Study of Some Contemporary Laminar Flow Models Over a Flat Plate Using Maple

Abstract

The paper uses a modern computing tool, Maple, to study some contemporary problems in laminar boundary layer flow over a flat plate. The purpose is to demonstrate that Maple is a powerful computational tool for solving realistic contemporary problems in laminar boundary layer theory. The specific problems (all pertaining to a flat plate) chosen for this study are (1) hydrodynamic boundary layer with slip flow condition, (2) velocity boundary layer on a moving plate, (3) hydrodynamic and thermal boundary layers with a linear shear flow. Each problem is of contemporary interest and allows a similarity analysis which reduces the continuity, momentum, and energy equations into ordinary nonlinear differential equations. Numerical solutions of these equations are generated and physical interpretations of the results provided. Maple worksheets for solving each problem are available from the author upon request. It is shown that the effort required to solve these problems with Maple is modest, consisting of few lines of easily learned commands. The use of Maple facilitates and enriches the study of laminar boundary flows in general.