# Newton's Law of Cooling - Heat transfer version

## Description

Convection-cooling is sometimes called “Newton’s law of cooling” in cases where the heat transfer coefficient is independent or relatively independent of the temperature difference between object and environment. This is sometimes true, but is not guaranteed to be the case (see other situations below where the transfer coefficient is temperature dependent).

Newton’s law, which requires a constant heat transfer coefficient, states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings. The rate of heat transfer in such circumstances is derived here.

Newton’s cooling law is a solution of the differential equation given by Fourier’s law

## Variables

dQ | thermal energy at time t (joule) |

dt | time (sec) |

h | heat transfer coefficient (W/m^{2}*K) |

A | surface area of the heat being transferred (m^{2}) |

T(t) | temperature of the object's surface and interior (since these are the same in this approximation) at time t (K) |

T_{env} | temperature of the environment; i.e. the temperature suitably far from the surface (K) |