NUMERICAL HEAT TRANSFER | MMV042 |

**Aim**

This course aims to provide the students with knowledge, understanding and skills concerning modern computational methods in heat transfer particularly for convective heat transfer. Practice on various parts of the numerical solution procedures as well as applications to engineering heat transfer problems are provided.

*Knowledge and understanding*

For a passing grade the student must

- be able to describe and understand the finite volume and the finite difference techniques and classify the governing partial differential equations.
- be able to explain important and basic concepts of the subject.
- be able to explain and discuss various methods for handling convection-diffusion terms, and algorithms for the pressure-velocity coupling (e.g., SIMPLE, SIMPLEC, SIMPLEX, PISO etc).
- be able to describe and explain solution methods for algebraic equations.

*Skills and abilities*

For a passing grade the student must

- be able to actively participate in discussions of relevant heat transfer problems and opportunities to solve such problems by numerical methods.
- be able to in oral and written ways present numerical solution methods and results from simulation of heat transfer problems.

*Judgement and approach*

For a passing grade the student must

- be able to define and formulate heat transfer problems for numerical solution
- be able to apply the finite volume and the finite difference techniques for heat transfer problems
- be able to develop own simple computer codes and use available more general computer codes.

**Contents**

In the introductory part an overview of various numerical solution methods is presented and the governing equations are classified. The finite volume and the finite difference techniques are mainly considered. The applicability and limitations of the methods are described. The treatment of convection-diffusion terms is extensive. Numerical diffusion is discussed in details. Algorithms for the pressure-velocity coupling (e.g., SIMPLE, SIMPLEC, SIMPLEX, PISO, etc) are presented. Staggered and non-staggered grids are explained and turbulence modelling is introduced briefly. Methods for solution of algebraic equations are presented. In the design tasks (assignments) the students will perform calculations with pocket calculators, write their own computer codes and apply a more general-purpose computer software. By solving a number of tutorial problems the skills for numerical soloution of heat transfer problems are strengthened. Experience on application to real heat transfer problems is established.

**Literature**

B Sunden & D Eriksson Complementary course material in MMV042 Numerical Heat Transfer , Div of Heat Transfer, Lund Institute of Technology, 2006.

H K Versteeg & M W Malalasekera An Introduction to Computational Fluid Dynamics-The Finite Volume Method, Longman Scientific & Technical, 1995

B Sunden, M Faghri, M Rokni & D Eriksson, The computer code SIMPLE_HT for the course computational heat transfer, publ No 2004/4, Div of Heat Transfer, Lund Institute of Technology, 2004.

**Code: **0195.
**Name: **Numerical Heat Transfer, Part A.

**Higher education credits: ** 4,5.
**Grading scale: **TH.
**Assessment:** After every study period (quarter) a written exam takes place. Thus two written exams are included. An exam has generally both theoretical questions and problems to be solved. The exam after the first study period (lp 1, quarter 1) encompasses 40 % theory and 60 % problem solving. The exam after the second study period (lp2) is mainly problem solving. Each exam has 50p (points). As the theoretical questions are solved closed books prevail while for the problem solving part the course material except solved problems is permitted. For the problem solving part also the textbook in the Heat Transfer course is permitted. The exam thus needs to be splitted which means that at first the theoretical questions are solved and as these have been handed in to the exam assistant, the problem solving part can be started.
**Contents:** Introduction, finite difference method - general, finite difference method - boundary layer, finite volume technique, convection-diffusion, pressure-velocity algorithms, turbulence modelling, problems solving.

**Code: **0295.
**Name: **Numerical Heat Transfer, Part B.

**Higher education credits: ** 4,5.
**Grading scale: **TH.
**Assessment:** In the second study period (lp2, quarter 2) some lectures will be given by representatives from some industries. The application of commercially available computer codes (so-called CFD codes) for solving flow and heat transfer problems will be presented. In addition lectures concerning, e.g., complex geometries, special problems etc. will also be given. Some of the PhD students in Heat Transfer will show how CFD methods are encountered in research projects.
**Contents:** Computer programme SIMPLE-HT, commercial CFD-codes, implementation of boundary conditions, arbitrary geometries, computer-based tutorial sessions.