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Thermal Solver
Contains thermal solver related guides, such as the TMG reference manual, thermal API guide, and error message list.
Thermal solver theory
Describes the theory and methods of the thermal solver.
Radiation exchange
Thermal radiation is a heat transfer due to electromagnetic radiation emitted by the surface of bodies due to their temperature.
Radiative conductance calculation methods
Radiative conductance quantifies the rate at which thermal radiation is exchanged between surfaces. The thermal solver supports several computational methods, each with distinct advantages and limitations depending on the complexity of the geometry, material properties, and computational resources available.
Gebhardt method
The thermal solver can compute radiative conductances using the Gebhardt method.

Thermal Solver
Contains thermal solver related guides, such as the TMG reference manual, thermal API guide, and error message list.
- Thermal solver guides
  Maya HTT's thermal solver is included in Simcenter 3D and in Simcenter Femap. This page contains links to thermal solver guides, which help you understand how the thermal solver works.
- Thermal solver reference
  Describes the format and contents of the thermal solver's input and output files
- Thermal solver theory
  Describes the theory and methods of the thermal solver.
  - Introduction
    This guide provides the theory and methods used by the thermal solver, including methods to calculate conduction, convection, and radiation, as well as modeling specific topics using the thermal solver.
  - Elements in the thermal solver
    The thermal solver uses elements to calculate conductive, convective, and radiative conductances, as well as hydraulic resistances.
  - Supported element types for radiation
    Radiating elements may be defined with 1 to 4 corner nodes. The elements may be linear or parabolic.
  - Conduction methods
    To model heat conduction, the thermal solver can use two finite volume methods, center of element method or element's center of gravity method, or the finite element method.
  - Convective heat transfer methods
    The thermal solver computes convection conductances for various geometrical configurations using correlations that depend on specified characteristic lengths, convective surfaces, and type of convection.
  - Radiation exchange
    Thermal radiation is a heat transfer due to electromagnetic radiation emitted by the surface of bodies due to their temperature.
    - Basic view factor concepts
    - View factor calculation using deterministic without ray-tracing
    - View factor calculation using deterministic ray-tracing
    - View factor calculation using the hemicube method
      The thermal solver uses the hemicube method to compute diffuse blackbody view factors.
    - View factor calculation using the Monte Carlo method
      The thermal solver uses the CPU-based Monte Carlo algorithm for calculating view factors in radiation modeling using ray-tracing technique when modeling advanced optical properties.
    - Radiative conductance calculation methods
      Radiative conductance quantifies the rate at which thermal radiation is exchanged between surfaces. The thermal solver supports several computational methods, each with distinct advantages and limitations depending on the complexity of the geometry, material properties, and computational resources available.
      - Oppenheim method
        The thermal solver can compute radiative conductances using the Oppenheim method.
      - Gebhardt method
        The thermal solver can compute radiative conductances using the Gebhardt method.
    - GPU-based radiation calculation methods
      GPU-based calculation methods for radiation exchange use the graphics processing unit (GPU) to perform accelerated radiation computation.
    - Radiation patches
      The radiation patches are used to accelerate the solution of radiative heat transfer when using the Oppenheim method. This approach is not supported by the Gebhardt method.
    - Comparison of radiation calculation methods
      This tables compares different radiation computation methods used for computing radiation exchange in thermal simulations.
    - Radiation enclosures
      The thermal solver separates elements into enclosures. An enclosure is defined to be a set of elements that view each other and only each other.
    - Diffuse reflectivity calculation
      This section describes the calculation of diffuse reflectivity for materials with angle-dependent specular reflectivity or transmissivity.
    - Effective property calculation
      For each element, the thermal solver calculates the effective properties from the surface properties and self-view factors.
    - Heat flux calculation in radiative heat transfer
      The thermal solver computes the incident, reflected, absorbed, and transmitted energy fluxes for radiative heat transfer analysis.
    - Plane stress view factor calculation when modeling with axisymmetric or 3D elements
      This section explains how the thermal solver computes the view factor for axisymmetric or mixed 2D axi-3D models with plane stress elements for radiation requests.
  - Solar heating
  - Steady state analysis
    In a steady state analysis, the thermal solver solves the temperatures of non-sink elements iteratively using the following algorithm.
  - Transient analysis
    Transient analysis is performed using the following algorithm.
  - Hydraulic network analysis
    When the hydraulic pressure-flow network is present in the model, the thermal solver solves it at each iteration or time step using the following algorithm.
  - Miscellaneous topics
  - Thermal solver theory bibliography
    The following bibliography lists all sources used to explain how the thermal solver works.
- Thermal solver API
  Allows you to create or add functionality to enhance the thermal solver capabilities.
- Thermal solver error message list
  Lists solver messages that the thermal solver generates to communicate issues with the model or the solve.

Gebhardt method

The thermal solver can compute radiative conductances using the Gebhardt method.

When gray body view factors, VF_Gij, between the elements are calculated by the Gebhardt method, the radiation emitted by the element i and absorbed by the element j after multiple diffuse reflections is equal to the absorbed portion of the radiation directly incident upon j, plus the radiation reflected by all surfaces:

The reflected radiation is assumed to be reflected perfectly diffusely, which means that it is reflected in proportion to the view factors of the element. If only geometric view factors are present in the VUFF file, then even if an element has specular reflectivity, its reflectivity is treated as perfectly diffuse.

If ray-traced view factors are present in VUFF using the VFTRACE option, the equivalent reduced diffuse properties of the view factor matrix are used for elements that have specular or transmissive surface properties. In this case, the specular and transmissive effects have been accounted for during the ray-tracing procedure.

Eliminating insignificant radiative conductances

Excessively weak radiative conductances calculated with the Gebhardt method may be eliminated or connected to the element i using a non-zero RK thermal solver control parameter. For each element i and j the largest gray body view factors not connected to a space element VF_Gimax and VF_Gimax are identified. Only those radiative conductances whose gray body view factors satisfy both specified inequalities are considered:

All others are considered insignificant.

The double inequality is necessary because when A_i << A_j the conductance may be insignificant for j but very important for i.

If RK > 0 the insignificant radiative conductances are not considered unless the coupling is to space.

If RK < 0 and a valid (non-zero, non-space) element number is specified, each insignificant radiative coupling between elements i and j is replaced by two equivalent couplings: one from element i to the specified element, and one from element j to the same element.

The gray body view factor matrices are not affected by RK.

It is necessary to exercise care with RK > 0 to avoid eliminating an excessive number of radiative couplings. RK = 1 eliminates all radiative couplings.

RK = 0 defaults to RK = 1.E-4.