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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.
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.
Finite volume methods
Element's center of gravity method
The element's center of gravity (CG) method creates conductances between the CG of the element and its boundary elements.
Conductance matrix for tetrahedra
Creation of conductance matrix between boundary elements of a tetrahedron

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 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.
  - 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.
    - Finite volume methods
      - Comparison between finite volume methods
        The thermal solver supports two finite volume conduction methods—the center of element method and the element's center of gravity (CG) method—to create conductive conductances from geometry.
      - Element's center of gravity method
        The element's center of gravity (CG) method creates conductances between the CG of the element and its boundary elements.
        Conductance matrix for beams
        Conductance matrix for triangles
        Conductance matrix for tetrahedra
        Creation of conductance matrix between boundary elements of a tetrahedron
        Creation of conductance matrix between boundary elements and CG of the tetrahedron
        Conductance matrix for quadrilateral elements
        Conductance matrix for wedge and hexahedron elements
        Conductance matrix for pyramid elements
        Interface conductances
      - Center of element method
        The following table lists element types supported by the center of element conduction method and how the thermal solver identifies their center of location and sub-elements to create conductances between elements.
      - Axisymmetric elements
        This topic describes how axisymmetric shell and solid elements are defined in thermal analysis.
      - Orthotropic materials
        This topic explains how orthotropic materials are handled in thermal analysis, detailing the process for stretching shell and solid elements based on their thermal conductivities in different material directions and the subsequent calculation of conductance.
    - Finite element method
      The finite element method computes the temperature values at discrete points, solid nodes, by solving the heat conduction equation.
  - 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.
  - Miscellaneous topics
  - References
- Thermal solver API guide
  Allows you to create or add functionality to enhance the thermal solver capabilities.

Creation of conductance matrix between boundary elements of a tetrahedron

A linear internal temperature field, T(x,y,z), is defined within the element:

where a₁, a₂, a₃, and a₄ are coefficients.

The boundary element temperatures T_{b_j} are defined at the midpoints of the tetrahedron edges:

where j=1, 2, 3, 4.

The weighting factors, e_ij, of the coefficients a₁, a₂, and a₃ are computed by substituting the boundary element temperatures into temperature field equation:

where i= 1, 2, 3, 4.

The unit normal vectors N_jon the tetrahedron edges, L_j, are defined based on the coordinates unit vectors i , j and k as:

where b_j, c_j and d_j are the coefficients of the surface unit normal vector.

The temperature gradient vector is constant over the tetrahedron and is given by:

The heat flow, q_j, into each boundary element is defined using Fourier’s law:

where A_j is the area of side surfaces of a tetrahedron.

Using Kirchhoff's law, the heat flows between boundary elements based on conductances, g_ij, are given by:

Conductances between boundary elements are given by:

The elemental capacitances and heat loads are distributed to the boundary elements using the boundary elements conductances as:

where:

C₁C₂, C₃, and C₄ are the capacitances.
C_tet is the weighting factor.