PhD projects

PhD opportunity!

Application deadline Thursday 15th January 2026.  

Modelling of flow transition and heat transfer for advanced geothermal systems (C3.5-MPS-Willis).  

A fully funded PhD opportunity to participate in the world-leading research undertaken by the EPSRC Doctoral Landscape Award at the University of Sheffield.

Are you passionate about fluid dynamics, applied mathematics, and solving real-world energy challenges? This PhD project offers an exciting opportunity to work at the intersection of advanced mathematics, energy innovation, and industrial impact. In collaboration with SLB (slb.com)—a global leader in energy technology—this project aims to revolutionise the understanding of turbulent flows in next-generation geothermal systems.

Project Overview

Fluid flow through pipes is a central mechanism for energy transfer across countless applications, from domestic heating systems to cutting-edge technologies like solar collectors and heat pumps. In Advanced Geothermal Systems (AGSs)—a promising frontier in sustainable energy—heat is transferred through closed-loop pipe networks, offering the potential for clean reliable power, independent of geographic location.

However, the efficiency of these systems hinges on the nature of the flow—whether it is smooth and orderly or chaotic and turbulent. Counterintuitively, increased heating can sometimes suppress turbulence, thereby reducing the effectiveness of heat transfer. Adding to this complexity, buoyancy effects—which introduce vertical flow components—disrupt traditional turbulence mechanisms, creating a rich and largely unexplored space of nonlinear flow behaviour.

Understanding and predicting these dynamics is a formidable challenge, and an exciting mathematical opportunity.

A New Approach: Dynamical Systems & Coherent Structures

This project builds on recent breakthroughs in dynamical-systems approaches to turbulence, particularly in isothermal flows. These approaches aim to uncover the hidden structures within chaos—such as travelling waves, periodic orbits, and other coherent structures—that underpin turbulent behaviour.

New optimisation techniques now make it possible to navigate the high-dimensional space of turbulent systems, allowing researchers to identify critical perturbations that can trigger or suppress turbulence. These tools will be applied to design flow modifications that can directly enhance heat transfer in AGS applications.

This is not just a fundamental mathematical study—it is aimed at solving energy challenges of global importance.

Research Environment & Training

The successful applicant will be jointly supervised by leading academics from the School of Mathematical and Physical Sciences (MPS) and the School of Mechanical, Aerospace and Civil Engineering (MAC) at the University of Sheffield, with strong support from SLB. Regular meetings with the industrial partner and the possibility of a research placement will ensure a strong link between theoretical development and practical application.

You’ll join the vibrant Sheffield Fluid Mechanics Group (Group Website)—a large, interdisciplinary community of researchers spanning mathematics, engineering, and physics. You will also collaborate closely with an ongoing PhD project in MAC focused on improving computational models of AGS flows.

The project includes training in:

• Nonlinear dynamical systems modelling
  
  

• Large-scale simulations and high-performance computing
  
  

• Parallel programming and optimisation techniques
  
  

These are high-value skills with applications across academia, industry, and data-intensive research.

Why Sheffield?

Sheffield offers a comprehensive graduate development programme, including training in research planning, academic writing, and leadership. You’ll have opportunities to supervise undergraduate research projects, helping you build valuable mentoring and teaching experience.

If you're excited by the idea of using advanced mathematics and computation to help shape the future of clean energy, this project offers a rare opportunity.

The University of Sheffield is one of the leading Russell Group universities in the UK. We carry out cutting-edge research with strong links to industry. When you enrol to do a PhD with us, you will be working with world-leading academics and have access to top of the range facilities. As a PhD student you will have the opportunity to gain skills not only to conduct research, but also to take your career to the next level, whether you want to stay in academia, go into industry or the public sector, or set up your own company. You will have access to a range of training and support services to help you excel in your studies and beyond.

Sheffield is also a great place to live!  Check it out...

Supervised by 

Dr Ashley Willis (School of Mathematical & Physical Sciences), second supervisor  Prof Shuisheng He (School of Mechanical Civil & Aerospace Engineering) and Dr Ashley Willis (School of Mathematical & Physical Sciences), and in Collaboration with SLB.

How to apply

Scholarship information and how to apply can be found here  EPSRC Doctoral Landscape Awards (DLA).  Please note that applications MUST be made via the link on this page: How To Apply 

Please email a.p.willis@sheffield.ac.uk to discuss your interest in and suitability for the project prior to submitting your application. 

Funding Notes

The award will fund the full (UK or Overseas) tuition fee and a maintenance stipend at the UKRI rate (currently £20,780 per annum) for 3.5 years, as well as a research grant to support costs associated with the project.