Newton’s law of heating and the heat equation

Document Type


Publication Date



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.

Publisher's Statement

Publisher's version of record: https://dx.doi.org/10.2140/involve.2009.2.419

Publication Title

Involve: A Journal of Mathematics