Phase Change Material

This subnode should be used to specify the properties of a phase change material according to the apparent heat capacity formulation, when modeling heat transfer in solids, fluids, and porous media. This formulation gets its name from the fact that the latent heat is included as an additional term in the heat capacity. Up to five transitions in phase per material are supported. Alternatively, a Stefan condition can be defined on boundaries by using the Phase Change Interface node.

Number of Phase Transitions

To display this section, click the button (

) and select in the dialog box. The to model is set in this section. In most cases, only one phase transition is needed to simulate solidification, melting, or evaporation. If you want to model successive melting and evaporation, or any couple of successive phase transformations, choose an alternative value in the list. The maximum value is 5.

Depending on the , several parts display in the section, and several sections display underneath.

Density

This section is only available when the subnode is added under the node. In this particular case, a single density should be defined for all phases to ensure mass conservation on the material frame. Default is taken . For , enter a value or expression for ρ. Note that this setting overrides the setting in the section of the parent node.

Phase Change

The parameters for the definition of the transition temperature intervals are set in this section.

Each transition is assumed to occur smoothly in a temperature interval between Tpc, j → j + 1 − ΔTj → j + 1 ⁄ 2 and Tpc, j → j + 1 + ΔTj → j + 1 ⁄ 2, releasing a total heat per unit volume equal to Lj →j + 1.

The Tpc, 1 → 2 should be set to define the center of the first transition interval. The default is 273.15 K. Enter any additional phase change temperatures as per the .

The ΔT1 → 2 should be set to define the width of the first transition interval. The default is 10 K. Enter any additional transition intervals as per the .

The value of ΔTj → j + 1 must be strictly positive. A value near 0 K corresponds to a behavior close to a pure substance.

Open the section for more details on these parameters.

The L1 → 2 should be set to define the latent heat per unit mass released during the first phase transition. Enter any additional latent heat values as per the .

The value of Lj → j + 1 must be positive. The default is 333 kJ/kg, which corresponds to the latent heat of fusion of water at a pressure of 1 atm.

About the Phases

The different phases are ordered according to the temperatures of fusion. Hence, the material properties of phase 1 are valid when T < Tpc, 1 → 2, while the material properties of phase 2 hold for T > Tpc, 1 → 2.

When more than one transition is modeled, the number of phases exceeds 2, and new variables are created (for example, Tpc, 2 → 3, ΔT2 → 3 or L2 → 3). The phase change temperatures Tpc, j → j + 1 are increasing and satisfy

This defines distinct domains of temperature bounded by Tpc, j − 1 → j and Tpc, j → j + 1 where the material properties of phase j only apply.

In addition, the values of ΔTj → j + 1 are chosen so that the ranges between Tpc, j → j + 1 − ΔTj → j + 1 ⁄ 2 and Tpc, j → j + 1 + ΔTj → j + 1 ⁄ 2 do not overlap. If this condition is not satisfied, unexpected behavior can occur because some phases would never form completely. The values of ΔTj → j + 1 must all be strictly positive.

Phase

In each section (based on the ), the thermal conductivity and thermodynamics properties of each phase must be set. Then, within the transition interval, there is a “mushy zone” with mixed material properties.

Select a [1,2,...], which can point to any material in the model. The default uses the .

When the subnode is added under a node, the following material properties should be set:

•

ki. The default uses the material values for phase i. For select , , , or based on the characteristics of the thermal conductivity, and enter another value or expression. When the material and spatial frames differ (due to the presence in the model of a node, or a Solid Mechanics physics interface for example), you can select on which frame the ki is specified, with the option, see Heat Conduction, Solid for details.

•

Cp, i. The default is 4200 J/(kg·K).

Note that these settings override the settings of the and sections of the parent node.

When the subnode is added under a or node, the following material properties should be set:

•

ki. The default uses the material values for phase i. For select , , , or based on the characteristics of the thermal conductivity, and enter another value or expression. The default is 1 W/(m·K).

•

ρi. The default is 1000 kg/m3.

•

Cp, i. The default is 4200 J/(kg·K).

•

γi. The default is , it calculates the ratio of specific heats by using Mayer’s relation:

considering that:

•

αp is the coefficient of thermal expansion (SI unit: 1/K):

•

χt is the isothermal compressibility (SI unit: 1/Pa):

Note that these settings override the settings of the and sections of the parent node. In porous media, phase change is considered in the fluid material only.


	Apparent Heat Capacity Method


	It is useful to choose three or more phase transitions to handle extra changes of material properties such as in mixtures of compounds, metal alloys, composite materials, or allotropic varieties of a substance. For example, α, γ, and δ-iron are allotropes of solid iron that can be considered as phases with distinct phase change temperatures.


	To satisfy energy and mass conservation in phase change models, particular attention should be paid to the density in time simulations. When the material density is not constant over time — for example, dependent on the temperature — volume change is expected. The transport velocity field and the density must be defined so that mass is conserved locally. A The Moving Mesh Interface (described in the COMSOL Multiphysics Reference Manual) can be used to take into account model deformation.


	Phase Change: Application Library path Heat_Transfer_Module/Phase_Change/phase_change Continuous Casting — Apparent Heat Capacity Method: Application Library path Heat_Transfer_Module/Thermal_Processing/continuous_casting_apparent_heat_capacity Cooling and Solidification of Metal: Application Library path Heat_Transfer_Module/Thermal_Processing/cooling_solidification_metal

Location in User Interface

Context Menus

Ribbon

Physics tab with , , or selected in the model tree:

Physics tab with selected in the model tree: