Fluids and Magnetohydrodynamics module (MA41006)

Fluid dynamics and magnetohydrodynamics (MHD) are essential to understanding how the natural world behaves, from how air flows over a wing to how plasma moves inside stars. This module explores the mathematics that describes these powerful, often beautiful systems. 

You’ll explore the structure of fluid motion through scalar and vector fields, streamlines, and conservation laws. Using key equations like Euler’s and Navier–Stokes, you’ll learn how to describe pressure, velocity, and forces in fluids. 

Later in the module, you'll explore advanced topics like vorticity and viscosity. You’ll also investigate how magnetic fields interact with fluids through MHD. This is essential for understanding astrophysical plasmas, fusion reactors, and space weather.  

Whether you're interested in applied mathematics, physics, or space science, this module will give you the tools to model and understand the dynamic behaviour of the natural world. 

What you will learn 

In this module, you will: 

• study fluid flow using scalar and vector fields, streamlines, and flux
• analyse the conservation of mass and momentum through core fluid equations
• investigate different flow types including incompressible, irrotational, and viscous flows
• explore vorticity and circulation in fluids
• understand how magnetic fields interact with fluids 

By the end of this module, you will be able to: 

• apply core conservation laws to describe fluid motion
• use mathematical models to study circulation and vorticity
• solve boundary value problems in fluid dynamics using analytical methods
• interpret the behaviour of plasma and conducting fluids in magnetic fields
• use advanced techniques from vector calculus to understand physical systems 

Assignments / assessment

• Coursework (20%)
• Final written exam, two hours (80%) 

Teaching methods / timetable

• Lectures
  • On-campus lectures covering the core theory and derivations presented clearly with supporting visuals
• Tutorials
  • Face-to-face problem solving in small groups or individually with lecturer support