Fig.3.1: Generalized heat balance over a layer volume element.

Input = Output + Accumulation +Reaction

		(3.1)
with out chemical reaction
		(3.2)
with
		(3.3)
		(3.4)
where
		(3.5)
		(3.6)
		(3.7)
Using the above approach and considering different pre-defined geometries, we can write:
		(3.8)
		(3.9)
the heat balance (eq. 3.7) reads now:
		(3.10)
The temperature profile has to be considered for all layers. In each layer the initial temperatures at t = 0 have to be introduced. If a layer is perfectly isolated on its left or right side, boundary condition (I, see Fig. 2.3) is derived from the symmetrical properties of the temperature profile at the wall surface. The other boundary conditions (II, Fig. 2.3) are derived from comparison of the heat transfers at the interface between the different layers. We have : - Boundary (I): Symmetry axis
		(3.11)
(if perfect insulation) - Boundary (II): Considering the ‘left’ and ‘right’ side of one interface, we can write at the interface between 2 layers:
		(3.12)