Rate of heat flow

The rate of heat flow is the amount of heat that is transferred per unit of time in some material, usually measured in watt (joules per second). Heat is the flow of thermal energy driven by thermal non-equilibrium, so that 'heat flow' is a redundancy (i.e. a pleonasm, and the same for ‘work flow’). Heat must not be confused with stored thermal energy, and moving a hot object from one place to another must not be called heat transfer. But, in spite of all these remarks, it is common in normal parlance to say ‘heat flow’, to talk of ‘heat content’, etc.
The equation of heat flow is given by Fourier's Law of Heat Conduction.
Rate of heat flow = - (heat transfer coefficient) * (area of the body) * (variation of the temperature) / (length of the material)
The formula for the rate of heat flow is:
where
If a piece of material whose cross-sectional area is formula_7 and thickness is formula_5 with a temperature difference formula_4 between its faces is observed, heat flows between the two faces in a direction perpendicular to the faces. The time rate of heat flow, formula_11, for small formula_2 and small formula_3, is proportional to formula_14. In the limit of infinitesimal thickness formula_5, with temperature difference formula_4, this becomes formula_17, where formula_18 is the time rate of heat flow through the area formula_7, formula_20 is the "temperature gradient" across the material, and formula_6, the proportionality constant, is the "thermal conductivity" of the material. People often use formula_6, formula_23, or the Greek letter formula_24 to represent this constant. The minus sign is there because the rate of heat flow is always negative—heat flows from the side at higher temperature to the one at lower temperature, not the other way around.