Scalar diffusion

Nimish Pujara
University of California-Berkeley,
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Summary

This problem set provides the students the chance to cement their understanding of scalar diffusion in a quiescent fluid. By plotting solutions to the diffusion of an initial mass concentrated at a single point into a Gaussian cloud and calculating its properties, students learn how diffusion causes the scalar cloud to grow.

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Learning Goals

Students should learn the concept of Gaussian distribution and how diffusion creates them. MATLAB (or other computational tools) are used to plot functions of space and time, which allow students to visualize the solution.

Context for Use

This problem set was used for an upper level undergraduate course or an introductory graduate course on advection and diffusion of mass. The computational skills required are fairly minimal and the problem includes hints on what MATLAB functions may be useful. This makes it a useful first assignment that covers the basics of the physics and computations.

Description and Teaching Materials

There are two files: a Word file containing the problem set and a MATLAB m file containing the code for the solution
Problem set - Scalar diffusion (Microsoft Word 2007 (.docx) 65kB Oct2 17)
MATLAB m file - Scalar diffusion (Matlab File 2kB Oct2 17)


Teaching Notes and Tips

Some students may need a reminder on how to generate an array of x-values on which to evaluate the solution.

Assessment

Students should be able to produce the correct plots and answer some basic questions about their interpretation.

References and Resources