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Multi-physics Modelling of Fracture Mechanics in Thermoelectric Coolers

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  • Full or part time
    Prof EA Patterson
    Prof W-C Wang
  • Application Deadline
    Applications accepted all year round
  • Funded PhD Project (Students Worldwide)
    Funded PhD Project (Students Worldwide)

About This PhD Project

Project Description

Project aim, objectives and outline:

Thermoelectric materials can be used to create cooling and refrigeration devices that do not have any moving parts, which offers the prospect of low cost, reliable and robust products. Thermoelectric coolers are based on the Peltier effect and commonly employ pairs of n- and p-type bismuth telluride pellets. When a current is passed across the pairs a temperature difference is generated that can be used to cool small components. Although this creates a cooling device with no moving parts, cracks can develop in the devices, due to a mismatch in the thermal coefficient of expansion, and lead to the premature failure of the device. Preliminary computational modelling at NTHU [1-3] has shown that warpage of the devices occurs during operation and this has been confirmed in experiments using electronic speckle pattern interferometry (ESPI) and digital image correlation (DIC) to measure strain fields. In parallel, research at Liverpool has led to the development of new methodologies for comparing data-rich strain fields from computational models with those acquired in experiments using techniques such as DIC and ESPI. These methodologies utilise image decomposition techniques [4] and allow quantitative comparisons to be made as part of processes of validation and updating of computational solid mechanics models [5]. In this project, these areas of research will be combined to investigate the quantitative validation of the computational models of the thermoelectric coolers in the spatial, temporal and thermal domains. The challenge will be to develop appropriate methodologies to allow validation to be performed in multiple dimensions, and time, and taking account of the multi-physics nature of the application, i.e. the response of the device to mechanical, electrical and thermal loads Ultimately, the experimental and numerical data will be employed to study the fracture mechanics mechanisms [6] governing the failure of the thermoelectric coolers in order to develop more durable designs. Thermoelectric coolers have applications in a wide range of devices including consumer electronics and the aerospace and so it is expected the research will involve some interaction with industry.

You will join a pair of research groups that are already working together and a dual PhD programme with more than 20 PhD students studying a wide range of topics at National Tsing Hua University in Taiwan and the University of Liverpool in the UK.

Expected Pattern of Study:

You should have a good MSc or MEng degree in engineering, physics or an associated field. It is anticipated that you will spend equal periods of time at NTHU and UoL withan initial period in UoL mastering the techniques of strain decomposition before moving to NTHU to perform numerical and experimental analysis of prototype TECs. The analysis of data and refinement of comparison techniques will be performed in UoL towards the end of the project.

You will have opportunities to present your work to the engineering community at conferences and in peer-reviewed journals. You will prepare a single thesis in English that, subject to examination, will lead to the award of PhD degrees by both universities. On completion of the project you will be an expert in stress and strain analysis, validation techniques for computational mechanics models and be skilled in both computational and experimental mechanics.

Facilities to be used at NTHU and UoL:

EPSI and DIC instrumentation at NTHU together with loading rigs for TECs. Strain decomposition algorithms and validation procedures at UoL.

The funding for this programme covers tuition fees and a contribution to living expenses of $10,000 New Taiwanese Dollars per month.


[1] Wang, W. C. and Chang, Y. L., 2011, Experimental Investigation of Thermal Deformation in Thermoelectric Coolers, Journal of the European Association for Experimental Mechanics, Vol. 47, No. 2, pp.232-237.

[2] Wang, W. C. and Wu, T. Y., 2011, Experimental and Numerical Analysis of Thermal Deformation in Thermoelectric Coolers, Proceedings of BSSM/SEM International Conference on Advances in Experimental Mechanics: Integrating Simulation and Experimentation for Validation (ISEV), Paper No. 107, 6 pages, Royal College of Physicians, Edinburgh, September 7-9.

[3] Wang, W. C. and Wu, T. Y., 2011, “Thermal Deformation Measurement in Thermoelectric Coolers by ESPI and DIC Method”, Proceedings of SEM Annual Conference & Exposition on Experimental and Applied Mechanics, Paper No. 132, 11 pages, Mohegan Sun, Connecticut, U. S. A., June 13-16

[4] Patki, A.S., Patterson, E.A., 2012, Decomposing strain maps using Fourier-Zernike shape descriptors, Experimental Mechanics, DOI 10.1007/s11340-011-9570-4.

[5] Wang, W., Mottershead, J.E., Sebastian, C.M., Patterson, E.A., 2011, Shape features and finite element model updating from full-field strain data, Int. J. Solids Struct. 48(11-12), 2011, 1644-1657.

[6] Du, Y., Diaz, F.A., Burguete, R.L., Patterson, E.A., 2011, ‘Evaluation using digital image correlation of stress intensity factors in an aerospace panel’, Experimental Mechanics, 51(1):45-57.

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