Finite difference solution of the laminar boundary layer equations including second-order effects

1968 ◽  
Author(s):  
J. LEVINE
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Laminar Boundary Layer ◽  
Second Order ◽  
Order Effects ◽  
Boundary Layer Equations ◽  
Finite Difference Solution ◽  
Second Order Effects ◽  
Difference Solution

Second-order effects in free convection

1974 ◽  
Vol 62 (4) ◽  
pp. 793-809 ◽  
Author(s):  
I. C. Walton
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Equations Of State ◽  
Asymptotic Series ◽  
Inviscid Flow ◽  
Second Order ◽  
The Body ◽  
Order Effects ◽  
Boundary Layer Equations ◽  
Second Order Effects

The equations of conservation of momentum, energy and mass together with the equations of state are examined for free convection from a vertical paraboloid. A transformation due to Saville & Churchill is applied to the first- and second-order boundary-layer equations, which are then solved using series about the stagnation point, using asymptotic series far up the body and in between by a method due to Merk. The second-order outer inviscid flow is given in terms of infinite integrals as a solution of Laplace's equation in paraboloidal co-ordinates.Eight second-order effects are distinguished, depending on longitudinal and transverse curvatures, the displacement flow, heat flux into the boundary layer and the variation of density, viscosity, thermometric conductivity and the coefficient of expansion with temperature. Expressions for the skin friction, heat-transfer coefficient and various flux thicknesses are obtained and a comparison of the second-order effects is made.

An analysis of second-order effects on laminar boundary-layer flow

1969 ◽  
Vol 35 (1) ◽  
pp. 145-169 ◽  
Author(s):  
M. Honda ◽  
Y. Kiyokawa
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Order Approximation ◽  
Second Order ◽  
Parabolic Partial Differential Equation ◽  
Order Effects ◽  
Displacement Thickness ◽  
Second Order Effects ◽  
Layer Flow

Treated in the present paper are the second-order effects, i.e. the effect of displacement thickness, longitudinal curvature, external shear and slip, on the two-dimensional laminar boundary-layer flow of incompressible fluid. The analysis is developed in terms of the stream-function co-ordinates proposed for the analysis of the rotational flow by the senior author previously. An inverse problem is set in the co-ordinates plane, and, within the framework of the second-order approximation, the problem is reduced to solving a parabolic partial differential equation for the total head. An implicit finite-difference scheme is then devised to solve the equation, and the practical computations are carried out for the flow along a flat plate or the one around a parabolic body, by making use of an electronic computer.

Application of a General Finite-Difference Method to Boundary Layer Flows

1972 ◽  
Vol 1 (3) ◽  
pp. 146-152
Author(s):  
S. D. Katotakis ◽  
J. Vlachopoulos
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Boundary Layer Flows ◽  
Boundary Layer Problem ◽  
Boundary Layer Equations ◽  
Temperature Boundary ◽  
Dimensional Boundary ◽  
Finite Difference Solution ◽  
Suction Or Injection ◽  
Layer Problem

A straight-forward and general finite-difference solution of the boundary layer equations is presented. Several problems are examined for laminar flow conditions. These include velocity and temperature boundary layers over a flat plate, linearly retarded flows and several cases of suction or injection. The results obtained are in excellent agreement with existing accurate solutions. It appears that any kind of steady, two-dimensional boundary layer problem can be solved thus with accuracy and speed.

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