17.4 Energy Equation

The enthalpy of the material is computed as the sum of the sensible enthalpy, $h$, and the latent heat, $\Delta H$:

where

and	$h_{\rm ref}$	=	reference enthalpy
	$T_{\rm ref}$	=	reference temperature
	$c_p$	=	specific heat at constant pressure

The liquid fraction, $\beta$, can be defined as

$$\beta = 0 \mbox{if} T < T_{\rm solidus}$$

$$\beta = 1 \mbox{if} T > T_{\rm liquidus}$$

$$\beta = \frac{T-T_{\rm solidus}}{T_{\rm liquidus} - T_{\rm solidus}} \mbox{if} T_{\rm solidus} < T < T_{\rm liquidus}$$ (17.4-3)

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

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

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

where	$H$	=	enthalpy (see Equation  17.4-1)
	$\rho$	=	density
	$\vec{v}$	=	fluid velocity
	$S$	=	source term

The solution for temperature is essentially an iteration between the energy equation (Equation  17.4-5) and the liquid fraction equation (Equation  17.4-3). Directly using Equation  17.4-3 to update the liquid fraction usually results in poor convergence of the energy equation. In ANSYS FLUENT, the method suggested by Voller and Swaminathan [ 362] is used to update the liquid fraction. For pure metals, where $T_{\rm solidus}$ and $T_{\rm liquidus}$ are equal, a method based on specific heat, given by Voller and Prakash [ 361], is used instead.