This relationship was derived from an empirical observation of convective cooling of hot bodies made by Isaac Newton in 1701, who stated that "the rate of loss of heat by a body is directly proportional to the excess temperature of the body above that of its surroundings." Accordingly, the temperature of a hot object (T_{1}) which is cooling down as a result of exposure to a convective flow at T_{2} < T_{1}, would vary as:

If the energy loss from the hot body to the cooler fluid is replenished by a heat flux q such that T_{1} remains constant then the steady state version of Newton's Law of Cooling can be expressed as

This rate equation is universally used to define the Heat Transfer Coefficient (α) for all convective flows (free, forced, single/multiphase, etc.) involving either heating or cooling. It should be noted that in some cases (α) is temperature dependent and then
is not a linear function of the driving force (T_{1} – T_{2}). It should also be noted that the defining driving force varies from system to system (boundary layer flows, tube flows, etc.), but the complexity of any particular process is usually reflected in the formulation of the expression for (α), whose value depends upon the nature and properties of the flow system and ranges from 10 W/m^{2}K for Natural Convection between air and a vertical plate to 100,000 W/m^{2}K for dropwise Condensation of saturated water vapor at a vertical plate.

The study of convective heat transfer is ultimately concerned with finding the value of the heat transfer coefficient, as defined by Newton's Law of Cooling, in terms of the physical parameters of the convection system.

Heat & Mass Transfer, and Fluids Engineering