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

## 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.

Item type: | Article |
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ID code: | 2179 |

Keywords: | heat equation, nonlocal boundary condition, Volterra integral equation, Mathematics |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics Faculty of Science > Mathematics and Statistics > Mathematics |

Related URLs: | |

Depositing user: | Strathprints Administrator |

Date Deposited: | 05 Jan 2007 |

Last modified: | 16 Jul 2013 18:26 |

URI: | http://strathprints.strath.ac.uk/id/eprint/2179 |

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