The thermostat problem with a nonlocal nonlinear boundary condition
Copyright policy )The thermostat problem with a nonlocal nonlinear boundary condition
Summary: 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.
- University of Strathclyde United Kingdom
air-conditioning, Heat equation, one-dimensional heat conduction, Volterra integral equation, 510, 004, Stefan problems, phase changes, etc., Integro-partial differential equations, Initial-boundary value problems for second-order parabolic equations, efficient insulation, Mathematics
air-conditioning, Heat equation, one-dimensional heat conduction, Volterra integral equation, 510, 004, Stefan problems, phase changes, etc., Integro-partial differential equations, Initial-boundary value problems for second-order parabolic equations, efficient insulation, Mathematics
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).14 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!