Latent Heat

Defining Latent Heat

Latent heat effects can be significant and must be included in many heat transfer problems involving phase change. When latent heat is given, it is assumed to be in addition to the specific heat effect (see Uncoupled heat transfer analysis for details).

The latent heat is assumed to be released over a range of temperatures from a lower (solidus) temperature to an upper (liquidus) temperature. To model a pure material with a single phase change temperature, these limits can be made very close.

As many latent heats as are necessary can be defined to model several phase changes in the material. Latent heat can be combined with any other material behavior in Abaqus, but it should not be included in the material definition unless necessary; it always makes the analysis nonlinear.

Direct Data Specification

If the phase change occurs within a known temperature range, the solidus and liquidus temperatures can be given directly. The latent heat should be given per unit mass.

Defining a Smooth Latent Heat Transition

Abaqus/Standard can calculate a smooth transition from solidus to liquidus temperature using

\begin{matrix} U_{θ} & = (L H) ξ^{3} (10 - 15 ξ + 6 ξ^{2}) for θ_{S} \leq θ \leq θ_{L}, \end{matrix}

where $U_{θ}$ is the internal energy, $L H$ is the latent heat, and $ξ = (θ - θ_{S}) / (θ_{L} - θ_{S})$ . The above function is such that the first and second derivatives of $U_{θ}$ are zero at $θ_{S}$ and $θ_{L}$ . This definition is intended to ramp up from one value to another. In addition, you can extend the solidus-liquidus temperature interval using a scale factor as follows:

θ_{S_n e w} = \frac{1}{2} {[θ_{S} + θ_{L} - (θ_{L} - θ_{S}) \cdot s c a l e f a c t o r]}_{}

θ_{L_n e w} = \frac{1}{2} {[θ_{S} + θ_{L} + (θ_{L} - θ_{S}) \cdot s c a l e f a c t o r]}_{}

User Subroutine

In some cases it may be necessary to include a kinetic theory for the phase change to model the effect accurately in Abaqus; for example, the prediction of crystallization in a polymer casting process. In such cases you can model the process in considerable detail using solution-dependent state variables (About User Subroutines and Utilities) and user subroutine HETVAL (Abaqus/Standard) or VHETVAL (Abaqus/Explicit).

Elements

Latent heat effects can be used in all diffusive heat transfer, coupled temperature-displacement, coupled thermal-electrical-structural and coupled thermal-electrical elements in Abaqus but cannot be used with convective heat transfer elements. Strong latent heat effects are best modeled with first-order or modified second-order elements, which use integration methods designed to provide accurate results for such cases.

See Freezing of a square solid: the two-dimensional Stefan problem for an example of a heat conduction problem involving latent heat.