Computational Heat Transfer (CHT)


This CHT (Computational Heat Transfer) course provides a singular focus on the thermal modeling and analysis process, providing a unique perspective by developing all concepts with practical examples. It is a computational course dedicated to heat transfer. In the treatment of the general purpose advection-diffusion (AD) equation, the course material provides a strong introductory basis in CFD. The present course attempts to couple both the computational theory and practice by introducing a multistep modeling paradigm from which to base thermal analysis. The first six lectures form a close parallel with the modeling paradigm to further ingrain the concepts. The seventh lecture is dedicated to special topics and brings in practical elements ranging from hypersonic CHT to solidification modeling. The CHT course is also designed around an array of practical examples and employs real-time InterLab sessions. The overall goal of the CHT course is to form a unison of theory and practice, emphasizing a definitive structure to the analysis process. The course has a strong value added feature with the delivery of a general purpose CHT-CFD analysis code (Hyperion-TFS) and a volume Hex Meshing tool (Hyperion-Mesh3D).

Key Topics:

  • Introduction and formulation of the basic equations of heat transfer
  • Decoupling systems and deriving boundary conditions
  • Discretization, physical and mathematical and presentation of the governing equations
  • Computational solutions to the discrete equation, showcase of solution methods
  • Validation of computational models and solutions
  • Special topics in CHT
  • Click below for full outline

Who Should Attend:

The CHT course is structured appeal to primary and secondary audiences. The practicing thermal engineer, working at the beginning and intermediate level, is the primary student of the CHT course. Secondary students include: high level analysts interested in the theoretical aspects of CHT and special topics, engineering managers who must allocate resources for CHT.

Course Information:

Type of Course: Instructor-Led Short Course
Course Level: Intermediate
Course Length: 2 days
AIAA CEU's available: Yes



I. Introduction to CHT and Paradigm
A. Introduction: basic features of thermal analysis
B. Structuring the analysis approach and example application
C. Emergence of CHT as a general purpose tool and CHT as a community

II. Formulation of the basic equations of heat transfer
A. General conservation equation and conserved quantities
B. Energy conservation equation
C. Flux terms, volume source terms
D. final simplified equation with application example

E. Decoupling systems and deriving boundary conditions
1. Fundamentals of boundary conditions
2. Types of boundary conditions
3. temperature and heat flux boundary conditions
4. Control of temperature at heat flux boundaries
5. Applicability of the Robin boundary condition

F. Discretization, physical and mathematical and presentation of the governing equations
1. Motivation for discretization, flux laws and control volume connectivity
2. Parallel: physical-spatial discretization and mathematical discretization
3. Strategic discretization and refinement and application of Cartesian based discretization

G. Computational solutions to the discrete equation, showcase of solution methods
1. Direct solutions to the vectorized conservation equation and limitations of direct methods
2. Transient solution methods
3. Explicit and implicit differencing with stability analysis
4. Development of general time differencing schemes and basic relaxation methods
5. Survey and application of semi-direct inversion methods, ADI, and conjugate gradient methods

H. Validation of computational models and solutions
1. Numerical consistency analysis and bench marking
2. Showcase exact solutions with comparisons to numerical schemes
3. Energy survey methods for validation, qualitative and quantitative energy surveys

I. Special topics in CHT (Sample of topics as follows)
1. Advection and flow flow loops
2. Radiation heat transfer
3. Phase change heat transfer
4. Hyperbolic heat conduction
5. Thermostat modeling 

III. CHT in hypersonic flow



The CHT course is designed with an interactive laboratory session (Interlab). The Interlab aspect of the CHT course will be screen projected however, students will not need a computer to participate. CHT students will receive complementary copies of the following software for the CHT course: Hyperion-TFS and Hyperion-Mesh3D. This software suite is developed by the author and will be used to setup, solve and post process immediate results for a series of problems which will be processed in the class. With Interlab, the students can observe the solutions, and they are encouraged to bring laptops to emulate and solve problems covered during the lectures.


Dr. Dean Schrage received his B.S. and M.S. degrees in mechanical engineering from University of Wisconsin -Milwaukee and his Ph.D. degree in mechanical and aerospace engineering from Case Western Reserve University. Dr. Schrage has worked exclusively in applied research and development in the field of thermal and fluid management - a combined experience totaling 25 years. He holds three U.S. patents and has authored numerous journal and conference papers. Dr. Schrage is actively immersed in development of commercial-grade simulation software and the application of these codes to practical industrial problems. Such software includes general purpose CFD and CHT codes (Hyperion-TFS), hybrid rapid solver technology (Hyperion-GCG) and specialized meshing and OpenGL geometry manipulation tools (Hyperion-Mesh3D and Hyperion-CADRazor).



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