Use of Mathematica as a Teaching Tool for
![Use of Mathematica as a Teaching Tool for (Computational) Fluid Dynamics and Transport Phenomena Use of Mathematica as a Teaching Tool for (Computational) Fluid Dynamics and Transport Phenomena](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-1.jpg)
![• Mixing Outline – Importance of dimensionless groups – Experimental study of mixing • Mixing Outline – Importance of dimensionless groups – Experimental study of mixing](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-2.jpg)
![Dimensionless groups • A big theme throughout the Junior-Level Fluid Dynamics course is the Dimensionless groups • A big theme throughout the Junior-Level Fluid Dynamics course is the](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-3.jpg)
![Mixing Experiment mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Mixing Experiment mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-4.jpg)
![Coloring Liquid Soap mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Coloring Liquid Soap mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-5.jpg)
![Toothpaste and Karo Syrup mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Toothpaste and Karo Syrup mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-6.jpg)
![They can be mixed mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept They can be mixed mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-7.jpg)
![Mixing questions using Dimensional analysis mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. Mixing questions using Dimensional analysis mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-8.jpg)
![Mixing Answers • Viscous mixing mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. Mixing Answers • Viscous mixing mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-9.jpg)
![Dimensionless groups do not need to be on technical subjects mjm@nd. edu http: //www. Dimensionless groups do not need to be on technical subjects mjm@nd. edu http: //www.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-10.jpg)
![Dimensionless Confucius Proverb • He who knows not and knows he knows not is Dimensionless Confucius Proverb • He who knows not and knows he knows not is](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-11.jpg)
![Dimensionless Proverb • Child ~ Wise person mjm@nd. edu http: //www. nd. edu/~mjm http: Dimensionless Proverb • Child ~ Wise person mjm@nd. edu http: //www. nd. edu/~mjm http:](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-12.jpg)
![Dimensional Analysis Note. Book mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Dimensional Analysis Note. Book mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-13.jpg)
![Mathematica Note Books Many of these (and other useful materials) are also available from Mathematica Note Books Many of these (and other useful materials) are also available from](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-14.jpg)
![Finite Difference and Finite Element solution to flow in a Rectangular Duct mjm@nd. edu Finite Difference and Finite Element solution to flow in a Rectangular Duct mjm@nd. edu](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-15.jpg)
![Objectives for “CFD” • BS engineers, whether we like it or not, will increasingly Objectives for “CFD” • BS engineers, whether we like it or not, will increasingly](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-16.jpg)
![As the aspect ratio is varied from one, the solution become increasingly inaccurate. The As the aspect ratio is varied from one, the solution become increasingly inaccurate. The](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-17.jpg)
![Comparison of solutions Analytical Finite diff. Finite element mjm@nd. edu http: //www. nd. edu/~mjm Comparison of solutions Analytical Finite diff. Finite element mjm@nd. edu http: //www. nd. edu/~mjm](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-18.jpg)
![Boundary-Layer flows mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Boundary-Layer flows mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-19.jpg)
![Boundary-Layer Flow (cont) mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Boundary-Layer Flow (cont) mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-20.jpg)
![Boundary Layer Flow mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Boundary Layer Flow mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-21.jpg)
![Problem set-up mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Problem set-up mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-22.jpg)
![Problem set-up continued mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Problem set-up continued mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-23.jpg)
![Flow over a flat plate solution mjm@nd. edu http: //www. nd. edu/~mjm http: //www. Flow over a flat plate solution mjm@nd. edu http: //www. nd. edu/~mjm http: //www.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-24.jpg)
![Flow past a wedge mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Flow past a wedge mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-25.jpg)
![Flow past a wedge mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Flow past a wedge mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-26.jpg)
![Solution code mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Solution code mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-27.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-28.jpg)
![Plots at different angles mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Plots at different angles mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-29.jpg)
![Solution of natural convection boundary - layer flow near a heated flat plate mjm@nd. Solution of natural convection boundary - layer flow near a heated flat plate mjm@nd.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-30.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-31.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-32.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-33.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-34.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-35.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-36.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-37.jpg)
![Demonstration of the effect of flow regime on pressure drop in multifluid flows mjm@nd. Demonstration of the effect of flow regime on pressure drop in multifluid flows mjm@nd.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-38.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-39.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-40.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-41.jpg)
![Surprising result mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Surprising result mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-42.jpg)
![Creeping flow past a stationary sphere mjm@nd. edu http: //www. nd. edu/~mjm http: //www. Creeping flow past a stationary sphere mjm@nd. edu http: //www. nd. edu/~mjm http: //www.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-43.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-44.jpg)
![Flow past a sphere problem mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. Flow past a sphere problem mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-45.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-46.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-47.jpg)
![mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-48.jpg)
![Velocity field magnitude mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept Velocity field magnitude mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-49.jpg)
![Conclusions • Some elements of mixing are incorporated into the fluid dynamics course – Conclusions • Some elements of mixing are incorporated into the fluid dynamics course –](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-50.jpg)
![Conclusions (cont. ) • Mathematica notebooks can be used to show students – Computations Conclusions (cont. ) • Mathematica notebooks can be used to show students – Computations](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-51.jpg)
- Slides: 51
![Use of Mathematica as a Teaching Tool for Computational Fluid Dynamics and Transport Phenomena Use of Mathematica as a Teaching Tool for (Computational) Fluid Dynamics and Transport Phenomena](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-1.jpg)
Use of Mathematica as a Teaching Tool for (Computational) Fluid Dynamics and Transport Phenomena Mark J. Mc. Cready University of Notre Dame mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Mixing Outline Importance of dimensionless groups Experimental study of mixing • Mixing Outline – Importance of dimensionless groups – Experimental study of mixing](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-2.jpg)
• Mixing Outline – Importance of dimensionless groups – Experimental study of mixing of viscous materials • Numerical solution to flow in a rectangular duct – Mathematica used to show finite difference vs finite element • Mathematica notebooks on computational fluid flow and heat transfer problems – Boundary-layer flow, Falkner-Skan problem – Natural convection thermal boundary layer • Mathematica notebooks for other fluid flow problems – Creeping flow past a sphere – Introduction to multiphase flows mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Dimensionless groups A big theme throughout the JuniorLevel Fluid Dynamics course is the Dimensionless groups • A big theme throughout the Junior-Level Fluid Dynamics course is the](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-3.jpg)
Dimensionless groups • A big theme throughout the Junior-Level Fluid Dynamics course is the importance of comparing competing or cooperating effects and how dimensionless groups inherently do this. • To make the point we did a laboratory exercise on mixing and combined with dimensional analysis. mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Mixing Experiment mjmnd edu http www nd edumjm http www nd educhegdept Mixing Experiment mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-4.jpg)
Mixing Experiment mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Coloring Liquid Soap mjmnd edu http www nd edumjm http www nd educhegdept Coloring Liquid Soap mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-5.jpg)
Coloring Liquid Soap mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Toothpaste and Karo Syrup mjmnd edu http www nd edumjm http www nd educhegdept Toothpaste and Karo Syrup mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-6.jpg)
Toothpaste and Karo Syrup mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![They can be mixed mjmnd edu http www nd edumjm http www nd educhegdept They can be mixed mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-7.jpg)
They can be mixed mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Mixing questions using Dimensional analysis mjmnd edu http www nd edumjm http www nd Mixing questions using Dimensional analysis mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-8.jpg)
Mixing questions using Dimensional analysis mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Mixing Answers Viscous mixing mjmnd edu http www nd edumjm http www nd Mixing Answers • Viscous mixing mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-9.jpg)
Mixing Answers • Viscous mixing mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Dimensionless groups do not need to be on technical subjects mjmnd edu http www Dimensionless groups do not need to be on technical subjects mjm@nd. edu http: //www.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-10.jpg)
Dimensionless groups do not need to be on technical subjects mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Dimensionless Confucius Proverb He who knows not and knows he knows not is Dimensionless Confucius Proverb • He who knows not and knows he knows not is](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-11.jpg)
Dimensionless Confucius Proverb • He who knows not and knows he knows not is a child, teach him, Cr~1 • He who knows not and knows not he knows not is a fool, shun him, Cr<<1 • He who knows and knows not he knows is asleep, awaken him, Cr>>1 • He who knows and knows he knows is wise, follow him Cr~1 mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Dimensionless Proverb Child Wise person mjmnd edu http www nd edumjm http Dimensionless Proverb • Child ~ Wise person mjm@nd. edu http: //www. nd. edu/~mjm http:](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-12.jpg)
Dimensionless Proverb • Child ~ Wise person mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Dimensional Analysis Note Book mjmnd edu http www nd edumjm http www nd educhegdept Dimensional Analysis Note. Book mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-13.jpg)
Dimensional Analysis Note. Book mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Mathematica Note Books Many of these and other useful materials are also available from Mathematica Note Books Many of these (and other useful materials) are also available from](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-14.jpg)
Mathematica Note Books Many of these (and other useful materials) are also available from Math. Source, at the Wolfram Research website. This and other courses that use Mathematica materials can be found at the Mathematica Courseware web site. A simple Mathematica primer, Mathematica_primer. 1. nb. (Notebook) Mathematica Primer(html) A basic introduction to dimensional analysis including physical motivation and how to solve pipe flow. dimensional. analysis. nb. (Notebook) dimensional. analysis. html (html) A simple primer on why we use log-log plots and what they mean, Primer on log-log and semilog plots. (Notebook) Primer on log-log and semilog plots(html) An exhaustive solution of the lubricated flow example ("core-annular flow") from Middleman 3. 2. 3, pp 79 -82). It demonstrates a number of Mathematica features and several important basic ideas from this course, lubricatedflow. nb (notebook format) lubricatedflow. html (html, this is not as good as the Mathematica version, but you don't need Math. Reader. ) This one shows how to use the chain rule to nondimensionalize differential equations. It also makes a point that the Resulting dimensionless terms are of order 1. Making a differential equation dimensionless (Notebook format) Making a differential equation dimensionless (html) mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Finite Difference and Finite Element solution to flow in a Rectangular Duct mjmnd edu Finite Difference and Finite Element solution to flow in a Rectangular Duct mjm@nd. edu](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-15.jpg)
Finite Difference and Finite Element solution to flow in a Rectangular Duct mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Objectives for CFD BS engineers whether we like it or not will increasingly Objectives for “CFD” • BS engineers, whether we like it or not, will increasingly](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-16.jpg)
Objectives for “CFD” • BS engineers, whether we like it or not, will increasingly be using computational packages and analytical instruments that are ”turn key” (they don’t understand how they work). We need to instill in them both a healthy skepticism that they need to verify the answers, and enough fundamental understanding of the different subject so that they can. mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![As the aspect ratio is varied from one the solution become increasingly inaccurate The As the aspect ratio is varied from one, the solution become increasingly inaccurate. The](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-17.jpg)
As the aspect ratio is varied from one, the solution become increasingly inaccurate. The finite different method works better mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Comparison of solutions Analytical Finite diff Finite element mjmnd edu http www nd edumjm Comparison of solutions Analytical Finite diff. Finite element mjm@nd. edu http: //www. nd. edu/~mjm](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-18.jpg)
Comparison of solutions Analytical Finite diff. Finite element mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![BoundaryLayer flows mjmnd edu http www nd edumjm http www nd educhegdept Boundary-Layer flows mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-19.jpg)
Boundary-Layer flows mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![BoundaryLayer Flow cont mjmnd edu http www nd edumjm http www nd educhegdept Boundary-Layer Flow (cont) mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-20.jpg)
Boundary-Layer Flow (cont) mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Boundary Layer Flow mjmnd edu http www nd edumjm http www nd educhegdept Boundary Layer Flow mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-21.jpg)
Boundary Layer Flow mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Problem setup mjmnd edu http www nd edumjm http www nd educhegdept Problem set-up mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-22.jpg)
Problem set-up mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Problem setup continued mjmnd edu http www nd edumjm http www nd educhegdept Problem set-up continued mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-23.jpg)
Problem set-up continued mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Flow over a flat plate solution mjmnd edu http www nd edumjm http www Flow over a flat plate solution mjm@nd. edu http: //www. nd. edu/~mjm http: //www.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-24.jpg)
Flow over a flat plate solution mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Flow past a wedge mjmnd edu http www nd edumjm http www nd educhegdept Flow past a wedge mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-25.jpg)
Flow past a wedge mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Flow past a wedge mjmnd edu http www nd edumjm http www nd educhegdept Flow past a wedge mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-26.jpg)
Flow past a wedge mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Solution code mjmnd edu http www nd edumjm http www nd educhegdept Solution code mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-27.jpg)
Solution code mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-28.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Plots at different angles mjmnd edu http www nd edumjm http www nd educhegdept Plots at different angles mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-29.jpg)
Plots at different angles mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Solution of natural convection boundary layer flow near a heated flat plate mjmnd Solution of natural convection boundary - layer flow near a heated flat plate mjm@nd.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-30.jpg)
Solution of natural convection boundary - layer flow near a heated flat plate mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-31.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-32.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-33.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-34.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-35.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-36.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-37.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Demonstration of the effect of flow regime on pressure drop in multifluid flows mjmnd Demonstration of the effect of flow regime on pressure drop in multifluid flows mjm@nd.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-38.jpg)
Demonstration of the effect of flow regime on pressure drop in multifluid flows mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-39.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-40.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-41.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Surprising result mjmnd edu http www nd edumjm http www nd educhegdept Surprising result mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-42.jpg)
Surprising result mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Creeping flow past a stationary sphere mjmnd edu http www nd edumjm http www Creeping flow past a stationary sphere mjm@nd. edu http: //www. nd. edu/~mjm http: //www.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-43.jpg)
Creeping flow past a stationary sphere mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-44.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Flow past a sphere problem mjmnd edu http www nd edumjm http www nd Flow past a sphere problem mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd.](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-45.jpg)
Flow past a sphere problem mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-46.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-47.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![mjmnd edu http www nd edumjm http www nd educhegdept mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-48.jpg)
mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Velocity field magnitude mjmnd edu http www nd edumjm http www nd educhegdept Velocity field magnitude mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-49.jpg)
Velocity field magnitude mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Conclusions Some elements of mixing are incorporated into the fluid dynamics course Conclusions • Some elements of mixing are incorporated into the fluid dynamics course –](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-50.jpg)
Conclusions • Some elements of mixing are incorporated into the fluid dynamics course – Laboratory experiment – Dimensional analysis • The main idea we attempt to convey about computational fluid dynamics is that it is wonderful if it works, but make sure your solution is correct. – Strategy is like using different excess Gibbs Free Energy models to design distillation columns with a process simulator mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
![Conclusions cont Mathematica notebooks can be used to show students Computations Conclusions (cont. ) • Mathematica notebooks can be used to show students – Computations](https://slidetodoc.com/presentation_image_h2/73548d48bca7808c8ece594f6b787e4b/image-51.jpg)
Conclusions (cont. ) • Mathematica notebooks can be used to show students – Computations – To do algebra that is too tedious for them to do – To allow them to explore the solution – To incorporate other media • Questions remain as to if our approach gives a significant or incremental benefit to the students. mjm@nd. edu http: //www. nd. edu/~mjm http: //www. nd. edu/~chegdept
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