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Open Access research that challenges the mind...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including those from the School of Psychological Sciences & Health - but also papers by researchers based within the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

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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 0272-4960

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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.