TITLE:
Incompressible Flow and Heat Transfer over a Plate: A Hybrid Integral Domain-Discretized Numerical Procedure
AUTHORS:
Okey Oseloka Onyejekwe
KEYWORDS:
Falkner Skan Equation, Energy Equation, Boundary Integral Theory, Hybrid Numerical Scheme, Complementary Differential Equation
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.13,
August
5,
2016
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.