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# Thermal Conductivity Simulation

### with VGSTUDIO MAX

Simulate thermal conductivity on CT scans of different materials using the Transport Phenomena Simulation Module for VGSTUDIO MAX.

## Simulation of Thermal Conductivity

Thermal conductivity measures a material's ability to allow the transport of heat.

The Transport Phenomena Simulation Module for VGSTUDIO MAX:

• Simulates the stationary temperature and thermal flux fields in a two-component material, where each material has a different thermal conductivity, with the boundary condition that inlet and outlet are connected to heat reservoirs, each at a different constant temperature.
• Works directly on voxel data and makes use of the sub-voxel accurate, local adaptive surface determination in VGSTUDIO MAX.
• Has "experiment mode" for performing a virtual experiment on the transportation of heat, as well as "tensor mode" for calculating the thermal conductivity tensor.

The thermal conductivity module is based on the following differential equations for stationary temperature and heat flux fields in a two-component material

where Ω is the entire simulation domain and Ωₐ is the domain of component a (with a = 1, 2). It is assumed that Ω₁  and Ω₂ do not overlap and their union equals Ω. T is the temperature, φ is the heat flux, kₐ is the thermal conductivity of component a, Δ is the Laplace operator, and grad is the gradient operator.

## Experiment Mode

In experiment mode, the software performs a virtual experiment on the CT data of a structure, simulating the transport of heat through the structure from an inlet plane towards an outlet plane parallel to each other. Sealed or embedded boundary conditions perpendicular to the inlet and outlet plane can be defined. A temperature difference must be specified as driving quantity for the flow. Heat flux (2D view) Heat flux (3D view) Relative temperature (2D view) Relative temperature (3D view) Streamlines of heat flux

## Tensor Mode

In tensor mode, the software calculates the effective tensor-valued thermal conductivity. The calculation of the thermal conductivity tensor can be done on the whole structure or for increments of the structure by means of an integration mesh. Tensor mode Effective thermal conductivity tensor per integration mesh cell Mean effective thermal conductivity (2D view) Mean effective thermal conductivity (3D view) Void fraction (2D view) Void fraction (3D view)

In addition to the tensors' eigenvalues and eigenvectors, the components of the effective thermal conductivity tensor with respect to the simulation coordinate system are provided in a table view.