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Session 2666

The Use of Mathcad’ in Viscous-Flow Courses

B. K. Hodge Mississippi State University

Abstract

Experiences using Mathcad in an introductory graduate-level viscous-flow course and an undergraduate intermediate fluid mechanics course are described. Many of the classical equations of laminar viscous flow are third- or fourth-order nonlinear ordinary differential equations that are boundary-value problems. Mathcad functions make numerical solution of these classical equations relatively simple and quick--thus permitting routine solutions either in class or as homework. Examples of Mathcad applications are given, and the problems encountered are discussed. The use of Mathcad was judged to enhance the presentation of course material, especially in the introductory viscous-flow course.

Background

A course in viscous flow is often a part of graduate education in mechanical engineering, especially for students focusing on the thermal sciences. At the undergraduate level, intermediate fluid mechanics, with an introduction to viscous flow, is a technical elective in many mechanical engineering programs. The thrust of the coverage of viscous-flow topics at both the undergraduate and introductory graduate levels is towards fundamentals and understanding, rather than intense numerical solutions.

Indeed, at the undergraduate level, most fluid mechanics textbooks (for example, Fox and McDonald (1992) Janna (1993), Munson et al. (1994)) present solutions with little or no detail as to the computational procedures employed. Numerical examples are generally centered about the Blasius equation (laminar flow over a flat plate in a zero-pressure gradient) and various integral techniques. Applications involving solutions are stressed more than computations leading to the solutions. Undergraduate students often fail to understand and appreciate the boundary-value nature of the Blasius equation and tend to view the tabulated Blasius solution as the results of black-box arithmetic.

Graduate-level first courses in viscous flow typically follow the pattern: derivation of the Navier- Stokes equations, closed-form solutions of the Navier-Stokes equations, similarity solutions of the Navier-Stokes equations, boundary-layer theory, solutions of classic laminar boundary-layer flows, and stability of laminar boundary layers. Compared to the undergraduate viscous flow coverage, emphasis at the graduate level is placed on techniques to solve many of the equations and usually several assignments involving computer program development and/or software exercises are made. However, solutions to many of the classical laminar boundary-layer

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Hodge, B. (1997, June), The Use Of Mathcad In Viscous Flow Courses Paper presented at 1997 Annual Conference, Milwaukee, Wisconsin. 10.18260/1-2--6865