Incompressible Laminar Boundary Layer Research Articles

Solution of nonlinear boundary layer equation for flat plate via optimal homotopy asymptotic method

In this article, we use the optimal homotopy asymptotic method (OHAM) to compute the solution of two‐dimensional incompressible laminar boundary layer flow over a flat plate (Blasius problem). The obtained results for the stream function and velocity profile were comparable in terms of accuracy with that obtained by Esmaeilpour and Ganji (2007) who studied the same problem using the homotopy perturbation method and results obtained by using a numerical method (RK4). The good agreement obtained shows the effectiveness of OHAM. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 197–203, 2014; Published online 19 June 2013 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21070

Laminar boundary layer flow of a nanofluid along a wedge in the presence of suction/injection

The behavior of an incompressible laminar boundary layer flow over a wedge in a nanofluid with suction or injection has been investigated. The model used for the nanofluid integrates the effects of the Brownian motion and thermophoresis parameters. The governing partial differential equations of this problem, subjected to their boundary conditions, are solved by the Runge-Kutta-Gill technique with the shooting method for finding the skin friction and the rate of heat and mass transfer. The result are presented in the form of velocity, temperature, and volume fraction profiles for different values of the suction/injection parameter, Brownian motion parameter, thermophoresis parameter, pressure gradient parameter, Prandtl number, and Lewis number. The conclusion is drawn that these parameters significantly affect the temperature and volume fraction profiles, but their influence on the velocity profile is comparatively smaller.

Computational Analysis of the Non – Linear Boundary Layer Flow over a Flat Plate Using Variational Iterative Method (VIM)

This paper applied the variational iterative method to solve the problem of the two-dimensional incompressible laminar boundary layer flow over a flat plat also called the Blasius problem. The problem is governed by the Navier-Stokes and continuity equations which were first transformed into an ordinary differential equation using similarity transforms and the resulting problem solved using variational iterative method. The results obtained for the similarity stream function and velocity were tabulated and were highly comparable in terms of accuracy with that obtained by Ganji et al. (2009) who studied the same problem using the homotopy perturbation technique and results obtained by Blasius. The results were found to be very accurate especially for η ≤ 4 when using the variational iterative method. The method is convenient as it greatly reduces the amount of computational work.

Asymptotic Behavior of Steady Flow Near a Symmetric 3D Stagnation Point

This paper deals with the asymptotic behaviors, as the similarity variable η → ∞, of the solutions of equations governing the steady laminar incompressible boundary layer flow of an electrically conducting fluid at the symmetric stagnation point of a 3D body; the discussions being based on the asymptotic integrations of second order linear differential equations. It has been found that the principal and linearly independent solutions will exhibit asymptotic behaviors only under certain physical conditions to be imposed on them.

Scaling Group Transformation for MHD Boundary Layer Slip Flow of a Nanofluid over a Convectively Heated Stretching Sheet with Heat Generation

Steady viscous incompressible MHD laminar boundary layer slip flow of an electrically conducting nanofluid over a convectively heated permeable moving linearly stretching sheet has been investigated numerically. The effects of Brownian motion, thermophoresis, magnetic field, and heat generation/absorption are included in the nanofluid model. The similarity transformations for the governing equations are developed. The effects of the pertinent parameters, Lewis number, magnetic field, Brownian motion, heat generation, thermophoretic, momentum slip and Biot number on the flow field, temperature, skin friction factor, heat transfer rate, and nanoparticle, volume fraction rate are displayed in both graphical and tabular forms. Comparisons of analytical (for special cases) and numerical solutions with the existing results in the literature are made and is found a close agreement, that supports the validity of the present analysis and the accuracy of our numerical computations. Results for the reduced Nusselt and Sherwood numbers are provided in tabular and graphical forms for various values of the flow controlling parameters which govern the momentum, energy, and the nanoparticle volume fraction transport in the MHD boundary layer.

Evolution and instability of unsteady nonlinear streaks generated by free-stream vortical disturbances

We investigate the influence of free-stream vortical disturbances on the evolution and instability of an incompressible laminar boundary layer, focusing on components of sufficiently long wavelength, which are known to penetrate into the boundary layer to generate streamwise elongated streaks. The free-stream disturbance is assumed to be sufficiently strong (but still of small amplitude) that the induced streaks acquire an O(1) streamwise velocity in the region where the boundary-layer thickness becomes comparable with the spanwise wavelength of the perturbation. The formation and evolution of the streaks are governed by the nonlinear unsteady boundary-region equations supplemented by appropriate upstream and far-field boundary conditions. This initial-boundary-value problem is solved for the special case where the free-stream disturbance is modelled by a pair of oblique vortical modes with the same frequency but opposite spanwise wavenumbers. Nonlinearity is found to inhibit the response. The nonlinear interaction alters the mean-flow profile appreciably, the shape of which is in quantitative agreement with experimental measurements. Wall-normal inflection points are detected in the instantaneous streamwise velocity profiles. The secondary stability analysis indicates that in the presence of free-stream disturbance with an intensity of 2.8%, the resulting streaky boundary layer becomes inviscidly unstable. The characteristic frequency, phase and group velocities, and growth rate of unstable sinuous modes are found to be in broad agreement with recent experiments. The present theoretical framework allows in principle a quantitative relation to be established between the characteristics of free-stream turbulence and the secondary instability, and this relation may be exploited to develop an efficient and physics-based approach for predicting bypass transition.

On the asymptotic behaviours of solutions of third order non-linear autonomous differential equation governing the MHD flow

(Communicated by M. Paˇ sic) Abstract. This paper deals with the asymptotic behaviour as t → ∞ of the solutions for a steady laminar incompressible boundary layer equations governing the MHD flow near the forward stagnation point of two-dimensional and axisymmetric bodies. The asymptotic behaviour of the solutions is based on the method of asymptotic integration of second order linear differential equations. The results pertaining to the asymptotic behaviour of the solutions are also expressed in the form of Theorems 4.1 and 4.2.

Conjugate heat transfer for free convection along a vertical plate fin

In this study, a new and effective improved Semi-Analytic and Semi-Empirical formula f(Pr)= {ie337-1} has been proposed to solve a conjugate problem with free convection in the incompressible laminar boundary layer flow and heat conduction in a solid wall for the flow passing a flat plate fin. A combination of flat-plate flow and flat-plate fin heat conduction has been considered in the present study. Finite-difference solutions for the interface temperature profiles and the heat transfer rates have been presented over the entire thermo-fluid-dynamic field for Prandtl numbers from 0.001 to 10000. First, the similar flow field has been solved by the Runge-Kutta method and the shooting methods, then the correlation equation of the local heat transfer coefficient have been obtained. Finally, the empirical formula has been substituted into the fin temperature heat conduction calculation processes to obtain the iterative solutions of the conjugate problems.

LAMINAR STABILITY ANALYSIS IN BOUNDARY LAYER FLOW

This study presents a numerical study concerning the flow control by suction and injection. The case study is over a symmetrical airfoil with suction and injection slots. The angle of attack is 3 degree with the Mach number 0.12. Introduction This paper aims to study the stability of incompressible laminar boundary layer by numerical simulation carried out on an aerodynamic profile with suction and injection flow. The method purpose in this paper for the study of laminar stability is based on small disturbance theory in witch a small sinusoidal disturbance is imposed on a given steady laminar flow to see whether the disturbance will amplify or decay in time. If the disturbance decays, the flow will stay laminar, if the disturbance amplifies sufficiently the flow become turbulent. n e The small disturbance theory does not predict the details of the nonlinear process by which the flow changes from laminar to turbulent. It establishes which shapes of velocity profiles are unstable, identifies those frequencies that amplify fastest and indicates how the parameters governing the flow can be changed to delay transition process. Mathematical Model Let be , , u v p a solution of the incompressible laminar boundary layer equations. Over this solution assign a disturbance . , , u v p ′ ′ ′ ; ; u u u v v v p p p ′ ′ = + = + = + ′ (1) Since the basic solution , , u v p and sizes u,v,p satisfy the boundary layer equations, following equations are obtained for disturbance: 0 y v x u = ∂ ′ ∂ + ∂ ′ ∂ (2)

Control of cross flow in the three-dimensional boundary layer using space-periodic body force action

The possibility of attenuation of the cross flow in the three-dimensional incompressible laminar boundary layer on a sideslipping wing under the action of body force sources simulating the time-average forces generated by a surface electric discharge is estimated. The effect of the distance between the sources and the sideslip angle of the wing on the cross flow velocity is investigated for the source intensity observed experimentally.

Role of non-uniform slot injection (suction) model on the separation of a laminar boundary layer flow

An analysis is performed to study the influence of non-uniform slot injection (suction) on a steady incompressible laminar boundary layer flow in a diverging channel with an exponentially decreasing free-stream velocity. The difficulties in obtaining the non-similar solutions at the starting point of the streamwise coordinate, at the edges of the slot and at the point of separation are overcome by applying an implicit finite difference scheme with the quasi-linearization technique and an appropriate selection of the finer step sizes along the streamwise direction. It is observed that the separation can be delayed by non-uniform slot suction and also by moving the slot downstream but the effect of non-uniform slot injection is just reverse.

Series solutions for unsteady laminar MHD flow near forward stagnation point of an impulsively rotating and translating sphere in presence of buoyancy forces

The similarity solution for the unsteady laminar incompressible boundary layer flow of a viscous electrically conducting fluid in stagnation point region of an impulsively rotating and translating sphere with a magnetic field and a buoyancy force gives a system of non-linear partial differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the homotopy analysis method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the magnetic parameter, buoyancy parameter and rotation parameter on the surface shear stresses and surface heat transfer. It is noted that the behavior of the HAM solution for the surface shear stresses and surface heat transfer is in good agreement with the numerical solution given in reference [H. S. Takhar, A. J. Chamkha, G. Nath, Unsteady laminar MHD flow and heat transfer in the stagnation region of an impulsively spinning and translating sphere in the presence of buoyancy forces, Heat Mass Transfer 37 (2001) 397].

Multiple slot suction/injection into an exponentially decreasing free stream flow

Abstract An analysis is performed to obtain the non-similar solution of a steady incompressible laminar boundary layer flow for an exponentially decreasing free stream velocity with non-uniform multiple slot injection (suction). The difficulties in obtaining the non-similar solutions at the starting point of the stream-wise coordinate, at the edges of the slot and at the point of separation are overcome by applying an implicit finite difference scheme in combination with the quasi-linearization technique and an appropriate selection of the finer step sizes along the stream-wise direction. Results are presented for ϵ = 0.001 and for different values of mass transfer parameter, − 0.075 ≤ A ≤ 1.0. It is observed that the separation can be delayed by non-uniform multiple slot suction and also by moving the slots downstream but the effect of non-uniform multiple slot injection is just reverse.

Non-uniform double slot injection (suction) on a forced flow over a slender cylinder

A general analysis has been developed to investigate the influence of non-uniform double slot injection (suction) on the steady non-similar incompressible laminar boundary layer flow over a slender cylinder, where the slender cylinder is inline with the flow. Non-similar solutions are obtained starting from the origin of the stream-wise coordinate along the stream-wise direction by using an implicit finite difference scheme in combination with the quasilinearization technique. Numerical results are reported to display the effects of non-uniform double slot injection/suction on skin friction coefficient and heat transfer rate at the wall. Further, the effects of viscous dissipation and Prandtl number on velocity and temperature profile, and skin friction and heat transfer co-efficients are also presented in this paper.

On the similarity solutions for a steady MHD equation

In this paper, we investigate the similarity solutions for the steady laminar incompressible boundary layer equations governing the magnetohydrodynamic (MHD) flow near the forward stagnation point of two-dimensional and axisymmetric bodies. This leads to the study of a boundary value problem involving a third order autonomous ordinary differential equation. Our main results are the existence, uniqueness and non-existence for concave or convex solutions.

Thermal radiation effects on MHD flow past a semi-infinite inclined plate in the presence of mass diffusion

MHD mixed free-forced heat and mass convective steady incompressible laminar boundary layer flow of a gray optically thick electrically conducting viscous fluid past a semi-infinite inclined plate for high temperature and concentration differences is studied. A uniform magnetic field is applied perpendicular to the plate. The density of the fluid is assumed to reduce exponentially with temperature and concentration. The usual Boussinesq approximation is neglected due to the high temperature and concentration differences between the plate and the ambient fluid. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The boundary layer equations governing the flow are reduced to ordinary differential equations, which are numerically solved by applying an efficient technique. The effects of the density/temperature parameter n, the density/concentration parameter m, the local magnetic parameter Mx and the radiation parameter R are examined on the velocity, temperature and concentration distributions as well as the coefficients of skin-friction, heat flux and mass flux.

Thermal radiation effects on magnetohydrodynamic flow past a semi-infinite vertical plate in the presence of mass diffusion

Magnetohydrodynamic (MHD) mixed free–forced heat and mass convective steady incompressible laminar boundary layer flow of a gray optically thick electrically conducting viscous fluid past a semi-infinite vertical plate for high temperature and concentration differences is studied. A uniform magnetic field is applied perpendicular to the plate. The density of the fluid is assumed to reduce exponentially with temperature and concentration. The usual Boussinesq approximation is neglected because of the high temperature and concentration differences between the plate and the ambient fluid. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The boundary layer equations governing the flow are reduced to ordinary differential equations, which are numerically solved by applying an efficient technique. The effects of the density–temperature parameter n, the density–concentration parameter m, the local magnetic parameter Mx, and the radiation parameter R are examined on the velocity, temperature, and con- centration distributions as well as the coefficients of skin-friction, heat flux, and mass flux.PACS No.: 44.27+g

Non-uniform slot injection (suction) into steady laminar water boundary layer flow over a rotating sphere

Abstract The influence of non-uniform slot injection (suction) into steady axi-symmetric laminar incompressible boundary layer flows with temperature dependent viscosity and Prandtl number has been examined from the origin of the streamwise coordinate to the exact point of separation. The difficulties in obtaining the non-similar solutions at the origin of the streamwise coordinate, at the edges of the slot and at the point of separation have been overcome by applying an implicit finite difference scheme with the quasilinearization technique and an appropriate selection of finer step size along the streamwise coordinate. The results indicate that the separation can be delayed by non-uniform slot suction and also by moving the slot downstream but the effect of non-uniform slot injection is just the opposite. Further, the effect of variable fluid properties is to move the point of separation downstream but rotation parameter has the reverse effect.

Numerical simulation of the aeroacoustic noise in the separated laminar boundary layer

The unsteady flow characteristics and the related noise of separated incompressible laminar boundary layer flows (Reδ*=614, 868, and 1,063) are numerically investigated. The characteristic lines of the wall pressure are examined to identify the primary noise source, related with the unsteady motion of the vortex at the reattachment point of the separation bubble. The generation and propagation of the vortex-induced noise in the separated laminar boundary layer are computed by the method of Computational Aero-Acoustics (CAA), and the effects of Reynolds number, Mach number and adverse pressure gradient strength are examined.

Invariant boundary-value problems of an optimally controlled boundary layer

The group properties of equations of the variational problem on finding a continuous law for velocity distribution of liquid injection into an incompressible laminar boundary layer in a planar case, which ensures the minimum friction force acting on the airfoil, are considered. It is shown that the optimal injection velocity on a wedge with x=0 is finite.