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ME
423
Computational Fluid Mechanics and Heat Transfer
Classification of partial differential equations, numerical techniques for solving fluid dynamics and heat transfer problems, finite difference, finite element, boundary element, and finite control volume methods, numerical solutions of parabolic, elliptic, and hyperbolic equations in fluid dynamics and heat transfer.
Prerequisites:
0630331,0630421
0630423
(3-0-3)

Textbook:

Darrell W. Pepper and Juan C. Heinrich, The Finite Element Method: Basic Concepts and Applications with MATLAB, MAPLE, and COMSOL, Third Edition, CRC Press (2017).

References:

Dale A. Anderson John C. Tannehill, Richard H Pletcher, Ramakanth Munipalli, and Vijaya Shankar, Computational Fluid Mechanics and Heat Transfer, by CRC Press (Taylor & Francis Group), 4th Edition, 2020.

Coordinator:

Thermal Science TAG

Prerequisites by Topics:

  1. Heat Transfer
  2. Fluid Dynamics
  3. Numerical Analysis

Objectives[^1]:

  1. Teach students ways of manipulating partial differential equations and different ways to solve them, with particular emphasis on those governing fluid and heat flow, i.e., the Navier-Stokes equations.
  2. Develop the skills needed to solve the governing equations of fluid and heat flow numerically, using the finite element and finite volume methods, with emphasis on the former.
  3. Train students in the use of modern software packages to solve multiphysics problems in CFD.
  4. Be exposed to additional, important issues relating to modeling fluid dynamics.

Topics:

  1. Preliminaries.
  2. Conservation equations.
  3. Diffusion problems.
  4. Pressure-velocity coupling flows.
  5. Unsteady flows of energy and fluids.
  6. Turbulence.
  7. Multiphysics, multiphase, and non-Newtonian fluid flow problems.
  8. Discretization methods.

Evaluation Methods:

  1. Homework
  2. Exams
  3. Quizzes
  4. Computer assignments
  5. Projects

Learning Outcomes:

Objective 1

  1. Be able to recognize and physically relate to the basic terms in the full Navier-Stokes equations.
  2. Be exposed to fundamental ways of solving fluid-flow-governing equations: analytical and numerical.
  3. Derive in Cartesian coordinates basic conservation equations for mass, momentum and energy.

Objective 2

  1. Be able to reduce the partial differential equations to an equivalent set of algebraic equations using the finite element paradigm.
  2. Be able to solve the resulting set of algebraic equations using appropriate solution methods.
  3. Know about other issues concerning fluid modeling such as stability, convergence, stiffness, etc.
  4. Apply appropriate postprocessing techniques to put the solution in a form that is easy to understand.
  5. Recognize the philosophy of CFD and begin the application of CFD to your special areas of interest.

Objective 3

  1. Apply appropriate postprocessing techniques to put the solution in a form that is easy to understand.
  2. Recognize the philosophy of CFD and begin the application of CFD to your special areas of interest.
  3. Know what turbulence modeling is and ways it is applied.

Objective 4

4.1 Develop sound working vocabulary in the discipline and be prepared to understand the literature in this field and follow more advanced lecture series and courses. 4.2 Be familiar with other special fluid models and ways of incorporating them into an existing Navier-Stokes solver.

4.3 Learn ways modern CFD software packages are scaled and linked together to solve complicated Multiphysics problems.

Course Classification

Student Outcomes Level Relevant Activities
H
1. An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics. Solution of Partial Differential Equations. FE and FCV equations. Integral and differential formulation, Use computer programming and commercial CFD packages.
2. An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors. M Special Design of problems.
3. An ability to communicate effectively with a range of audiences. L Project report. Presentation.
4. An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts.
5. An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives.
6. An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions.
7. An ability to acquire and apply new knowledge as needed, using appropriate learning strategies. L Literature review of recent advances for project report.

[^1]: Numbers in parentheses refer to the student outcomes.