Translator Disclaimer
2009 Newton's law of heating and the heat equation
Mark Gockenbach, Kristin Schmidtke
Involve 2(4): 419-437 (2009). DOI: 10.2140/involve.2009.2.419

Abstract

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.

Citation

Download Citation

Mark Gockenbach. Kristin Schmidtke. "Newton's law of heating and the heat equation." Involve 2 (4) 419 - 437, 2009. https://doi.org/10.2140/involve.2009.2.419

Information

Received: 25 November 2008; Revised: 15 June 2009; Accepted: 13 July 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1185.35117
MathSciNet: MR2579561
Digital Object Identifier: 10.2140/involve.2009.2.419

Subjects:
Primary: 35K05

Rights: Copyright © 2009 Mathematical Sciences Publishers

JOURNAL ARTICLE
19 PAGES


SHARE
Vol.2 • No. 4 • 2009
MSP
Back to Top