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>