Consider a composite slab of thickness , consisting of two parallel, perfectly fused layers of different thermal properties initially at uniform temperature ,that is immersed at time in a well-stirred, insulated tank containing a fluid at constant temperature .

The heat equation describing this system is:

with

at both and , and

,

where is the space coordinate (), is the thermal diffusivity (), is the thermal conductivity () and is the heat transfer coefficient between the slab and the surrounding fluid ().

To solve this problem, it is convenient to introduce the following dimensionless variables:

and

. Thus the equations become

,

,

at both and , and

with

and

,

where is the Biot number, the ratio of internal resistance to conductive heat transfer in the slab to the external resistance of convective heat transfer from the slab to the surrounding fluid; is the dimensionless coordinate of separation between the two layers; and the subscripts and refer to thermal properties of the layers and , respectively.