#### Postgraduate Modules

The following postgraduate modules are normally offered for/by the Department of Mechanical and Mechatronic Engineering during the **first semester** of the academic year (February to June) and requires attendance of classes on campus.

20753-834 Applied Mathematics B (Partial Differential Equations)

38571-814 Engineering Mathematics (Linear Algebra)

36323-876 Numerical Methods

40622-814 Advanced Design

62960-814 Advanced Dynamics

13773-814 Advanced Fluid Dynamics

13803-813 Advanced Heat Transfer

13722-814 Advanced Strength of Materials

53716-814 Air-conditioning and Refrigeration

14410-874 Biomedical Engineering Design

53643-813 Finite Element Analysis

14216-874 Holonic Communication and Control

53511-814 Industrial Heat Exchangers

53678-414 Numerical Fluid Dynamics

13863-814 Research Methodology

13014-814 Robotics

11295-814 Solar Thermal Energy Systems

Offering of modules is subject to availability and is revised annually.

Most of the modules referred to at the top of the page are offered as block modules since 2020. Some modules will be offered as 2 compulsory blocks and some modules as 1 block. Please view the module schedule carefully.

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. MEng Research students who want to attend a Renewable Energy (RE) block module in the 2nd semester should attach a motivation by supervisor to the application.

#### Renewable Energy Modules

*Visit the Centre for Renewable and Sustainable Energy Studies page*

**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.

##### PREREQUISITES:

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.

##### PREREQUISITES:

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

**40622-814 Advanced Design**

The objective of this module is to enable students who have mastered mathematics at an undergraduate engineering level (or similar) to formulate and solve general optimization problems at an advanced graduate level. Emphasis is placed on an understanding of the algorithms themselves, and students are required to code rudimentary, vanilla versions of these algorithms. Methods considered include Mathematical Programming (MP) approaches and Metaheuristics (MH). Typical MP methods covered include 1-D line search methods, steepest descent, conjugate gradient methods, penalty and augmented Lagrangian methods, the Karush–Kuhn–Tucker (KKT) conditions, optimality criterion (OC) statements, sequential linear and quadratic programming (SLP and SQP respectively), convergence, robustness, and approximation methods to overcome difficulties due to indefinite or negative definite Hessian matrices in SQP-like methods. Typical MH methods covered include particle swarm optimization (PSO), genetic algorithms (GAs) and differential evolution (DE).

##### PREREQUISITES:

Computer programming 143

Numerical methods 262

Students must be familiar with basic computer programming, e.g. MATLAB (or SCILAB), undergraduate-level linear algebra and matrix analysis.

This module is not suitable if any other optimization module was completed previously.

**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

Programming in MATLAB, Python or a similar programme is a requirement.

**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 Materials**

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.

**53716-814 Air-conditioning and Refrigeration**

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

**14410-874 Biomedical Engineering Design**

Biomedical engineering involves applying the concepts, knowledge and approaches of virtually all engineering disciplines to solve or improve healthcare related problems. The challenges creates by the diversity and complexity of living systems in the unique context of South Africa requires creative, knowledgeable and imaginative people working in multidisciplinary teams to monitor, restore and enhance normal body function. In this course students will be exposed to healthcare challenges faced in South Africa and will work together in teams to help address these issues using novel engineering approaches. This course will provide instruction and resources for students to design solutions to real-world healthcare problems for the developing world. Students will learn and execute the entire biomedical engineering design process from understanding a healthcare related problem to demonstrating and testing proof-of-concept functionality in a prototype in the environment of under-resourced segments of the South African health care system.

##### PREREQUISITE:

Any Engineering Design module or similar.

**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

**14216-874 Holonic Communication and Control**

The holonic systems theory states that complex systems are naturally constructed through a collection of autonomous and cooperative functional entities, called holons. Holons should thus encapsulate and control their own functionality so that they can function independently, but should also have the ability to communicate with other holons. This communication allows for the coordination of holon functionalities to accomplish complex tasks (which are beyond the capability of any of the individual holons).

This module will introduce the theory of holonic systems (including existing reference design architectures), but will focus on the design and implementation of a holonic system in a case study scenario. The implementation will take the form of a software development project, which builds on object oriented, multi-agent and actor based software development approaches. Through this case study implementation, the inherent benefits of the holonic systems approach will be demonstrated.

##### PREREQUISITE:

The software development project in this module will make use of the Java programming language. As such, experience in software development in Java, or similar languages like C, C++ and C#, is required.

**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)

**53678-414 Numerical Fluid Dynamics**

Derivation of governing differential equations for fluid flow; discretization for steady and unsteady flow problems; numerical solution of convection- diffusion processes; numerical modelling of the Navier-Stokes equations: the SIMPLE-based algorithms; numerical modelling of turbulence; complex computational domains; error and uncertainty analysis in computational fluid dynamics

##### PREREQUISITES:

Engineering Mathematics 214

Fluid Mechanics 244

**13863-814 Research Methodology – compulsory to all MEng students (Research & Structured)**

This is a new module, and the contents may change slightly. To name but a few, envisaged topics include “the Scientific Method”, conclusive proofs, research ethics, plagiarism (including self-plagiarism), literature studies and critical literature review, the use of e-data bases and the library, design of experiments (including numerical experiments), safety, engineering robustness, numerical and analytical modeling, statistics, surveys, data analysis, plotting, curve fitting, pitfalls of extrapolation, good writing practices when writing articles and theses, using LaTeX en MS Word, scientific “social media”, predatory publishing, and finally, dissemination of research. The definitive outcome of the module is a research proposal, being a requirement for continuation with a research-based Masters study at the end of the first semester.

##### PREREQUISITES:

A four year undergraduate degree in Engineering (or similar).

**13014-814 Robotics**

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

**11295-814 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.