Maths in Industry Study Group

I spent the whole of last week in a workshop with the Maths in Industry Study Group, a wonderful initiative where people from outside the Maths field are invited to pose problems that are set in the "real world" that lend themselves to a mathematical solution. I was invited, along with my colleague Dr Ryan Bradley, to present a problem based on a low-cost housing prototype that Ryan built in 2017 and has been monitoring ever since.

The house is built of cement stabilised blocks, made from crushed recycled bricks, not just the walls, but most innovatively for the curved vaulted roofs. These follow a catenary shape (the shape of a hanging chain, but inverted) and the double vault has earned the small house the nickname of Big Mac, with its similarity to the MacDonalds logo. It is a double-storey building with living rooms on the ground floor and bedrooms above.

The problem we posed to the mathematicians was to model the heat flow through the vaults, as these should perform much better than other more conventional roofing materials, keeping the house cooler in summer and warmer in winter. This is vitally important for low-cost housing, as their inhabitants do not have the financial resources to pay for space heating or cooling.

Ryan and his students have measured the indoor and outdoor temperatures since the house was completed, so we could provide the mathematicians with a rich data set. In essence, what we were looking for was a mathematical model that would allow us to plug in different designs for future prototypes and have a good idea of how they were likely to perform climatically.

The process followed by the group on our project was fascinating, initially reducing the problem to a single dimension and then building on this highly simplified model to include for the specifics of vault shape and plan configuration. One of the group took a somewhat different angle, setting up a two-dimensional computer model, which shows great promise and which he will be refining with us in the months to come. Ryan and I are looking for grant funding to build another prototype, so this study should be very valuable in the months to come.

There were six industry problems in total for this year's workshop, the others included: optimising a game farm in Mpumalanga to benefit local communities; modelling mosquito nets to curb malaria; analysing photo images to aid in processing sugar; modelling the potential extinction of the African Penguin; and a novel water purification method using UV light. In all, it was a fascinating week with highly pertinent projects, a testament to the organisers and especially Prof David Mason, who has headed up this initiative in South Africa for many years. Ryan and hope to be back in a couple of years with a new prototype.

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Welcome to my blog

Sitting outside the Wits Architecture Building My name is Anne. I have just retired from the University of the Witwatersrand in Johannesburg, South Africa where I was an Associate Professor in the School of Civil and Environmental Engineering, working in the environmental engineering and project management domain. Prior to that, I was a lecturer in the School of Architecture and Planning, teaching many aspects of architecture, including architectural history, design and skills in graphics. Before lecturing at the University, I worked briefly in local government as a junior architect and then in a commercial firm of architects. After this I ran a private architectural practice with a focus on architectural heritage design. I have qualifications in architecture, construction management and employment creation through construction. Now that I have retired, I want to continue to provide educational context about architecture, engineering, design and project management in a different forum ...

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