Skip to main content

Study information

# Magnetic Fields and Fluid Flows - 2023 entry

MODULE TITLE CREDIT VALUE Magnetic Fields and Fluid Flows 15 MTHM031 Dr Joanne Mason (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 0 0
 Number of Students Taking Module (anticipated) 21
DESCRIPTION - summary of the module content

This module deals with the motion of electrically conducting fluids in the presence of magnetic fields, a subject known as magnetohydrodynamics (MHD). MHD flows play a crucial role in the dynamics of a variety of astrophysical systems (including stars, planets, accretion discs and galaxies). MHD flows are also studied in the laboratory with a view towards engineering applications (e.g. electromagnetic stirring and fusion plasmas). In this module, you will see how the mutual interaction of the fluid flow and the electromagnetic field reveals a variety of new and interesting phenomena. You will learn how to formulate a real physical problem in terms of a system of partial differential equations. We will solve these using a variety of techniques of applied mathematics.

Pre-requisite module: MTH3007 Fluid Dynamics, or equivalent

AIMS - intentions of the module

The aim of this module is to give you an introduction to the subject of electrically conducting fluid dynamics. This module can be seen as an extension of the third year module MTH3007 on viscous fluids. You will learn how the equations of fluid dynamics are modified when electromagnetic effects are taken in account. The mathematical theory will be illustrated with examples from astrophysics, geophysics and laboratory plasma physics.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

1 Define the concepts and equations governing the interaction of magnetic fields and electrically conducting flows;

2 Prove some important theorems and analyse the solutions of the MHD equations using a variety of techniques of applied mathematics;

Discipline Specific Skills and Knowledge:

3 Formulate a real physical problem mathematically;

4 Explain mathematical solutions in terms of physical effects;

Personal and Key Transferable / Employment Skills and Knowledge:

5 Develop communication skills via in-class discussions;

6 Practice time management skills in order to meet coursework deadlines.

SYLLABUS PLAN - summary of the structure and academic content of the module

Fundamentals and Simple Examples:

- Motivation for studying magnetic fields and fluid flow;

- A brief introduction to electrodynamics: Maxwell’s equations;

- The equations of electrically conducting fluid dynamics;

- Basic properties of the induction equation, including the diffusive limit, the perfectly conducting limit and Alfvén’s theorem of flux freezing;

Magnetohydrostatics and Steady MHD Flows:

- Force-free fields, including potential fields and field-parallel currents;

- Pressure balanced configurations and plasma confinement;

- Steady unidirectional flow;

MHD Waves:

- Alfvén waves in an infinite, inviscid, incompressible fluid of infinite electrical conductivity;

- Phase velocity and group velocity;

- Damped Alfvén waves;

An Introduction to Dynamo Theory:

- Observational evidence for astrophysical magnetic fields;

- Formulation of the kinematic dynamo problem;

- Poloidal and toroidal fields;

- Antidynamo theorems;

- Qualitative picture of large-scale dynamo action, involving differential rotation and helical turbulence;

- Mean-field electrodynamics;

- Parker’s dynamo waves.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 33 117 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled Learning and Teaching Activities 27 Lectures Scheduled Learning and Teaching Activities 6 Examples classes Guided Independent Study 30 Problem sheets Guided Independent Study 87 Reading, revision, preparation

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Problem sheets containing a mixture of short answer questions and more comprehensive exercises 6 hours/4 questions per problem sheet (5 sheets) 1-6 Examples class, solutions and general comments, uploaded to ELE

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams Practical Exams 20 80 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written Exam – Closed Book 80 2 hours (Summer) 1-4 Oral on request
Coursework - based on questions submitted for assessment 20 2 assignments, 30 hours total 1-6 Annotated script and written/verbal feedback

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
Written Exam* Written Exam (100%) All August Ref/Def Period
Coursework* Coursework 1-6 August Ref/Def Period

*Please refer to reassessment notes for details on deferral vs. Referral reassessment

RE-ASSESSMENT NOTES
Deferrals: Reassessment will be by coursework and/or written exam in the deferred element only. For deferred candidates, the module mark will be uncapped.

Referrals: Reassessment will be by a single written exam worth 100% of the module only. As it is a referral, the mark will be capped at 50%.
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Reading list for this module:

Type Author Title Edition Publisher Year ISBN
Set Roberts, P.H. An Introduction to Magnetohydrodynamics Forum Library 538.6 ROB Longman 1967 0582447283
Set Choudhuri, A.R. The Physics of Fluids and Plasmas Forum Library 530.4 CHO Cambridge University Press 1998 0521555434
Set Ferraro, V.C.A. and Plumpton, C. An Introduction to Magneto-Fluid Mechanics Forum Library 538.6 FER Oxford University Press 1966 0198531311
Set Priest, E. Solar Magnetohydrodynamics Forum Library 523.7 PRI D. Reidel Publishing Company 1982 902771374X
CREDIT VALUE ECTS VALUE 15 7.5
PRE-REQUISITE MODULES MTH3007
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 7 No Tuesday 10th July 2018 Thursday 26th January 2023
KEY WORDS SEARCH Fluid Dynamics; Magnetic Fields; MHD; Applications of Vector Calculus

Please note that all modules are subject to change, please get in touch if you have any questions about this module.