Overall Heat Transfer Coefficient
Newton's Law of Cooling states that q'' = hΔT, where q'' is the Heat Flux (W / m2), and h is the Heat Transfer Coefficient (W / m2/K). Since q'' = q/A, q = hAΔT.
The thermal resistance of a wall is given R = L/kA, where L is the length of the wall, k is the conductivity of the material (W / mK), and A is the effective area. An additional 1/hA is required at each side of the wall to account for the thermal resistance of moving from air to the wall material and back again. Adding these together gives us the equation for the wall:
This can be visualised as a 'Thermal Circuit', with the 3 thermal resistances shown on the diagram:
If the wall is made out of several materials, then the thermal resistances of each section are added together to find the total resistance.
The equation now looks like this for the composite wall:
By factoring out the Area, the fractions inside the bracket are now the overall heat transfer coefficient (U). The overall heat transfer coefficient (U) can now be used in place of the original heat transfer coefficient (h).
q = hAΔT is now q = UAΔT, with Rtot = 1/UA.