The thermostat problem with a nonlocal nonlinear boundary condition

G. Kalna, S. McKee

Research output: Contribution to journalArticle

10 Citations (Scopus)

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.
LanguageEnglish
Pages437-462
Number of pages25
JournalIMA Journal of Applied Mathematics
Volume69
Issue number5
DOIs
Publication statusPublished - 2004

Fingerprint

Thermostats
Thermostat
Nonlocal Boundary Conditions
Nonlinear Boundary Conditions
Air conditioning
Boundary conditions
Conditioning
Unit
Heat
Heat losses
Heat conduction
Insulation
Heat Conduction Equation
Fluxes
Temperature
Controllers
Unstable
Paradigm
Controller
Hot Temperature

Keywords

  • heat equation
  • nonlocal boundary condition
  • Volterra integral equation

Cite this

@article{ec097978f42042cf834efba5bcce0393,
title = "The thermostat problem with a nonlocal nonlinear boundary condition",
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.",
keywords = "heat equation, nonlocal boundary condition, Volterra integral equation",
author = "G. Kalna and S. McKee",
year = "2004",
doi = "10.1093/imamat/69.5.437",
language = "English",
volume = "69",
pages = "437--462",
journal = "IMA Journal of Applied Mathematics",
issn = "0272-4960",
number = "5",

}

The thermostat problem with a nonlocal nonlinear boundary condition. / Kalna, G.; McKee, S.

In: IMA Journal of Applied Mathematics, Vol. 69, No. 5, 2004, p. 437-462.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The thermostat problem with a nonlocal nonlinear boundary condition

AU - Kalna, G.

AU - McKee, S.

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

KW - heat equation

KW - nonlocal boundary condition

KW - Volterra integral equation

UR - http://www.dcce.ibilce.unesp.br/sbmac_regional_XI/XXIV%20-%20No1/00Kalna.pdf

UR - http://dx.doi.org/10.1093/imamat/69.5.437

U2 - 10.1093/imamat/69.5.437

DO - 10.1093/imamat/69.5.437

M3 - Article

VL - 69

SP - 437

EP - 462

JO - IMA Journal of Applied Mathematics

T2 - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

SN - 0272-4960

IS - 5

ER -