ME 412: Numerical Thermo-Fluid Mechanics

Class Description:

Numerical techniques for the solution of the equations governing conduction and convective heat transfer in steady and unsteady fluid flows: finite-difference and finite-volume techniques, basic algorithms and applications to real-world fluid-flow and heat-transfer problems. Prerequisite: ME 310 and ME 320; or equivalents; or consent of instructor. 3 undergraduate hours or 3 or 4 graduate hours. For graduate hour credit, graduate students are required to complete an additional project.


1. Introduction, role of numerical solutions

2. Preliminary topics (error, stability, and convergence)

3. One-dimensional steady heat conduction

4. One-dimensional unsteady heat conduction

5. Steady 2D heat conduction; iterative and direct methods

6. 2D unsteady heat conduction

7. Heat conduction in complex geometries

8. Fully-developed flow in complex ducts

9. 1D and 2D linear convection equation

10. Nonlinear convection equation

11. Derivation of Navier-Stokes equations

12. 2D unsteady fluid flows

13. 2D steady flows

14. 3D Duct flows

15. Concluding remarks, recent advances


ME: MechSE or technical elective.

EM: Possible secondary field, with approval.

All Courses