The Thermal Fluid Systems graduate curriculum is designed to give all students in the program proficiency in fluid mechanics, heat transfer and thermodynamics, as well as the mathematical, experimental and computational tools needed to work in these disciplines. It is also designed to provide students the opportunity to pursue in-depth study in each of these broad disciplines. The coursework component of the TFS graduate program includes five or six required courses for students pursuing M.S. or Ph.D. degrees respectively. The required courses are defined in the following section, followed by a listing of the courses making up the TFS graduate curriculum.

To access the most recent course syllabi for these courses, please refer to the Syllabi Database.

## 1. Required Courses

Graduate students pursuing degrees in Thermal Fluid Systems are required to take the following courses:

- In fluid mechanics:
- ME 381P1: Fundamentals of Incompressible Flow
- In heat transfer, either:
- ME 381R4: Fundamentals of Heat and Mass Transfer, or
- ME 381R1, ME 381R2 & ME 381R3 (see descriptions in section 2.2 below)
- In thermodynamics:
- ME 381Q1: Advanced Thermodynamics
- In experimental methods, for M.S. students who do not take the computational methods course (see below) and all Ph.D. students take one of the following:
- ME 382P1: Advanced Experimental Methods for Thermal/Fluid Systems
- ME 382P2: Lasers and Optics
- In computational methods, for M.S. students who do not take an experimental methods course (see above) and all Ph.D. students:
- ME 382N3: Computational Methods for Thermal/Fluid Systems
- In mathematics, one of the following:
- PGE 381K: Engineering Analysis
- ASE 380P1: Mathematical Methods in Applied Mechanics I (same as EM386K)
- ME 380Q1: Engineering Analysis: Analytical Methods

For Ph.D. students who come to The University of Texas with an M.S., the course work experience from the student's M.S. program will be evaluated to determine which of the above requirements have been satisfied in the M.S. program. Furthermore, students may petition to substitute substantially similar courses for those listed above, provided they provide a reason that the substituted course is more appropriate for their program.

For students pursuing interdisciplinary programs, requirements will be adjusted to include mathematics, experimental methods and/or computation, and disciplinary courses that are appropriate for the program.

## 2. Courses in the Thermal/Fluid Systems Curriculum

In the following subsections, courses at The University of Texas that are recommended for their coverage of topics in the TFS curriculum are listed. Many of these courses are offered by other departments, but they are none-the-less useful for TFS graduate students. Courses that satisfy or partially satisfy requirements as defined in section 1 are so indicated by SR or PSR respectively. Courses are organized into six groups (fluids, heat transfer, thermo, experiments, computations and math).

## 2.1 Fluid Mechanics Courses

### Fundamental of fluid mechanics:

- ME 381P1: Fundamentals of Incompressible Flow SR

### Turbulence:

- ME 381P3: Dynamics of Turbulent Flow
- ASE 382Q9: Turbulent Mixing

### Compressible flow:

- ASE 382Q7: Advanced Problems in Compressible Flow

### Micro/nano scale flow:

- ME 381P4: Multiscale Flow & Transport Phenomena

### Multi-phase flow:

- ME 381R6: Multiphase Flow and Heat Transfer

### Turbomachinery:

- ME 381P2: Compressible Flow and Turbomachinery
- ME 381P5: Advanced Turbomachinery

### Stratified/Buoyancy driven flows:

- CE 380S: Environmental Fluid Dynamics

### Modeling and Simulation:

- ASE 382R5: Advanced Computational Methods
- ME 382N1: Introduction to Computational Fluid Mechanics

## 2.2 Heat Transfer Courses

### Fundamentals of heat & mass transfer:

- ME 381R4: Fundamentals of Heat and Mass Transfer SR

### Conductive and convective heat & mass transfer:

- ME 381R1: Advanced Conductive Heat Transfer PSR
- ME 381R2: Advanced Convective Heat and Mass Transfer PSR
- ChE 387M: Mass Transfer

### Radiative heat transfer:

- ME 381R3: Radiative Heat Transfer PSR
- ME 381R5: Radiation in Participating Media

### Heat transfer in multi-phase flows:

- ME 381R6: Multiphase Flow and Heat Transfer

### Micro-scale heat & mass transfer:

- ME 381R7: Nanoscale Energy Transport and Conversion
- ME 381P4: Multiscale Flow & Transport Phenomena

### Heat & mass transfer in reacting flows:

- ME 382R5: Principles of Combustion Theory

## 2.3 Thermodynamics & Combustion Courses

### Fundamentals:

- ME 381Q1: Advanced Thermodynamics SR
- ME382Q3: Advanced Thermo/Fluid Systems

### Macro-thermodynamic applications:

- ME 386P3: Introduction to Thermodynamics of Materials
- ME 386P6: Kinetic Processes in Materials

### Statistical thermodynamics:

- ME 381Q4: Molecular Gas Dynamics (same as ASE382R6)
- ASE 382Q10: Plasmas and Reactive Flows

### Combustion:

- ME 382R1: Fundamentals of Combustion
- ME 382R5: Advanced Combustion
- ME 382R6: Combustion Engine Processes
- ME 382T: Fire Science
- ASE 382Q9: Turbulent Mixing
- ASE 396: Turbulence & Combustion Modeling

### Energy Technology:

- ME 382Q2: Introduction to Renewable Energy
- ME 382Q4: Energy Technology and Policy

## 2.4 Experimental Methods Courses

- ME 382P1: Advanced Experimental Methods for Thermal/Fluid Systems SR
- ME 382P2: Optics and Lasers Laboratory SR

## 2.5 Computational Methods Courses

### Introduction to computational methods:

- ME 382N3: Computational Methods for Thermal/Fluid Systems SR

### Numerical PDE's:

- CAM 394F: Finite Element Methods (same as EM394F & ASE384P4)
- CE 381R: The Finite Element Method
- CAM 386K: Numerical Treatment of Differential Equations

### Computational statistics:

- SSC 384.9: Computational Statistics

### Computational fluid dynamics:

- ME 382N1: Introduction to Computational Fluid Mechanics
- ASE 382R5: Advanced Computational Methods
- CAM 393N: Numerical Methods for Flow and Transport Problems

### Molecular and atomic-scale algorithms:

- ASE 382Q8: Lagrangian Methods in Computational Fluid Dynamics

### Practical scientific computation:

- SSC 292: Introduction to Scientific Programming
- SSC 394: Scientific and Technical Computing
- SSC 394C: Parallel Computing for Scientists and Engineers

## 2.6 Mathematical Methods Courses

### Introduction to mathematical methods:

- PGE 381K: Engineering Analysis SR
- ASE 380P1: Mathematical Methods in Applied Mechanics I SR (same as EM386K)
- ME380Q1: Engineering Analysis: Analytical Methods SR

### Analytical methods:

- ASE 380P2: Analytical Methods II (complex analysis, integral transforms, ODE's PDE's, asymptotics)
- EM 386L: Mathematical Methods in Applied Mechanics II (Complex analysis, ODE's, PDE's)
- CAM 386M: Functional Analysis in Theoretical Mechanics (same as EM 386M: Functional Analysis and Linear Operators)

### Probability and statistics:

- SSC 384.1: Applied Probability
- SSC 384.7: Bayesian Statistical Analysis

### Advanced applied mathematics:

- CAM 385C: Methods of Applied Mathematics
- CAM 385D: Methods of Applied Mathematics