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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 methods
Thermal radiation is a heat transfer due to electromagnetic radiation emitted by the surface of bodies due to their temperature.
Basic view factor concepts
Understanding view factors
View factors quantify the fraction of radiation emitted by one element that reaches another, considering various reflection and transmission scenarios. They are important in radiative heat transfer calculations.

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 methods
    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 classifications
        Thermal solver view factors have three main classifications: view factors, orbital view factors, and heat flux view factors.
      - Understanding view factors
        View factors quantify the fraction of radiation emitted by one element that reaches another, considering various reflection and transmission scenarios. They are important in radiative heat transfer calculations.
      - View factor sum and residual view factor
      - Orbital view factors
      - Shadowing surfaces
      - Elemental subdivision algorithm
        For certain operations such as shadowing checks and ray-tracing elements need to be subdivided into sub-elements.
    - View factor calculation without ray-tracing
    - View factor calculation using deterministic ray-tracing
    - View factors calculation using the hemicube method
      The thermal solver uses the hemicube method to compute diffuse blackbody view factors.
    - 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.
  - 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.

Understanding view factors

View factors quantify the fraction of radiation emitted by one element that reaches another, considering various reflection and transmission scenarios. They are important in radiative heat transfer calculations.

The view factor VF_ij from element i to element j is defined as the fraction of the radiation emitted by i that arrives at j without any intermediate diffuse reflections (but including specular reflections and transmissions), assuming perfectly diffuse and uniform emission in all directions. View factors are sub-classified into ray-traced and non-ray-traced view factors. Sometimes view factors are referred to as black body view factors (BBVF).

The non-ray-traced view factor is the view factor between the two elements if no specular reflection or transmission occurs. It depends solely upon the geometrical relationship between the two elements and the shadowing elements between them.

The ray-traced view factor is the view factor that also accounts for all specular reflections or transmissions between the two elements.

A heat flux view factor is a view factor to a diffuse radiative heat source of arbitrary shape.

View factor has the reciprocity property:

VF_ij, VF_ji are the view factors from i to j and from j to i.
A_i, A_j are the areas of elements i and j.

Gray body view factors

Radiative heat transfer between elements i and j is described by:

where:

Q_ij is the net radiative heat load from element i to element j.
σ is Stefan-Boltzmann's constant.
T_i, T_j are the absolute temperatures of elements i and j.
ϵ_i, ϵ_j are the emissivities of elements i and j, defined on MAT cards.
A_i, A_j are the surface areas of elements i and j.
VF_Gij is the gray body view factor from i to j, which is the fraction of the emitted or reflected radiant heat load leaving the surface i and absorbed by j after multiple diffuse reflections from all the elements.

As with the black body view factor, the gray body view factor has the reciprocity property: