Module manager: Oliver Harlen
Email: o.g.harlen@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2026/27
MATH1000 Core Mathematics, AND MATH2400 Mathematical Modelling
| MATH1000 | Core Mathematics |
| MATH2400 | Mathematical Modelling |
None
This module is not approved as an Elective
Many flows found in nature such as avalanches and glaciers or in industrial applications such as 3D printing and coatings involve complex fluids, whose properties can be very different from those of simple Newtonian fluids like air and water. This course gives an introduction into the often-surprising behaviour of these fluids and how they can be modelled mathematically using differential equations.
In this module students will study constitutive equations describing different types of non-Newtonian fluid behaviour exhibited by natural and industrial fluids, including pseudo-plastic, yield stress and viscoelastic fluids. They will also use these models to calculate the flow of these materials for some unidirectional and quasi-unidirectional flows.
On successful completion of the module students will have demonstrated the following learning outcomes: 1. Identify and categorise characteristic phenomena of Newtonian and non-Newtonian fluids. 2. Obtain the governing equations and boundary conditions for a range of environmental and industrial flow and use relevant dimensionless numbers to identify the dominant terms. 3. Calculate unidirectional and nearly unidirectional flows for Newtonian and some simple non-Newtonian fluid models.
Transport of mass and momentum – definition of stress and strain-rate. 2. Constitutive equation for Newtonian fluids and the Navier-Stokes equations. The Reynolds number. Boundary conditions. 3. Some simple one-dimensional flow problems of environmental or industrial relevance (e.g. flow down an inclined plane, channel and pipe flows). 4. Flow phenomena of non-Newtonian fluids in simple flows (including some simple constitutive models): i. steady shear – shear thinning/thickening, viscoplasticity; ii. normal stresses in shear flow; iii. time dependant flows - 'memory' effects and linear viscoelasticity, time-dependent modulus, storage and loss modulus; iv. Dimensionless numbers: Deborah and Weissenberg numbers. 5. Lubrication approximation for Newtonian and non-Newtonian fluids. Darcy’s law for porous media. Viscous gravity currents. Extensional flows e.g. filament stretching and fibre-spinning. 6. Gravity driven inertial flows. Shallow water equations. The Froude number. Inertial gravity currents. Hydraulic jump and bore formation. Additional topics that build on these may be covered as time allows. Further details of possible topics will be delivered closer to the time that the module runs.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lectures | 33 | 1 | 33 |
| Private study hours | 117 | ||
| Total Contact hours | 33 | ||
| Total hours (100hr per 10 credits) | 150 | ||
Formative feedback will be provided on regular example sets or other similar learning activity.
Check the module area in Minerva for your reading list
Last updated: 12/05/2026
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