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Assessment of Navier–Stokes’ Equations in a Fluid Mechanics Course

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Conference

2011 ASEE Annual Conference & Exposition

Location

Vancouver, BC

Publication Date

June 26, 2011

Start Date

June 26, 2011

End Date

June 29, 2011

ISSN

2153-5965

Conference Session

Outreach Projects: Promoting Energy Efficiency and Education in General

Tagged Division

Energy Conversion and Conservation

Page Count

18

Page Numbers

22.257.1 - 22.257.18

Permanent URL

https://peer.asee.org/17538

Download Count

25

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Paper Authors

biography

Mysore Narayanan Miami University

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DR. Mysore Narayanan obtained his Ph.D. from the University of Liverpool, England in
the area of Electrical and Electronic Engineering. He joined Miami University in 1980 and
teaches a wide variety of electrical, electronic and mechanical engineering courses. He has been
invited to contribute articles to several encyclopedias and has published and presented dozens of
papers at local, regional , national and international conferences. He has also designed,
developed, organized and chaired several conferences for Miami University and conference
sessions for a variety of organizations. He is a senior member of IEEE and is a member of
ASME, SIAM, ASEE, and AGU. He is actively involved in CELT activities and regularly
participates and presents at the Lilly Conference. He has been the recipient of several Faculty
Learning Community awards. He is also very active in assessment activities and has presented
dozens of papers at various Assessment Institutes. His posters in the areas of Bloom’s
Taxonomy and Socratic Inquisition have received widespread acclaim from several scholars in
the area of Cognitive Science and Educational Methodologies. He has received the Assessment of
Critical Thinking Award twice and is currently working towards incorporating writing
assignments that enhance students’ critical thinking capabilities.

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Abstract

Assessment of Navier-Stokes’ Theorem in a Fluid Mechanics CourseAbstractThe Navier-Stokes equations are indeed the foundation of fluid mechanics. Stokes’theorem is used in nearly every branch of mechanics as well as electromagnetics.Stokes' Theorem also plays a vital role in many secondary theorems such as thosepertaining to vorticity and circulation. However, the divergence theorem is amathematical statement of the physical fact that, in the absence of the creation ordestruction of matter, the density within a region of space can change only by having itflow into, or away from the region through its boundary. This is also known as Gauss’sTheorem. At present, our students who take a fluid mechanics course in their junior orsenior year are not learning about Stokes’ Theorem or Green’s Theorem or Gauss’Theorem. They also do not have a background of vector differential calculus or vectorintegral calculus. Many scholars believe that Navier Stokes Equations and theContinuum Equations form the two giant cornerstones of modern day fluid dynamics.In the year 2000 the Navier-Stokes Equation was designated as a Millennium Problem.The solution for each Millennium Problem is worth a Million Dollars. Navier-StokesEquation is one of seven mathematical problems selected by the Clay MathematicsInstitute of Cambridge, Massachusetts for this special million dollar award. It isessential to generate new techniques and modern mathematical methods for addressingand analyzing flow in complex fluids such as gels, suspensions, liquid crystals and foams.We all should however be recognize the fact that classical fluid mechanics has been verysuccessful in providing us with a quantitative understanding of turbulent flow such asshock waves. The students are unable to calculate the Gradient of a scalar field. Theyare unaware of of the need for determining the Divergence of a vector field or theimportance of calculating the Curl of vector field. The author introduced the importanceof these concepts to the students when he taught a course in hydraulics and fluidmechanics about 12 years ago. He also collected some assessment data and he presentshis findings in this paper.

Narayanan, M. (2011, June), Assessment of Navier–Stokes’ Equations in a Fluid Mechanics Course Paper presented at 2011 ASEE Annual Conference & Exposition, Vancouver, BC. https://peer.asee.org/17538

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