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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.
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.
Duct thermal discretization methods
The thermal solver provides multiple methods to compute the thermal exchange in duct flow networks.

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.
  - 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.
    - Hydraulic flow resistances for incompressible flows
      Hydraulic resistances are modeled with 2-node hydraulic elements.
    - Straight ducts
      For straight ducts, the flow is assumed to be fully developed, and the flow resistance factor (RF) is calculated using a specific formula based on duct characteristics.
    - Nozzles and diffusers
      The thermal solver computes the flow resistance factor for nozzles and diffusers based on the angles α and β, and various coefficients.
    - Duct geometry consideration for rough and curved ducts
      For fully developed flow through straight, smooth ducts, the thermal solver supports a wide range of friction factor and heat transfer correlations for different duct geometries.
    - Rough duct correlations
      Rough duct correlations use different friction factors for laminar, turbulent, and transitional flow. Nusselt numbers used in the correlations for rough ducts also change depending to flow conditions.
    - Head loss coefficients in curved ducts
      Understanding the pressure loss in bends using head loss coefficients for both laminar and turbulent flow conditions.
    - Heat transfer correlations in curved ducts
      Understanding heat transfer coefficients in curved ducts and the proposed correlation for different bend angles.
    - Head loss in sharp duct bends and duct branches
      The thermal solver uses the head loss in sharp duct bends and duct branches.
    - One-way conductance
      Modeling the heat transported by the fluid through one-way conductance for each flow resistance.
    - Duct thermal discretization methods
      The thermal solver provides multiple methods to compute the thermal exchange in duct flow networks.
  - 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.

Duct thermal discretization methods

The thermal solver provides multiple methods to compute the thermal exchange in duct flow networks.

It is recommended to use the exponential advection method, which models each hydraulic element with an exponential temperature profile along the element length, accounting for both advection and conduction in duct flow networks.

Advection and conduction with a constant temperature profile

In the standard thermal solver formulation for advection and conduction in a duct flow network, the outlet temperature, T_out, of a hydraulic duct element i is assumed to be equal to the element’s center of gravity (CG) temperature, T_cg. The heat balance equation is:

where:

G_1w is the one-way advection conductance for inflow.
T_in is the inlet temperature.
T_j is the temperature of the element j or of the environment.
G_ij are conductances to other elements j or to the environment.
Q_i is the applied heat.

This formulation gives slightly different results compared to the analytical solution when the wall temperature T_j is constant. Therefore, a more accurate formulation is introduced.

Exponential advection formulation

In the exponential advection formulation, conduction and applied heat are distributed uniformly along the element length l ∈ [0,L]. The temperature profile T(l) is governed by the differential heat conduction equation on the element:

The following boundary condition is applied to the previous equation:

This equation gives an exponential temperature profile along the element. The value of T_cg is set to the average temperature from this profile and used for environmental conduction. The outlet temperature T_out becomes the inlet for the next downstream duct. By comparing this solution with the original advection-convection scheme, the solver determines correction heat loads at T_in, T_cg, and T_out to obtain more precise temperatures. This formulation restores the analytical exponential solution when the wall temperature is constant.