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.

A New Approach for the Derivation of the Similarity Equation of the 2-D Unsteady Boundary Layer Equations

2012 ◽  
Author(s):  
Md. Abdus Sattar
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Similarity Solutions ◽  
Length Scale ◽  
Local Similarity ◽  
Unsteady Boundary Layer ◽  
Similarity Equation ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
The One

A local similarity equation for the hydrodynamic 2-D unsteady boundary layer equations has been derived based on a time dependent length scale initially introduced by the author in solving several unsteady one-dimensional boundary layer problems. Similarity conditions for the potential flow velocity distribution are also derived. This derivation shows that local similarity solutions exist only when the potential velocity is inversely proportional to a power of the length scale mentioned above and is directly proportional to a power of the length measured along the boundary. For a particular case of a flat plate the derived similarity equation exactly corresponds to the one obtained by Ma and Hui[1]. Numerical solutions to the above similarity equation are also obtained and displayed graphically.

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.

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.

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.

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