This Demonstration illustrates the transient cooling of a composite solid: a slab, cylinder or sphere that is suddenly immersed in a cooling bath. The slab consists of two parallel layers, while the cylinder and sphere consist of two concentric layers. The individual layers have different thermal properties and are in perfect thermal contact with one another.
The composite body is initially at a uniform dimensionless temperature ; at time , it is immersed in a fluid in a well-stirred, insulated tank at constant temperature .
The equation describing this system is:
where is the dimensionless temperature and is the dimensionless distance. Here applies to a rectangle, cylinder or sphere. The equation is solved with initial condition and boundary conditions at and at .
is the Biot number, the ratio of internal resistance to conductive heat transfer in the solid to the external resistance of convective heat transfer of the solid to the surrounding fluid, and
where is the thermal diffusivity, is the dimensionless line of separation between the two layers, and the subscripts and refer to thermal properties of the inner and outer layers.