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The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by researchers from the Department of Computer & Information Sciences involved in mathematically structured programming, similarity and metric search, computer security, software systems, combinatronics and digital health.

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The thermostat problem with a nonlocal nonlinear boundary condition

Kalna, G.["lib/metafield:join_name.last" not defined]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.