December 6, 2021

Mechanical Engineering 531, graduate-level conduction heat transfer (offered MWF 8:30-9:20 am winter quarter 2022), is ideal for students who want to reinforce graduate-level math proficiency through application to purely conducting thermal energy in steady, transient, multi-dimensional problems as well as composites, including isotropic and anisotropic solids. Assigned problems include a comparison of exact analytical solutions with numerical results; the use of ANSYS Fluent or Star CCM+ software is supported. 

To encourage participation and collaboration with Earth and Space Sciences, ME 531 is offered in the context of Earth’s interior heat balance, with the simplifying assumption of stagnant mantle layers between Earth’s solid core and its surface crust. The analysis begins with an overall heat balance to estimate Earth’s (“steady”) interior thermal distribution, assuming uniform interior material composition, uniform thermal generation rate, and uniform average surface temperature. We then progress to model spatially variable chemical composition and thermal conductivity, on the basis of geophysicists’ best estimations of Earth’s interior material compositions. Finally, we’ll model spatially non-uniform thermal generation rates on the basis of geophysicists’ best estimations of viscous dissipation, chemical reaction / radioactive decay rates within molten mantle layers, and at the core/mantle interface. Students interested in modeling long-time-scale transient conduction (from 10k years ago to present, or even starting from the estimated origin of the Earth) will be encouraged/guided to do so.