scholarly journals A NUMERICAL METHOD FOR SOLVING THE BOUNDARY LAYER EQUATIONS FOR GAS FLOW IN CIRCULAR TUBES WITH TRANSFER AND PROPERTY VARIATIONS.

1969 ◽  
Author(s):  
C Bankston ◽  
D McEligot
Keyword(s):  
Boundary Layer ◽  
Numerical Method ◽  
Gas Flow ◽  
Circular Tubes ◽  
Boundary Layer Equations

scholarly journals Analysis of the axisymmetrical ionized gas boundary layer adjacent to porous contour of the body of revolution

2016 ◽  
Vol 20 (2) ◽  
pp. 529-540
Author(s):  
Slobodan Savic ◽  
Branko Obrovic ◽  
Nebojsa Hristov
Keyword(s):  
Boundary Layer ◽  
Gas Flow ◽  
Mhd Flow ◽  
The Body ◽  
Generalized Solutions ◽  
Body Of Revolution ◽  
Ionized Gas ◽  
Bodies Of Revolution ◽  
Boundary Layer Equations ◽  
Longitudinal Coordinate

The ionized gas flow in the boundary layer on bodies of revolution with porous contour is studied in this paper. The gas electroconductivity is assumed to be a function of the longitudinal coordinate x. The problem is solved using Saljnikov's version of the general similarity method. This paper is an extension of Saljnikov?s generalized solutions and their application to a particular case of magnetohydrodynamic (MHD) flow. Generalized boundary layer equations have been numerically solved in a four-parametric localized approximation and characteristics of some physical quantities in the boundary layer has been studied.

A numerical method for integrating the unsteady boundary-layer equations when there are regions of backflow

1973 ◽  
Vol 58 (3) ◽  
pp. 561-579 ◽  
Author(s):  
J. H. Phillips ◽  
R. C. Ackerberg
Keyword(s):  
Boundary Layer ◽  
Numerical Method ◽  
Unique Feature ◽  
Iterative Technique ◽  
Unsteady Boundary Layer ◽  
Boundary Layer Equations ◽  
Computation Step ◽  
Finite Difference Equations ◽  
Mesh Spacing ◽  
Time Variables

A numerical method for integrating the unsteady twodimensional boundarylayer equations using a second-order-accurate implicit method, which allows for arbitrary mesh spacing in the space and time variables, is developed. A unique feature of the method is the use of an asymptotic solution valid at the downstream end of the integration mesh which permits backflow to be taken into account. Newton's iterative technique is used to solve the nonlinear finite-difference equations a t each computation step, using a rapid algorithm for solving the resulting linearized equations. The method is applied to a flow which is periodic in time and contains regions of backflow. The numerical computations are compared with known numerical and asymptotic solutions and the agreement is excellent.

scholarly journals ROBUST NUMERICAL METHODS FOR BOUNDARY‐LAYER EQUATIONS FOR A MODEL PROBLEM OF FLOW OVER A SYMMETRIC CURVED SURFACE

2006 ◽  
Vol 11 (4) ◽  
pp. 365-378
Author(s):  
A. R. Ansari ◽  
B. Hossain ◽  
B. Koren ◽  
G. I. Shishkin
Keyword(s):  
Boundary Layer ◽  
Numerical Methods ◽  
Numerical Method ◽  
Original Problem ◽  
Model Problem ◽  
Curved Surface ◽  
Finite Domain ◽  
Third Order ◽  
Boundary Layer Equations ◽  
Self Similar

We investigate the model problem of flow of a viscous incompressible fluid past a symmetric curved surface when the flow is parallel to its axis. This problem is known to exhibit boundary layers. Also the problem does not have solutions in closed form, it is modelled by boundary‐layer equations. Using a self‐similar approach based on a Blasius series expansion (up to three terms), the boundary‐layer equations can be reduced to a Blasius‐type problem consisting of a system of eight third‐order ordinary differential equations on a semi‐infinite interval. Numerical methods need to be employed to attain the solutions of these equations and their derivatives, which are required for the computation of the velocity components, on a finite domain with accuracy independent of the viscosity v, which can take arbitrary values from the interval (0,1]. To construct a robust numerical method we reduce the original problem on a semi‐infinite axis to a problem on the finite interval [0, K], where K = K(N) = ln N. Employing numerical experiments we justify that the constructed numerical method is parameter robust.

scholarly journals Ionized gas boundary layer on a porous wall of the body within the electroconductive fluid

2004 ◽  
Vol 31 (1) ◽  
pp. 47-71 ◽  
Author(s):  
Branko Obrovic ◽  
Slobodan Savic
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Gas Flow ◽  
Numerical Solutions ◽  
Porous Wall ◽  
The Body ◽  
Generalized Equations ◽  
Ionized Gas ◽  
Boundary Layer Equations ◽  
Longitudinal Coordinate

This paper investigates the ionized gas flow in the boundary layer, when the contour of the body within the fluid is porous. Ionized gas is exposed to the influence of the outer magnetic field induction Bm = Bm(x), which is perpendicular to the contour of the body within the fluid. It is presumed that the electroconductivity of the ionized gas is a function only of the longitudinal coordinate, i.e. ? = ?(x). By means of adequate transformations, the governing boundary layer equations are brought to a generalized form. The obtained generalized equations are solved in a four-parameter localized approximation. Based on the obtained numerical solutions, diagrams of important physical values and characteristics of the boundary layer have been made. Conclusions have also been drawn.

On Numerical Methods for a Boundary Layer on a Body of Revolution

2003 ◽  
Vol 3 (3) ◽  
pp. 405-416 ◽  
Author(s):  
Bayezid Hossain ◽  
Ali R. Ansari ◽  
Gregorii I. Shishkin
Keyword(s):  
Boundary Layer ◽  
Numerical Methods ◽  
Numerical Method ◽  
Original Problem ◽  
Finite Domain ◽  
Body Of Revolution ◽  
Robust Methods ◽  
Type Problem ◽  
Boundary Layer Equations ◽  
Self Similar

Abstract The flow of a viscous incompressible uid past a body of revolution with aparabolic profile when the stream is parallel to its axis falls into a class of problems that exhibit boundary layers. This problem does not have solutions in closed form, and is modeled by boundary-layer equations. Using a self-similar approach based on a Blasius series expansion (up to two terms), the boundary-layer equations can be reduced to a Blasius-type problem consisting of a system of three 3rd order ordinary differential equations on a semi-infinite interval. Numerical methods need to be employed to attain the solutions of these equations and their derivatives, which are required for the computation of the velocity components, on a finite domain with accuracy independent of the viscosity v, which can take arbitrary values from the interval (0; 1]. Numerical methods for which the accuracy of the velocity components depend on the number of mesh points N, used to solve the Blasius-type problem, and do not depend on the viscosity v, are referred to as robust methods. To construct a robust numerical method we reduce the original problem on a semi-infinite axis to a problem on the finite interval [0;K], where K = K(N) = lnN. Employing numerical experiments, we justify that the constructed numerical method is parameter robust.

An effective numerical method for solving viscous–inviscid interaction problems

2005 ◽  
Vol 363 (1830) ◽  
pp. 1157-1167 ◽  
Author(s):  
Marina A Kravtsova ◽  
Vladimir B Zametaev ◽  
Anatoly I Ruban
Keyword(s):  
Boundary Layer ◽  
Numerical Method ◽  
Corner Point ◽  
Boundary Layer Separation ◽  
Separated Flows ◽  
Governing Equations ◽  
Body Contour ◽  
Boundary Layer Equations ◽  
Finite Difference Equations ◽  
Dimensional Boundary

This paper presents a new numerical method to solve the equations of the asymptotic theory of separated flows. A number of measures was taken to ensure fast convergence of the iteration procedure, which is employed to treat the nonlinear terms in the governing equations. Firstly, we selected carefully the set of variables for which the nonlinear finite difference equations were formulated. Secondly, a Newton–Raphson strategy was applied to these equations. Thirdly, the calculations were facilitated by utilizing linear approximation of the boundary-layer equations when calculating the corresponding Jacobi matrix. The performance of the method is illustrated, using as an example, the problem of laminar two-dimensional boundary-layer separation in the flow of an incompressible fluid near a corner point of a rigid body contour. The solution of this problem is non-unique in a certain parameter range where two solution branches are possible.

A Mixed Analytical/Numerical Method for Velocity and Heat Transfer of Laminar Power-Law Fluids

2016 ◽  
Vol 9 (3) ◽  
pp. 315-336 ◽  
Author(s):  
Botong Li ◽  
Liancun Zheng ◽  
Ping Lin ◽  
Zhaohui Wang ◽  
Mingjie Liao
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Numerical Method ◽  
Power Law ◽  
Infinite Plate ◽  
Temperature Fields ◽  
Boundary Layer Equations ◽  
Flow And Heat Transfer ◽  
Power Law Fluids ◽  
Power Law Function

AbstractThis paper presents a relatively simple numerical method to investigate the flow and heat transfer of laminar power-law fluids over a semi-infinite plate in the presence of viscous dissipation and anisotropy radiation. On one hand, unlike most classical works, the effects of power-law viscosity on velocity and temperature fields are taken into account when both the dynamic viscosity and the thermal diffusivity vary as a power-law function. On the other hand, boundary layer equations are derived by Taylor expansion, and a mixed analytical/numerical method (a pseudosimilarity method) is proposed to effectively solve the boundary layer equations. This method has been justified by comparing its results with those of the original governing equations obtained by a finite element method. These results agree very well especially when the Reynolds number is large. We also observe that the robustness and accuracy of the algorithm are better when thermal boundary layer is thinner than velocity boundary layer.

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