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Chaotic Rayleigh-Benard Convection in a Rectangular Box in a High Magnetic Field

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  • Full or part time
    Prof Molokov
  • Application Deadline
    Applications accepted all year round
  • Funded PhD Project (Students Worldwide)
    Funded PhD Project (Students Worldwide)

About This PhD Project

Project Description

Eligibility: UK/EU/International
Tuition Fees + Bursary £15000 per year
Three years fixed term

PI: Prof Sergei Molokov: http://www.coventry.ac.uk/research/research-directories/researchers/sergei-molokov/


During the solidification of metals, such as steels, aluminium and various alloys, as well as various semiconductors, an unwanted effect often occurs, namely micro- and macro-segregation of the components of the solidified material. This leads to very undesirable effects, such as strongly anisotropic distribution of dopands, as well as weakened structural properties of the material. One of the main reasons for these effects is buoyant convection which inevitably sets in in a non-uniformly heated or cooled material. The main effect of the convection is that it quickly becomes unstable and then turbulent, which is the cause of various striations and other nonuniformities. It had been observed quite a long time ago that an application of a sufficiently strong magnetic field suppresses oscillating convection to a certain degree by means of the magnetohydrodynamic (MHD) interaction. These observations have led to modifications of several industrial processes, such as casting of steels, aluminium, as well as devices for semiconductors crystal growth, where magnetic fields are widely used to control the solidification processes. However, these nonuniformities in the composition of material have been seen to persist even in relatively high magnetic fields, the origin of this phenomenon remain unclear.

The aim of the study is to gain understanding of the persistent oscillations in high magnetic field and to recommend the shape, the required strength, and the best direction of the magnetic field to improve the quality in casting and semiconductor crystal growth.
Modelling of heat and mass transfer in high magnetic fields is a very demanding task computationally, as the MHD interaction induces boundary layers of very low thickness which need to be resolved computationally. Therefore, full equations of fluid dynamics require separation of scales and high resolution of these boundary layers and up to now are usually available for low fields only. The approach to be used, developed and tested over almost 30 years, is to combine the analytical (asymptotic) approach with numerical methods to gain good understanding of the physical phenomena in high magnetic fields. This approach allows to treat the thinnest boundary layers analytically, and thus to work without the necessity to resolve them. After that the hydrodynamic equations are modelled coupled with the equations of heat and mass transfer. This approach will be adopted in the proposed study. The geometry is a rectangular box heated from below and cooled from above. This leads to a convective flow owing to unstable temperature stratification. This is called the Rayleigh-Benard problem. The box has different aspect ratios in a magnetic field with three different directions. Then for each orientation and aspect ratio the MHD-heat-mass-transfer equations will be studied and conclusions will be drawn depending on these parameters. It is expected that for even the slightest supercritical values of heating the motion of the fluid will become chaotic with many interesting effects.

Although the project is theoretical, the theory to be developed will be subsequently tested experimentally in magnets producing high magnetic field.


Our research in Manufacturing and Materials Engineering builds on our historic research strengths at Coventry, and adds new research teams through investment and growth. It integrates seamlessly with the Institute for Advanced Manufacturing and Engineering, our flagship collaboration with Unipart Manufacturing.

This area of research will take a holistic approach to fabrication and manufacturing, focusing on the three strands of Materials, Processes, and Products; and underpinned by our expertise in Metrology and Advanced Experimentation.
We aim to be the research partner of choice for manufacturing industry in adding value, effecting knowledge transfer, generating intellectual property, and raising new technologies from concept up through the Manufacturing Readiness Levels.

Our summary research themes:
• Process Control / Product Verification.
• Advanced Metrology and Experimentation
• Supply Chain Management
• Materials for Advanced Technologies
• Integrated Product Enhancement

How to apply: http://www.coventry.ac.uk/research/research-students/how-to-apply/

Link to CU page: http://www.coventry.ac.uk/research/research-students/research-studentships/chaotic-rayleigh-benard-convection-in-a-rectangular-box-in-a-high-magnetic-field/
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