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Driving innovations in manufacturing: Open Access research from DMEM

Strathprints makes available Open Access scholarly outputs by Strathclyde's Department of Design, Manufacture & Engineering Management (DMEM).

Centred on the vision of 'Delivering Total Engineering', DMEM is a centre for excellence in the processes, systems and technologies needed to support and enable engineering from concept to remanufacture. From user-centred design to sustainable design, from manufacturing operations to remanufacturing, from advanced materials research to systems engineering.

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The thermostat problem with a nonlocal nonlinear boundary condition

Kalna, G. and McKee, S. (2004) The thermostat problem with a nonlocal nonlinear boundary condition. IMA Journal of Applied Mathematics, 69 (5). pp. 437-462. ISSN 1464-3634

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Abstract

The thermostat controller for an air-conditioning system is usually placed in a position at some distance from the unit and this can lead to large swings in temperature. This paper addresses this question by studying a paradigm - a one-dimensional heat conduction equation with and without heat loss, and where the flux of heat extracted or input by the unit is considered to be a function of the temperature at the other end. The essential results are that the system can be unstable and that this is exacerbated both by a more powerful air-conditioning unit and by more efficient insulation.