Ansys Fluent solves the energy equation in the following form:

(5–1)

where is the effective conductivity (), where is the turbulent thermal conductivity, defined according to the turbulence model being used, and is the diffusion flux of species . The first three terms on the right-hand side of Equation 5–1 represent energy transfer due to conduction, species diffusion, and viscous dissipation, respectively. includes volumetric heat sources that you have defined and the heat generation rate from chemical reactions shown in Equation 5–11. However, this reaction source does not apply for the total enthalpy equation (see Energy Sources Due to Reaction for details).

In Equation 5–1,

The enthalpy is defined for ideal gases as

(5–2)

and for incompressible materials includes the contribution from pressure work

(5–3)

In Equation 5–2 and Equation 5–3, is the mass fraction of species and the sensible heat of species is the part of enthalpy that includes only changes in the enthalpy due to specific heat

(5–4)

The value used for in the sensible enthalpy calculation depends on the solver and models in use. For the pressure-based solver is 298.15 K, except for PDF models (in which case is a user input for the species) and for the inviscid model (in which case is 0 K). For the density-based solver is 0 K, except when modeling species transport with reactions, in which case is a user input for the species.

The internal energy is defined uniformily for compressible and incompressible materials as

(5–5)

In the above formulas and are gauge and operating pressure, respectively. Such definitions of enthalpy and internal energy accommodate an incompressible ideal gas in the common formulation:

(5–6)

The energy equation is solved in moving (relative) frames of reference. In moving frames of reference, the energy transport equation uses rothalpy as a conservative quantity. See Equation 2–6 for the energy equation in moving frames of reference.

When the non-adiabatic non-premixed combustion model is enabled, Ansys Fluent solves the total enthalpy form of the energy equation:

(5–7)

Under the assumption that the Lewis number (Le) = 1, the conduction and species diffusion terms combine to give the first term on the right-hand side of the above equation while the contribution from viscous dissipation appears in the non-conservative form as the second term. The total enthalpy is defined as

(5–8)

where is the mass fraction of species and

(5–9)

is the formation enthalpy of species at the reference temperature .

Equation 5–1 includes pressure work and kinetic energy terms, which are often negligible in incompressible flows. For this reason, the pressure-based solver by default does not include the pressure work or kinetic energy when you are solving incompressible flow. If you want to include these terms, use the define/models/energy? text command. When asked to include pressure work in energy equation? and include kinetic energy in energy equation?, respond by entering yes in the console window.

Pressure work and kinetic energy are always automatically accounted for when you are:

Equation 5–1 and Equation 5–7 describe the thermal energy created by viscous shear in the flow.

When the pressure-based solver is used, Ansys Fluent’s default form of the energy equation does not include them (because viscous heating is often negligible). Viscous heating will be important when the Brinkman number, , approaches or exceeds unity, where

(5–10)

represents the temperature difference in the system and represents the characteristic velocity of the system.

When your problem requires inclusion of the viscous dissipation terms and you are using the pressure-based solver, you should enable the terms using the Viscous Heating option in the Viscous Model Dialog Box. Compressible flows typically have . Note, however, that when the pressure-based solver is used, Ansys Fluent does not automatically enable the viscous dissipation if you have defined a compressible flow model.

When the density-based solver is used, the viscous dissipation terms are always included when the energy equation is solved.

Equation 5–1 and Equation 5–7 both include the effect of enthalpy transport due to species diffusion.

When the pressure-based solver is used, the term

is included in Equation 5–1 by default. If you do not want to include it, you can disable the Diffusion Energy Source option in the Species Model Dialog Box.

When the non-adiabatic non-premixed combustion model is being used, this term does not explicitly appear in the energy equation, because it is included in the first term on the right-hand side of Equation 5–7.

When the density-based solver is used, this term is always included in the energy equation.

Sources of energy, , in Equation 5–1 include the source of energy due to chemical reaction:

(5–11)

where is the enthalpy of formation of species , is the molecular weight of species , and is the volumetric rate of creation of species .

In the energy equation used for non-adiabatic non-premixed combustion (Equation 5–7), the heat of formation is included in the definition of enthalpy (see Equation 5–8), so reaction sources of energy are not included in .

When one of the radiation models is being used, in Equation 5–1 or Equation 5–7 also includes radiation source terms. For details, see Modeling Radiation.

When the electric potential equation Equation 18–1 is being solved, in Equation 5–1 also includes Joule heating source terms.

It should be noted that the energy sources, , also include heat transfer between the continuous and the discrete phase. This is further discussed in Coupling Between the Discrete and Continuous Phases.

In solid regions, the energy transport equation used by Ansys Fluent has the following form:

(5–12)

The second term on the left-hand side of Equation 5–12 represents convective energy transfer due to rotational or translational motion of the solids. The velocity field is computed from the motion specified for the solid zone. (For details, see Solid Conditions in the User's Guide). The terms on the right-hand side of Equation 5–12 are the heat flux due to conduction and volumetric heat sources within the solid, respectively.

Ansys Fluent  can solve the conduction equation in solid zones and shells with the thermal conductivity specified as a matrix. The heat flux vector is written as:

(5–13)

where is the thermal conductivity tensor, by default in global coordinates.

(5–14)

can also be calculated as:

(5–15)

where is user specified local thermal conductivities.

(5–16)

A is the transformation matrix and has three principal directions for each cell of a mesh.

(5–17)

A matrix is provided in current orthotropic material panel along with . See Anisotropic Thermal Conductivity for Solids in the User's Guide for details on specifying anisotropic conductivity for solid materials.

A transformation matrix has constant directions, and therefore would not follow curved geometry. For curved geometries, the transformation matrix is calculated for each cell to appropriately calculate . For details on the specifying anisotropic conductivity for curved geometry, see Anisotropic Thermal Conductivity with Curvilinear Coordinate System (CCS) in the Fluent User's Guide.

The net transport of energy at inlets consists of both the convection and diffusion components. The convection component is fixed by the inlet temperature specified by you. The diffusion component, however, depends on the gradient of the computed temperature field. Thus the diffusion component (and therefore the net inlet transport) is not specified a priori.

In some cases, you may want to specify the net inlet transport of energy rather than the inlet temperature. If you are using the pressure-based solver, you can do this by disabling inlet energy diffusion. By default, Ansys Fluent includes the diffusion flux of energy at inlets. To turn off inlet diffusion, use the define/models/energy? text command and respond no when asked to Include diffusion at inlets?

Inlet diffusion cannot be turned off if you are using the density-based solver.