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Newton's law of
heating and the heat equation
Mark Gockenbach and Kristin Schmidtke
Vol. 2 (2009), No. 4, 419–437
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Abstract |
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Newton’s law of heating models the average temperature in an object by a simple ordinary differential equation, while the heat equation is a partial differential equation that models the temperature as a function of both space and time. A series solution of the heat equation, in the case of a spherical body, shows that Newton’s law gives an accurate approximation to the average temperature if the body is not too large and it conducts heat much faster than it gains heat from the surroundings. Finite element simulation confirms and extends the analysis. |
Keywords
heat equation, Newton's law of heating, finite elements,
Bessel functions
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Mathematical Subject Classification 2000
Primary: 35K05
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Milestones
Received: 25 November 2008
Revised: 15 June 2009
Accepted: 13 July 2009
Published: 28 October 2009
Communicated by Suzanne Lenhart
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Authors |
| Mark Gockenbach | |
| Department of Mathematical
Sciences Michigan Technological University 1400 Townsend Drive Houghton, MI 49931-1295 United States |
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| Kristin Schmidtke | |
| Department of Mathematical
Sciences Michigan Technological University 1400 Townsend Drive Houghton, MI 49931-1295 United States |
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