School of Mathematical Sciences

Energy projects

A list of currently available energy projects within the MASS doctoral training centre. For queries in relation to a particular project, please contact the supervisors associated with that project. Click on a project name to view more details below.

Thermal characterisation of the building fabric under uncertainty

Supervisors:  Dr Marco Iglesias (Mathematical Sciences),  Dr Yupeng Wu (Engineering)

The built environment is responsible for 45% of all UK carbon emissions with approximately 27% attributed to the domestic sector and 18% to non-domestic buildings. Reducing the energy demand in the built-environment is thus essential for the UK decarbonisation policy which legislates an 80% reduction of its 1990 green house gas emissions by 2050. The existing housing stock is a primary target for reductions of the energy demand since it is estimated that up to 85% of existing buildings will be standing by 2050. An accurate characterisation of the thermal performance of the existing housing stock in the UK is thus needed to inform large-scale cost-effective policies for retrofit intervention that can effectively contribute towards achieving those decarbonisation targets. Unfortunately, existing approaches for the in-situ characterisation of the building fabric (including ISO standards) cannot accurately characterise the thermal performance of buildings in the presence of thermal bridge effects that arise from heterogeneities, irregularities and/or abrupt changes and discontinuities in the thermophysical properties of the building fabric. In particular, these approaches cannot capture thermal bridge effects due to fabric degradation and moisture condensation which are likely to be found in existing dwellings.

This challenging research will develop novel thermal imaging algorithms capable of characterising, with an accurate measure of uncertainty, the thermal performance of the building fabric in the presence of a general class of thermal bridge effects. This project will build upon state-of-the-art Bayesian algorithms for inverse problems that have been successfully applied for tomographic inversions in the context of groundwater flow [1], electrical impedance tomography [1], resin transfer moulding [2], and the characterisation of thermophysical properties of walls [3,4]. The techniques developed in this project will be validated with real experiments. Although highly ambitious, this proposed research has enormous potential to revolutionise current approaches for in-situ characterisation of the thermal performance of buildings thereby enhancing the predictive capabilities of existing housing stock models.

[1] Iglesias, M.A. 2016. “A Regularizing Iterative Ensemble Kalman Method for PDE-Constrained Inverse Problems.” Inverse Problems 32 (2):025002.

[2] Iglesias, M.A., M. Park, and M. Tretyakov. 2017. “Bayesian Inverse Problems in Resin Transfer Molding.” Submitted Preprint available at:

[3] Iglesias, M.A., Sawlan Z., Scavino M., Tempone R., and C. Wood. 2018. “Bayesian Inferences of the Thermal Properties of a Wall Using Temperature and Heat Flux Measurements.” International Journal of Heat and Mass Transfer 116 (Supplement C):417–31.

[4] De Simon,L. M. A. Iglesias, B. Jones and C. Wood. 2017. “Quantifying Uncertainty in Thermal Properties of Walls by Means of Bayesian Inversion.” Submitted Preprint available at:


Sustainability applications of first-principles calculation of physical properties, via machine learning

Supervisors:  Dr Richard Graham (Mathematical Sciences),  Dr Richard Wheatley (Chemistry)

Carbon capture and storage (CCS) has the potential to hugely reduce CO2 emissions. However, CO2 from combustion contains many impurities, which affect the cost and safety of CCS. This PhD project will develop a fundamental understanding of impure CO2 by modelling the interactions between the constituent molecules. These interactions can be calculated from first-principles, but such calculations are too expensive numerically for most applications. We have recently developed a machine-learning technique that, via a small number of ab-initio calculations, can efficiently model the entire energy surface. This project will exploit this technique to create first-principles predictions of properties that are important to the safety, design and cost of CO2 pipelines.

Energy storage bed dynamics –the ever-expanding magnesium bed conundrum

Supervisors:  Prof John King (Mathematical Sciences),  Prof Gavin Walker (Engineering),  Dr Richard Wheatley (Chemistry)

In order to facilitate high penetration of renewable energy in to the grid, energy storage is needed to better manage the supply and demand for the grid. Hydrogen offers a high energy density solution and, rather than storing the hydrogen as a gas at high pressures, solid state storage of hydrogen in a metal like magnesium offers a low pressure and low cost technology. The hydrogenation of magnesium is very exothermic (74.5 kJ mol-1) and the material is also being investigated as a thermal energy store (i.e. using the exotherm of hydrogenation to liberate the stored thermal energy back as heat at 400°C).

A fear was that cycling a magnesium bed at high temperatures would lead to sintering and a loss of void space. However, the startling result was that the powdered magnesium bed when cycled at temperatures of 350-400°C, rather than losing porosity, gained porosity. The form of the bed had changed from a loose powder to a metal porous plug which had swelled in dimensions to fill the available head space in the vessel. Further cycling at temperature below 350°C results in the bed resorting back to a more densely packed loose powder.

The intriguing question is to uncover the fundamental mechanism(s) behind this process and to develop a predicative model based on the physical and chemical processes occurring. For the application, understanding these processes will enable optimisation of the porous structure for heat and mass flow; moreover, there is also concern the expanding bed may exert significant stress on the wall of the storage vessel eventually leading to failure of the vessel.
This challenging research project will develop new mathematical models based on the chemical and physical processes occurring in order to develop a model that simulates the expanding porous bed phenomenon. Some of these processes include: nucleation, growth of the metal hydride phase, crystal lattice expansion leading to defect formation, decrepitation, atomic diffusion and surface energy minimisation, annealing.  The models developed will thus need to encompass a wide range of physical phenomena; the focus will be on partial-differential-equation/moving-boundary formulations, building on the established sintering literature but, for the reasons described above (specifically, to generate increased, rather than decreased, porosity), of necessity raising significant additional challenges.  The project will accordingly equip the student with an unusually wide experience of experimental and modelling questions and of mathematical techniques, as applied in a context with clear energy and sustainability implications. 


Form, function and utility in small community energy networks

Supervisors:  Prof Mark Gillott (Architecture and Built Environment),  Dr Keith Hopcraft (Mathematical Sciences), Dr Parham Mirzaei Ahrnjani (Architecture & Built Environment)

This is a unique and exciting opportunity to undertake research that spans across the disciplines of energy engineering and mathematical sciences. Successful applicants will be joining a strong interdisciplinary team from academia and industry who are currently working on the delivery of the Energy Research Accelerator (ERA) Community Energy System (CES) demonstrator at the 15 acre Trent Basin site in Nottingham. The project will investigate the energy challenges and complexity science issues associated with heat and electrical power generation, storage and use arising from the connections between micro-generation output, grid/heat loads, weather, and energy/power demands (including occupant behavior) combined with variable load energy storage devices in order to provide energy stability, a reduction of cost and associated carbon emissions from fossil fuel use. The PhD research will develop new multi-vector CES models that utilise ‘big data’ obtained from a dedicated onsite monitoring platform at the housing development applied to a heterogeneous network of users. The work will ultimately help inform the design, implementation and operation of local community energy schemes in the UK. Applicants should have a Bachelor Science or Engineering (at least 2i) and/or a Master of Science or Engineering in Mathematical Sciences, Engineering or Energy related disciplines.


School of Mathematical Sciences

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