Temperature-dependent Solid Volumetric Heat Capacity Model

Overview

In this model, solid volumetric specific heat capacity is assumed to be a linear function of temperature:

$C = C_{0} + \frac{ dC }{ dT } (T - T_{0})$

where: $C$ is the solid volumetric heat capacity at temperature T; $C_{0}$ is the reference solid volumetric heat capacity at the reference temperature; $T_{0}$ is the reference temperature; $\frac{ dC }{ dT }$ is the gradient of the volumetric heat capacity with respect to temperature, which equals to zero for the cases with constant solid volumetric heat capacity;

Parameters

The temperature-dependent solid volumetric heat capacity model is called in the <SolidInternalEnergy> block of the input XML file. This model must be assigned a unique name via the name attribute. This name is used to attach the model to regions of the physical domain via a solidInternalEnergyModelName attribute in the <CompressibleSolidConstantPermeability> block.

The following attributes are supported:

XML Element: SolidInternalEnergy

Name	Type	Default	Description
dVolumetricHeatCapacity_dTemperature	real64	0	Derivative of the solid volumetric heat capacity w.r.t. temperature [J/(m^3.K^2)]
name	groupName	required	A name is required for any non-unique nodes
referenceInternalEnergy	real64	required	Internal energy at the reference temperature [J/kg]
referenceTemperature	real64	required	Reference temperature [K]
referenceVolumetricHeatCapacity	real64	required	Reference solid volumetric heat capacity [J/(kg.K)]

Example

<Constitutive>
   ...
   <SolidInternalEnergy
     name="rockInternalEnergy"
     referenceVolumetricHeatCapacity="4.56e6"
     dVolumetricHeatCapacity_dTemperature="1e6"
     referenceTemperature="0"
     referenceInternalEnergy="0"/>
   ...
</Constitutive>