting from Prandtl boundary layer theory. The governing non-linear coupled partial differential equations describing laminar flow are converted to a self-simi- lar type third order ordinary differential equation known as the Falkner-Skan equation. For the purposes of a numerical solution, the Falkner-Skan equation is converted to a system of first order ordinary differential equations. These are numerically addressed by the conventional shooting and bisection methods coupled with the Runge-Kutta technique. However the accompanying energy equation lends itself to a hybrid numerical finite element-boundary integral application. An appropriate complementary differential equation as well as the Green second identity paves the way for the integral representation of the energy equation. This is followed by a finite element-type discretization of the problem domain. Based on the quality of the results obtained herein, a strong case is made for a hybrid numerical scheme as a useful approach for the numerical resolution of boundary layer flows and species transport. Thanks to the sparsity of the resulting coefficient matrix, the solution profiles not only agree with those of similar problems in literature but also are in consonance with the physics they represent.

A Study on Gas–Liquid Film Thicknesses and Heat Transfer Characteristics of Vapor–Gas Condensation Outside a Horizontal Tube

Noncondensable gases deteriorate heat transfer in the condensation process. It is therefore necessary to study vapor–gas condensation heat transfer process and analyze main factors influencing the process. Based on the double-film theory and the Prandtl boundary layer theory, this investigation developed a mathematical model of gas–liquid film thicknesses and local heat transfer coefficient for studying laminar film condensation in the presence of noncondensable gas over a horizontal tube. Induced velocity in the gas film, gas–liquid interfacial shear stress, and pressure gradient were considered in the study. Importantly, gas–liquid film separations were analyzed in depth in this paper. It obtained the distributions of gas–liquid film thicknesses, local heat transfer coefficient, condensate mass flux, and gas–liquid interfacial temperature along the tube surface, and analyzed the influences of bulk velocity, total pressure, bulk mass concentration of noncondensable gas and wall temperature on them, providing a theoretical guidance for understanding and enhancing vapor–gas condensation heat transfer. Gas film thickness and gas–liquid film separations have certain effects on vapor–gas condensation heat transfer. The average dimensionless heat transfer coefficients are in agreement with the data from related literatures.

Self-similar evolution of a body eroding in a fluid flow

Erosion of solid material by flowing fluids plays an important role in shaping landforms, and in this natural context is often dictated by processes of high complexity. Here, we examine the coupled evolution of solid shape and fluid flow within the idealized setting of a cylindrical body held against a fast, unidirectional flow, and eroding under the action of fluid shear stress. Experiments and simulations both show self-similar evolution of the body, with an emerging quasi-triangular geometry that is an attractor of the shape dynamics. Our fluid erosion model, based on Prandtl boundary layer theory, yields a scaling law that accurately predicts the body's vanishing rate. Further, a class of exact solutions provides a partial prediction for the body's terminal form as one with a leading surface of uniform shear stress. Our simulations show this predicted geometry to emerge robustly from a range of different initial conditions, and allow us to explore its local stability. The sharp, faceted features of the terminal geometry defy the intuition of erosion as a globally smoothing process.

Examples of boundary layers associated with the incompressible Navier-Stokes equations

The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated. All of them are associated with the incompressible Navier-Stokes equations for Newtonian fluids equipped with various Dirichlet boundary conditions (specified velocity). These examples include a family of (nonlinear 3D) plane parallel flows, a family of (nonlinear) parallel pipe flows, as well as flows with uniform injection and suction at the boundary. We also identify a key ingredient in establishing the validity of the Prandtl type theory, i.e., a spectral constraint on the approximate solution to the Navier-Stokes system constructed by combining the inviscid solution and the solution to the Prandtl type system. This is an additional difficulty besides the wellknown issue related to the well-posedness of the Prandtl type system. It seems that the main obstruction to the verification of the spectral constraint condition is the possible separation of boundary layers. A common theme of these examples is the inhibition of separation of boundary layers either via suppressing the velocity normal to the boundary or by injection and suction at the boundary so that the spectral constraint can be verified. A meta theorem is then presented which covers all the cases considered here.

Design and validation of a wind tunnel system for odour sampling on liquid area sources

The aim of this study is to describe the methods adopted for the design and the experimental validation of a wind tunnel, a sampling system suitable for the collection of gaseous samples on passive area sources, which allows to simulate wind action on the surface to be monitored. The first step of the work was the study of the air velocity profiles. The second step of the work consisted in the validation of the sampling system. For this purpose, the odour concentration of some air samples collected by means of the wind tunnel was measured by dynamic olfactometry. The results of the air velocity measurements show that the wind tunnel design features enabled the achievement of a uniform and homogeneous air flow through the hood. Moreover, the laboratory tests showed a very good correspondence between the odour concentration values measured at the wind tunnel outlet and the odour concentration values predicted by the application of a specific volatilization model, based on the Prandtl boundary layer theory. The agreement between experimental and theoretical trends demonstrate that the studied wind tunnel represents a suitable sampling system for the simulation of specific odour emission rates from liquid area sources without outward flow.

Experimental determination of the diffusion boundary layer width of micron and submicron particles

Experimental determination of the diffusion boundary layer width of micron and submicron particles

Linear temporal and spatial stability formulations of two-dimensional surface waves on evaporating, isothermal, or condensing liquid films

When a liquid film is under the evaporating or condensing condition, the flow stability is clearly different from that under an isothermal condition due to the thermal non-equilibrium effect at the interface, especially under a lower Reynolds number. Based on Prandtl's boundary layer theory and complete boundary conditions, the universal temporal and spatial stability formulations are established using the collocation method for two-dimensional surface waves of the evaporating or condensing and isothermal liquid films draining down an inclined wall. The evolution equations indicate that the flow stability is closely related to the Reynolds number, thermocapillarity, inclination angle, liquid property, and evaporation, isothermal, or condensation actions. The effects of the above factors are investigated with neutral stability curves at different Reynolds numbers, and stability characteristics are fully indicated in theory for evaporating or condensing films. Results show that the evaporation process destabilizes the film flow and condensation process stabilizes the film flow. Thermocapillarity has a stabilizing effect in an evaporation condition and an adverse effect in the condensation condition. For a lower Reynolds number, the vapor recoil and thermocapillary take dominant effects when compared to the inertia force in determining flow stability. At a higher Reynolds number, the flow stability is controlled by the inertia force. Present study indicates that the disturbance increases with an increase of the Reynolds number and inclination angle, and decreases with increase of Ka numbers. Furthermore, the effects of liquid properties and inclination angle are always significant. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(4): 243–257, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20062