For the simulation of flow induced crystallization under nonisothermal conditions, the energy equation must be added to the others. In the present context, it is given by the following equation where is the material derivative:

(12–15)

In this equation, the left-hand side is the internal energy depending on the melt density and heat capacity . The right-hand side of the equation has the diffusion term characterized by the thermal conductivity k, the dissipation term, and a term related to the release of latent heat. The term related to the latent heat involves the heat of crystallization per unit mass and the average absolute degree of crystallinity of the system .

It is assumed that the thermal conductivity k depends only on the temperature and is independent of the degree of transformation x. A third order polynomial expression is enabled for this temperature dependence:

(12–16)

where, is a scaling temperature factor. For the heat capacity , a significant dependence with respect to x is reported next to temperature dependence. Hence, you get the following expression for the mixed dependence of :

(12–17)

The heat of crystallization per unit mass is obtained as:

(12–18)

where is the reference heat of fusion and is a scaling factor for the temperature. The energy equation is coupled with the degree of transformation x through the release of latent heat and its material properties. It is also coupled with the stresses in both amorphous and semicrystalline phases through the dissipation term : .