## Postgraduate modules

The following postgraduate modules are normally offered for/by the Department of Mechanical and Mechatronic Engineering during the first (1^{st}) semester of the academic year (February to June) and requires attendance of classes on campus on a daily basis.

38571-814 Engineering Mathematics (Linear Algebra)

20753-834 Applied Mathematics B (Partial Differential Equations)

36323-876 Numerical Methods

13014-814 Robotics

23965-814 Advanced Control Systems

40622-814 Advanced Design

62960-814 Advanced Dynamics

13773-814 Advanced Fluid Dynamics

13803-813 Advanced Heat Transfer

13722-814 Advanced Strength of Materials

53643-813 Finite Element Analysis

62952-814 Computational Fluid Dynamics

11295-714/814 Solar Thermal Energy Systems

* 53716-814/844 Air-conditioning and Refrigeration

* 53511-814 Industrial Heat Exchangers

* Not offered every year.

The module offering is revised annually. The total time required per module is approximately twelve (12) hours per week for fifteen (15) weeks. The time table for the contact sessions is only compiled at the start of the semester. Contact time is typically 2-3 hours per module per week.

During the first (1^{st}) and second (2^{nd}) semester, students may choose from the modules that are available at the Centre of Renewable and Sustainable Energy Studies (CRSES). Please note that these modules will only be presented when 5 or more students register for the relevant module. These modules are normally presented in a block-format and students typically have to do some preparatory self-study, attend lectures for one week and complete large assigments after the block.

The modules listed at the top of the page are semester modules. Students attending block-format modules during the first (1^{st}) semester will therefore miss some of the semester module contact sessions.

Students have to attend lectures and examinations in Stellenbosch.

### Renewable Energy Modules

### 38571-814 Engineering Mathematics (Linear Algebra)

Vector spaces, subspaces, bases, matrix factorization, diagonalization, application to the solution of systems of ordinary differential equations, introduction to iterative methods for the solution of large systems of algebraic equations.

#### PREREQUISITE:

Engineering mathematics 214

### 20753-834 Applied Mathematics B (Partial Differential Equations)

Derivation of simple PDEs from first principles, Fourier analysis, separation of variables and transform techniques for linear second-order PDEs, characteristics, Lagrange's method for first-order PDEs, finite differences.

#### PREREQUISITE:

Engineering mathematics 214

### 36323-876 Numerical Methods

Focus on numerical methods for matrix computations.
Effective solution of square linear systems, least squares problems, the
eigenvalue problem. Direct and iterative methods, special attention to sparse
matrices and structured matrices. Numerical instability and ill-conditioning.
Model problems from partial differential equations and image
processing.

PREREQUISITE:

An undergraduate module on matrices/linear algebra plus some computing skills in an environment such as MATLAB or Python.

### 13014-814 Robotics 814

Mathematical modelling of robots; Rigid motions and homogeneous transformations; Forward and inverse kinematics; Denevit-Hartenberg convention; Velocity kinematics: the Jacobian, singularities; Path and trajectory planning; Independent joint control; Robot dynamics: Euler-Lagrange equations, kinetic and potential energy, equations of motion, properties of robot dynamic equations, Newton-Euler formulation; Force control; Computer Vision: camera calibration, image segmentation, vision and servo control.

#### PREREQUISITE:

Modelling 334 or equivalent

### 23965-814 Advanced Control Systems

Contents: This module is concerned with control systems design and analysis for MIMO (multi-input-multi-output) systems with uncertainties. It covers basic linear algebra, block diagram algebra for MIMO systems, loop shaping analysis and design, internal stability, generalized Nyquist stability criterion, all stabilizing controllers, MIMO robustness, generalized plant, linear fractional transformation (LFT), nominal/robust stability/performance (NS, NP, RS, RP), representing uncertainties, optimal control (LQ, Kalman filter and LQG), and H-infinity optimal control.

#### PREREQUISITE:

Students must be familiar with basic computer programming, e.g. MATLAB (SCILAB), undergraduate-level control systems theory and elementary matrix analysis.

### 40622-814 Advanced Design

Mathematical principles of optimisation searches, e.g. golden search procedure, steepest gradient, etc.; problems and dangers; discussions; criteria; applications in mechanical engineering.

#### PREREQUISITES:

Computer programming 143

Numerical methods 262

### 62960-814 Advanced Dynamics

Formulate and solve the dynamics of a particle or system of particles: Relative to static or moving axis system; in terms of generalized coordinates and constraints; in terms of virtual displacement and work; in terms of the Lagrange and Hamilton energy principles; for impulsive forces. Formulate and solve the kinematics and dynamics of a rigid body: In terms of rotation kinematics; with the modified Euler rotation equations of motion; for impulsive forces and moments.

#### PREREQUISITES:

Engineering Mathematics 214

Modelling 334

Computer Programming using MATLAB

### 13773-814 Advanced Fluid Dynamics

Principles of turbulent flow; Reynolds stresses; turbulence modelling and mixing length; pipe and plate flow; calculation of turbulent boundary layers with pressure gradient; origin of turbulence; transition from laminar to turbulent flow; turbulent jets and wakes; compressible boundary layers.

#### PREREQUISITES:

Engineering mathematics 244

Computer programming 143

Thermo-fluid Dynamics 344

### 13803-813 Advanced Heat Transfer

The objective of this module is to enable a person with an undergraduate engineering level of mathematics, thermodynamics, fluid mechanics and heat transfer to approach and solve typical problems in conduction, convection, radiation and multi-phase flow and heat transfer at the appropriate graduate level. The emphasis is placed on the methods whereby heat transfer problems may be mathematically structured and the available mathematical techniques and solution procedures.

#### PREREQUISITES:

Heat Transfer 414

Fluid Mechanics 244

### 13722-814 Advanced Strength of Material

A graduate course in Applied Structural Mechanics. A number of advanced theory in strength of materials and numerical analysis are taught. The advanced theory in strength of materials include introduction to Continuum Mechanics with the main mathematical tool, Tensor Analysis, composite materials, advanced failure criterions, plasticity and fracture mechanics. The numerical analysis include application of the theory to solve computational problems in solid mechanics.

#### PREREQUISITE:

Strength of materials W334

#### RECOMMENDED:

Proficiency in a computer programming language.

### 53643-813 Finite Element Analysis

Revision of strength of materials concepts; principle of virtual work; truss/beam elements; plane stress/strain elements; isoparametric formulation; 3D elements; axisymmetric elements; plate and shell elements; structural symmetry; dynamic analysis; buckling analysis; use of finite element software to solve simple problems.

#### PREREQUISITE:

Strength of Materials W334

### 62952-814 Computational Fluid Dynamics

Governing differential equations for convection - diffusion processes; discretization for steady and unsteady cases; numerical modelling of the Navier-Stokes equations: the SIMPLE-based algorithms; Numerical modelling of turbulence; complex computational domains: boundary fitted coordinate systems.

#### PREREQUISITES:

Engineering Mathematics 214

Fluid Mechanics 244

### 11295-714/814 Solar Thermal Energy Systems

This module focuses on concentrating solar power (CSP) but also covers solar water heating (SWH) and other solar thermal applications. Whilst
considering the current
solar technology, the emphasis of the module is on first principles and technical fundamentals. The content will cover: Introduction and review of thermal sciences (heat transfer, thermodynamics etc); solar energy physics and radiation principles; the solar resource and resource measurements; optics for solar thermals; solar thermal collectors; principles of energy balance for concentrating and non-concentrating solar thermal energy systems; power generation; thermal energy storage; other applications; modelling and analysis techniques; basic economics.

#### PREREQUISITE:

An undergraduate degree in engineering. The student must be comfortable with basic computer programming. Knowledge of some thermal science will be a benefit.

### 53716-814/844 Air-conditioning and Refrigeration

(offered only on a self-study basis)

Air conditioning systems (general); psychrometrics; direct contact heat and mass transfer; heat load calculations; air handling and distribution equipment; vapour compression system analysis; conventional air-conditioning and storage systems; air conditioning controls; special systems.

#### PREREQUISITES:

Fluid Mechanics 244

Energy Systems M 434

### 53511-814 Industrial Heat Exchangers

Air-cooled heat exchangers and cooling towers: Fundamental fluid dynamics, heat transfer and mass transfer as applicable to heat exchangers; testing and characteristics of finned tubes and fans; thermal-flow design of air-cooled finned tube heat exchangers including water, oil and process fluid coolers and steam and refrigerant condensers; mechanical and natural draught dry- and wet cooling towers, hybrid cooling towers.

#### PREREQUISITE:

Heat Transfer 414 Pass (P ³ 50)