ME 521

ME 521
Conduction Heat Transfer

This course discusses various analytical methods for solving heat conduction problems. The main focus is on the method of Separation of Variables and its various modifications in different coordinate systems. Numerical solution is also discussed using the Finite Element Method.

Prerequisite(s): CS 108 and ME 421 or consent of instructor.

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Finite Element Project

Heat Conduction in Two Dimensions

For this project, the student should select any 2-D conduction problem for which an analytical solution is available. It may be in either cartesian or cylindrical coordinates.

You will then perform a numerical analysis to determine the transient solution for the problem by modifying the provided FEM code. Finally, write a report summarizing your work.

For this project, the student is expected to:

  • Perform a resolution study by comparing various mesh sizes and time-step sizes
  • Compare the analytical solution to the numerical solution to validate your results
  • Use grid streching/compression to show you are able to achieve higher accuracy with fewer elements than a uniform mesh
  • Select different initial conditions to show they all give the same steady-state solution
  • Change boundary conditions and compare results

Sample Result

 Consider a rectangular plate with initial temperature of 300 and a uniform heat generation with a magnitude of 10000.

Project Materials

The project handout and sample code/materials may be downloaded here.