Mechanical Engineering ETDs

Publication Date

Fall 12-12-2020


Heterogeneity in materials leads to increased complication of physics, at the level or scale where heterogeneity exists, making analysis and material behavior predictions more difficult. As a result of the intricate descriptions or understanding of the physics required to determine the behavior of a heterogenous material or system, practitioners frequently prefer the use of effective properties or responses. This body of work is dedicated to performing computational analyses on the thermal behavior of heterogeneous materials and evaluating the corresponding analyses using formal verification approaches. Custom finite element method code was used for solving the heat equation in a variety of two-dimensional heterogeneous systems. Formal verification methods—including the method of manufactured solutions and the grid convergence index—were used to assess code performance and solution veracity. Functional correlations were drawn between properties of heterogeneity and effective thermal responses.


effective properties, thermal analysis, porous media, verification & validation

Degree Name

Mechanical Engineering

Level of Degree


Department Name

Mechanical Engineering

First Committee Member (Chair)

Nima Fathi

Second Committee Member

Yu-Lin Shen

Third Committee Member

Patrick J. McDaniel

Fourth Committee Member

Jens Lorenz

Document Type




Available for download on Thursday, December 12, 2024