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