scholarly journals On The Numerical Solutions of Boundary Layer Equations of Williamson Fluid Past a Moving Plate

2020 ◽  
Vol 8 (2) ◽  
pp. 75-80
Author(s):  
Manisha Patel ◽  
Jayshri Patel ◽  
M.G.Timol
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Flow Problem ◽  
Governing Equations ◽  
Moving Plate ◽  
Williamson Fluid ◽  
Boundary Layer Equations ◽  
Reduced Equations ◽  
Layer Flow ◽  
Graphical Presentation

Laminar boundary layer flow of Williamson fluid over a moving plate is discussed in this paper. The governing equations of the flow problem are transformed into similarity equations using similarity technique. The reduced equations are numerically solved by finite difference method. The graphical presentation is discussed.

Transformations of the boundary-layer equations for rotating flows

1968 ◽  
Vol 33 (1) ◽  
pp. 113-126
Author(s):  
N. Rott ◽  
J. T. Ohrenberger
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Compressible Flow ◽  
Incompressible Flow ◽  
Flow Problem ◽  
Rotating Flows ◽  
Governing Equations ◽  
Boundary Layer Equations ◽  
Axis Of Symmetry ◽  
Semi Empirical

The boundary layer on an axisymmetric surface above which the flow is rotating about the axis of symmetry is considered. Transformations of the governing equations which permit the generalizations of a known solution for one meridian shape in incompressible flow to a family of meridian shapes are shown to exist. For compressible flow, a transformation of the Stewartson-Illingworth type was found which reduces a compressible flow problem to an incompressible case. Also, remarks are made concerning the invariance of the turbulent boundary-layer integral equations assuming particular semi-empirical shear laws.

Study of Some Contemporary Laminar Flow Models Over a Flat Plate Using Maple

2008 ◽  
Author(s):  
Abdul Aziz
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Laminar Boundary Layer ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Slip Flow ◽  
Moving Plate ◽  
Flow Models ◽  
Layer Flow ◽  
Energy Equations

The paper uses a modern computing tool, Maple, to study some contemporary problems in laminar boundary layer flow over a flat plate. The purpose is to demonstrate that Maple is a powerful computational tool for solving realistic contemporary problems in laminar boundary layer theory. The specific problems (all pertaining to a flat plate) chosen for this study are (1) hydrodynamic boundary layer with slip flow condition, (2) velocity boundary layer on a moving plate, (3) hydrodynamic and thermal boundary layers with a linear shear flow. Each problem is of contemporary interest and allows a similarity analysis which reduces the continuity, momentum, and energy equations into ordinary nonlinear differential equations. Numerical solutions of these equations are generated and physical interpretations of the results provided. Maple worksheets for solving each problem are available from the author upon request. It is shown that the effort required to solve these problems with Maple is modest, consisting of few lines of easily learned commands. The use of Maple facilitates and enriches the study of laminar boundary flows in general.

Non-similarity solutions to the corner boundary-layer equations (and the effects of wall transpiration)

1999 ◽  
Vol 400 ◽  
pp. 125-162 ◽  
Author(s):  
PETER W. DUCK ◽  
SIMON R. STOW ◽  
MANHAR R. DHANAK
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
A Priori ◽  
Leading Edge ◽  
Flow Region ◽  
Similarity Solutions ◽  
Leading Order ◽  
Governing Equations ◽  
Boundary Layer Equations ◽  
Pressure Term

The incompressible boundary layer in the corner formed by two intersecting, semi-infinite planes is investigated, when the free-stream flow, aligned with the corner, is taken to be of the form U∞F(x), x representing the non-dimensional streamwise distance from the leading edge. In Dhanak & Duck (1997) similarity solutions for F(x) = xn were considered, and it was found that solutions exist for only a range of values of n, whilst for ∞ > n > −0.018, approximately, two solutions exist. In this paper, we extend the work of Dhanak & Duck to the case of non-90° corner angles and allow for streamwise development of solutions. In addition, the effect of transpiration at the walls of the corner is investigated. The governing equations are of boundary-layer type and as such are parabolic in nature. Crucially, although the leading-order pressure term is known a priori, the third-order pressure term is not, but this is nonetheless present in the leading-order governing equations, together with the transverse and crossflow viscous terms.Particular attention is paid to flows which develop spatially from similarity solutions. It turns out that two scenarios are possible. In some cases the problem may be treated in the usual parabolic sense, with standard numerical marching procedures being entirely appropriate. In other cases standard marching procedures lead to numerically inconsistent solutions. The source of this difficulty is linked to the existence of eigensolutions emanating from the leading edge (which are not present in flows appropriate to the first scenario), analogous to those found in the computation of some two-dimensional hypersonic boundary layers (Neiland 1970; Mikhailov et al. 1971; Brown & Stewartson 1975). In order to circumvent this difficulty, a different numerical solution strategy is adopted, based on a global Newton iteration procedure.A number of numerical solutions for the entire corner flow region are presented.

scholarly journals MHD Mixed Convective Boundary Layer Flow of a Nanofluid through a Porous Medium due to an Exponentially Stretching Sheet

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
M. Ferdows ◽  
Md. Shakhaoath Khan ◽  
Md. Mahmud Alam ◽  
Shuyu Sun
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Boundary Layer Equations ◽  
Exponentially Stretching Sheet ◽  
Layer Flow ◽  
Exponentially Stretching

Magnetohydrodynamic (MHD) boundary layer flow of a nanofluid over an exponentially stretching sheet was studied. The governing boundary layer equations are reduced into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration schemes. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. The numerical solutions for the wall skin friction coefficient, the heat and mass transfer coefficient, and the velocity, temperature, and concentration profiles are computed, analyzed, and discussed graphically. Comparison with previously published work is performed and excellent agreement is observed.

scholarly journals On the Numerical Analysis of Unsteady MHD Boundary Layer Flow of Williamson Fluid Over a Stretching Sheet and Heat and Mass Transfers

Computation ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 55 ◽  
Author(s):  
Stanford Shateyi ◽  
Hillary Muzara
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Weissenberg Number ◽  
Convection Boundary Layer ◽  
Electric Parameter ◽  
Williamson Fluid ◽  
Layer Flow ◽  
Mass Transfers

A thorough and detailed investigation of an unsteady free convection boundary layer flow of an incompressible electrically conducting Williamson fluid over a stretching sheet saturated with a porous medium has been numerically carried out. The partial governing equations are transferred into a system of non-linear dimensionless ordinary differential equations by employing suitable similarity transformations. The resultant equations are then numerically solved using the spectral quasi-linearization method. Numerical solutions are obtained in terms of the velocity, temperature and concentration profiles, as well as the skin friction, heat and mass transfers. These numerical results are presented graphically and in tabular forms. From the results, it is found out that the Weissenberg number, local electric parameter, the unsteadiness parameter, the magnetic, porosity and the buoyancy parameters have significant effects on the flow properties.

A singularity in thermal boundary-layer flow on a horizontal surface

1992 ◽  
Vol 242 ◽  
pp. 419-440 ◽  
Author(s):  
P. G. Daniels
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Rational Numbers ◽  
Velocity Fields ◽  
Boundary Layer Equations ◽  
Layer Flow ◽  
Buoyancy Flows ◽  
Temperature And Velocity Fields

A thermal boundary layer, in which the temperature and velocity fields are coupled by buoyancy, flows along a horizontal, insulated wall. For sufficiently low local Froude number the solution terminates in a singularity with rising skin friction and falling pressure. The structure of the singularity is obtained and the results are compared with numerical solutions of the horizontal boundary-layer equations. A novel feature of the analysis is that the powers of the streamwise coordinate involved in the structure of the singularity do not appear to be simple rational numbers and are determined from the solution of a pair of ordinary differential equations which govern the flow in an inner viscous region close to the wall. Modifications of the theory are noted for cases where either the temperature or a non-zero heat transfer are specified at the wall.

Similarity Solutions of Laminar, Incompressible Boundary Layer Equations of Non-Newtonian Fluids

1968 ◽  
Vol 90 (1) ◽  
pp. 71-74 ◽  
Author(s):  
A. G. Hansen ◽  
T. Y. Na
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Engineering Application ◽  
Similarity Solutions ◽  
Newtonian Fluids ◽  
Important Conclusion ◽  
Arbitrary Continuous Function ◽  
Boundary Layer Equations ◽  
Eyring Model ◽  
Layer Flow

A similarity analysis is made of the steady, two-dimensional, laminar boundary layer flow of non-Newtonian fluids. The important conclusion drawn from this analysis is that for non-Newtonian fluids of any model, similarity solutions exist only for the case of a wedge flow of 90 deg. The only limitation is that the stress and rate-of-strain can be related by an arbitrary continuous function. The result in this paper further extends a recent work by Lee and Ames [11]. Numerical solutions for the Powell-Eyring model are presented in dimensionless form as an engineering application of the theory.

Boundary layer flow over a moving plate in a flowing fluid considering non-linear radiations

2016 ◽  
Vol 26 (5) ◽  
pp. 1617-1630 ◽  
Author(s):  
Ammar Mushtaq ◽  
M. Mustafa ◽  
T. Hayat ◽  
A. Alsaedi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Numerical Solutions ◽  
Moving Plate ◽  
Flowing Fluid ◽  
Content Type ◽  
Electrically Conducting ◽  
Special Cases ◽  
Self Similar ◽  
Layer Flow

Purpose – The purpose of this paper is to consider a laminar two-dimensional incompressible flow of an electrically conducting fluid over a moving flat plate with a parallel free stream. Design/methodology/approach – The governing equations are first reduced into self-similar forms and then solved for the numerical solutions by shooting method. Findings – The results are compared with the available studies is some special cases and found in excellent agreement. It is noticed that an increase in the magnetic field strength leads to a decrease in the momentum boundary layer thickness and enhancement in the rate of heat transfer from the plate. It is also observed that temperature and heat transfer from the plate increase when radiation effect is strengthened. Originality/value – A recently proposed idea of nonlinear radiative heat transfer with Joule heating and viscous dissipation effects is analyzed.

Effect of variable viscosity on boundary layer flow along a continuously moving plate with variable surface temperature

2004 ◽  
Vol 40 (5) ◽  
pp. 421-424 ◽  
Author(s):  
V. M. Soundalgekar ◽  
H. S. Takhar ◽  
U. N. Das ◽  
R. K. Deka ◽  
A. Sarmah
Keyword(s):  
Boundary Layer ◽  
Surface Temperature ◽  
Boundary Layer Flow ◽  
Variable Viscosity ◽  
Moving Plate ◽  
Variable Surface ◽  
Layer Flow ◽  
Variable Surface Temperature

On Spectral Relaxation Approach to Radiating Powell-Eyring Fluid Flow over a Stretching Disk with Newtonian Heating

2018 ◽  
Vol 387 ◽  
pp. 461-473 ◽  
Author(s):  
K. Gangadhar ◽  
D. Vijaya Kumar ◽  
S. Mohammed Ibrahim ◽  
Oluwole Daniel Makinde
Keyword(s):  
Boundary Layer ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Relaxation Method ◽  
Newtonian Heating ◽  
Nonlinear Boundary Value Problems ◽  
Local Skin ◽  
Boundary Layer Equations ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

In this study we use a new spectral relaxation method to investigate an axisymmetric law laminar boundary layer flow of a viscous incompressible non-Newtonian Eyring-Powell fluid and heat transfer over a heated disk with thermal radiation and Newtonian heating. The transformed boundary layer equations are solved numerically using the spectral relaxation method that has been proposed for the solution of nonlinear boundary layer equations. Numerical solutions are obtained for the local wall temperature, the local skin friction coefficient, as well as the velocity and temperature profiles. We show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to common numerical methods for solving nonlinear boundary value problems. We show that the convergence rate of the spectral relaxation method is significantly improved by using method in conjunction with the successive over-relaxation method. It is observed that CPU time is reduced in SOR method compare with SRM method.

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