Temperature-dependent Thermal Conductivity Model

Overview

In this model, thermal conductivity of porous medium is defined as a linear function of temperature:

$k = k_{0} + \frac{ dk }{ dT } (T - T_{0})$

where: $k$ is the thermal conductivity at temperature T, which is a vector; $k_{0}$ is the reference thermal conductivity at the reference temperature; $T_{0}$ is the reference temperature; $\frac{ dk }{ dT }$ is the gradient of the thermal conductivity with respect to temperature, which equals to zero for the cases with constant thermal conductivity; note that this term is also in vector form, whose components could vary with directions.

Parameters

The temperature-dependent thermal conductivity model is called in the <SinglePhaseThermalConductivity> 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 CellElementRegion of the physical domain in the <ElementRegions> block.

The following attributes are supported:

XML Element: SinglePhaseThermalConductivity

Name	Type	Default	Description
defaultThermalConductivityComponents	R1Tensor	required	xx, yy, and zz diagonal components of the default thermal conductivity tensor [J/(s.m.K)]
name	groupName	required	A name is required for any non-unique nodes
referenceTemperature	real64	0	The reference temperature at which the conductivity components are equal to the default values
thermalConductivityGradientComponents	R1Tensor	{0,0,0}	xx, yy, and zz diagonal components of the thermal conductivity gradient tensor w.r.t. temperature [J/(s.m.K^2)]

Example

<Constitutive>
   ...
   <SinglePhaseThermalConductivity
     name="thermalCond_nonLinear"
     defaultThermalConductivityComponents="{ 1.5, 1.5, 1.5 }"
     thermalConductivityGradientComponents="{ -12e-4, -12e-4, -12e-4 }"
     referenceTemperature="20"/>
   ...
</Constitutive>