15.4. Energy Equation

The enthalpy of the material is computed as the sum of the sensible enthalpy, , and the latent heat, :

(15–1)

where

(15–2)

and

 
 

= reference enthalpy

= reference temperature

= specific heat at constant pressure

The liquid fraction, , can be defined as

(15–3)

The latent heat content can now be written in terms of the latent heat of the material, :

(15–4)

The latent heat content can vary between zero (for a solid) and (for a liquid).

For solidification/melting problems, the energy equation is written as

(15–5)

where

 

= enthalpy (see Equation 15–1)

= density

= fluid velocity

= source term

The solution for temperature is essentially an iteration between the energy equation (Equation 15–5) and the liquid fraction equation (Equation 15–3). Directly using Equation 15–3 [680] to update the liquid fraction usually results in poor convergence of the energy equation. In Ansys Fluent, the method suggested by Voller and Swaminathan is used to update the liquid fraction. For pure metals, where and are equal, a method based on specific heat, given by Voller and Prakash  [679], is used instead.