Abstract
This work deals with incompressible two-dimensional viscous flow over a semi-infinite plate ac-cording to the approximations resulting from Prandtl boundary layer theory. The governing non-linear coupled partial differential equations describing laminar flow are converted to a self-simi- lar type third order ordinary differential equation known as the Falkner-Skan equation. For the purposes of a numerical solution, the Falkner-Skan equation is converted to a system of first order ordinary differential equations. These are numerically addressed by the conventional shooting and bisection methods coupled with the Runge-Kutta technique. However the accompanying energy equation lends itself to a hybrid numerical finite element-boundary integral application. An appropriate complementary differential equation as well as the Green second identity paves the way for the integral representation of the energy equation. This is followed by a finite element-type discretization of the problem domain. Based on the quality of the results obtained herein, a strong case is made for a hybrid numerical scheme as a useful approach for the numerical resolution of boundary layer flows and species transport. Thanks to the sparsity of the resulting coefficient matrix, the solution profiles not only agree with those of similar problems in literature but also are in consonance with the physics they represent.
Highlights
Ever since its first appearance in literature [1] the boundary layer theory under certain assumptions often leads toHow to cite this paper: Onyejekwe, O.O. (2016) Incompressible Flow and Heat Transfer over a Plate: A Hybrid Integral Domain-Discretized Numerical Procedure
Points of inflection occur for all retarded flows (β 0). This is in line with the physics of boundary layer flows
A robust numerical algorithm involving an element-driven hybridization of the boundary integral theory has been applied to the solution of the energy equation for physical relevant flows of the Falkner-Skan equation
Summary
Ever since its first appearance in literature [1] the boundary layer theory under certain assumptions often leads to. The boundary layer equations adequately describe flows predicted by the F-S equations; the assumptions resulting from the similarity theory do not take care of the prescribed initial condition in general so the resulting solutions are accurate in some asymptotic sense (Ostrach [3]). This explains why the value of the scalar must be adequately and iteratively accounted for as the independent variable approaches an infinite value. Boundary layer flow involving heat and energy transfer over a plate is very important in several engineering applications, for example, in polymer industry where plastic is produced or in general, for all cases involving the processing of sheet-like materials.
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