The Pitfalls of Readily Available Solutions: Physically Consistent Global Analysis of Species Transport from a Spherical Particle [Focus on Education]

This column provides an example in which an engineer looking up a solution in a well-known book or paper ends up with the wrong answer, and further analysis indicates that both the model statement and its reported analytical solution are incomplete. In this particular diffusion problem, global asymptotic stability was proved simply by exploiting physical understanding of the problem. It is important to assign physical problems for analyzing stability to students rather than mathematical abstractions. Otherwise, students will forget to take practical considerations into account once the model has been written, and will turn to a textbook, paper, Mathematica, or the World Wide Web to obtain an analytical solution without evaluating whether the problem statement or its solution is physically meaningful or correct. This column gives an example of a more subtle mistake that can be used for setting up a teachable moment for engineering students with a basic understanding of partial differential equations (PDEs).