#### Title

Newton’s law of heating and the heat equation

#### Document Type

Article

#### Publication Date

10-28-2009

#### 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.

#### Publication Title

Involve: A Journal of Mathematics

#### Recommended Citation

Gockenbach, M.,
&
Schmidtke, K.
(2009).
Newton’s law of heating and the heat equation.
*
Involve: A Journal of Mathematics,
2*(4), 419-437.
http://dx.doi.org/10.2140/involve.2009.2.419

Retrieved from: https://digitalcommons.mtu.edu/math-fp/19

## Publisher's Statement

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