Heat Transfer Field Functions Reference

The following primitive field functions are available for the Fluid Energy models (Segregated Fluid Enthalpy, Segregated Fluid Temperature, Coupled Energy) and Solid Energy models (Segregated Solid Energy, Coupled Solid Energy).

In the case of boundary heat flux functions, positive values mean heat is flowing out of the domain. This is opposite to the convention used with the Heat Flux boundary and region values.

Common Field Functions

Boundary Conduction Heat Flux

The magnitude of the conduction heat flux vector normal to the boundary, defined as

({\dot{q} ″}_{c o n d u c t i o n} \cdot a) / | a |

, summed from boundary conduction, boiling, and radiation heat flux.

This quantity includes molecular and turbulent diffusion effects at the boundary (positive denotes transfer out of the domain). The advection contribution at open flow boundaries is separately included in the Boundary Advection Heat Flux.

Boundary Conduction Heat Transfer

The heat transferred by conduction at the boundary, defined as

{\dot{q} ″}_{c o n d u c t i o n} \cdot a

, summed from boundary conduction, boiling, and radiation heat flux.

Boundary Heat Flux

The magnitude of the heat flux vector normal to the boundary, defined as

(\dot{q} ″ \cdot a) / | a |

, summed from all forms of heat flux—boundary conduction, convection, boiling, and radiation.

For harmonic balance cases, the value of the heat flux is a time-mean.

Boundary Heat Flux on External Side

The magnitude of the heat flux vector normal to the surface for the outward facing side. This field function is only available on outer wall surfaces when the region's Radiation Transfer Option is set to External or Internal and External.

Boundary Heat Transfer

The heat transferred at the boundary, defined as

\dot{q} ″ \cdot a

For harmonic balance cases, the value of the heat transfer is a time-mean.

Effective Conductivity

The effective thermal conductivity given by

k_{eff} = k + (μ_{t} C_{p}) / σ_{t}

where

σ_{t}

is the turbulent Prandtl number.

For porous regions this field function is given by

$k_{eff} = α [k + (μ_{t} C_{p}) / σ_{t}] + (1 - α) k_{s o l i d}$

External Ambient Temperature

The boundary ambient temperature that you specify for convection thermal boundary conditions. This field function is only available on boundaries for which the Convection option has been selected as the Thermal Specification.

External Heat Transfer Coefficient

The boundary external heat transfer coefficient that you specify for convection thermal boundary conditions. This field function is only available on boundaries for which the Convection option has been selected as the Thermal Specification.

Heat Transfer Coefficient

The wall boundary heat transfer coefficient defined by:

$h = ({\dot{q} ″}_{c o n d u c t i o n} \cdot a) / [| a | (T_{ref} - T_{f})]$

where

$T_{f}$ is the wall boundary temperature.
$T_{ref}$ is the specified Reference Temperature in the field function.

For a multiphase fluid, the heat transfer coefficient is defined using the volume-fraction-weighted version of the Boundary Conduction Heat Flux field function.

In a multiphase continuum, a version of this field function is created for each phase.

For harmonic balance cases, the value of the coefficient is a time-mean.

Internal Wall Heat Flux Coefficient, A

Internal Wall Heat Flux Coefficient, B

Internal Wall Heat Flux Coefficient, C

Internal Wall Heat Flux Coefficient, D

The internally calculated contributions to the constant coefficients of wall heat flux $A$ , $B$ , $C$ , $D$ .

In a multiphase continuum, versions of these field functions are created for each phase.

See User Wall Heat Flux Coefficient Specification.

Local Heat Transfer Coefficient

The local heat transfer coefficient is the heat transfer coefficient between the near-wall cell and the boundary. It is dependent upon the distance between the boundary and the near-wall cell, the thermal properties of the media and, in the case of turbulent flow, the near-wall turbulence state. Because of the dependence on the mesh, do not consider this quantity as a bulk heat transfer coefficient.

In a multiphase continuum, a version of this field function is created for each phase. These field functions are volume fraction weighted for each phase. The local heat transfer coefficient is the sum of the local heat transfer coefficients for each phase. This summation is valid because the phase-specific coefficients are already volume fraction weighted.

For harmonic balance cases, the value of the coefficient is a time-mean.

Local Heat Transfer Reference Temperature

The local heat transfer reference temperature is the effective temperature that can be used to linearize the total heat flux to the boundary with respect to the boundary temperature:

{\dot{q} ″}_{t o t a l} = h_{local} (T_{ref} - T_{w})

where:

$h_{local}$ is the local heat transfer. coefficient
$T_{w}$ is the boundary temperature.

The effect of radiation is explicitly included in this quantity. This quantity is useful for export to external CAE packages with the local heat transfer coefficient.

In a multiphase continuum, a version of this field function is created for each phase. These field functions are not volume fraction weighted.

For a multiphase fluid, the local heat transfer reference temperature is given by:

\sum_{}^{} (h_{i} \times T r_{i}) / \sum_{}^{} h_{i}

where:

$h_{i}$ is the local heat transfer coefficient of phase $i$
${T r}_{i}$ is the local heat transfer reference temperature of phase $i$

For harmonic balance cases, the value of the temperature is a time-mean.

Net Wall Heat Flux Coefficient, A

Net Wall Heat Flux Coefficient, B

Net Wall Heat Flux Coefficient, C

Net Wall Heat Flux Coefficient, D

The net wall heat flux coefficients $A$ , $B$ , $C$ , $D$ .

In a multiphase continuum, versions of these field functions are created for each phase.

See User Wall Heat Flux Coefficient Specification.

Porous Solid Conductivity

Solid conductivity that is valid only for porous regions. This field function reflects the data that you enter as part of the Solid Thermal Conductivity physics value.

In a multiphase continuum, a version of this field function is created for each phase.

Specific Heat

The specific heat as specified for the material.

In a multiphase continuum, a version of this field function is created for each phase.

Temperature

The temperature as calculated by the energy solver.

In a multiphase continuum, a version of this field function is created for each phase.

Temperature Coefficient

The temperature coefficient is defined as:

\frac{T - T_{r e f}}{Δ T_{r e f}}

where:

$T$ is the temperature.
$T_{r e f}$ and $Δ T_{r e f}$ are the Reference Temperature and the Reference Temperature Delta that you specify in the field function, respectively.

In a multiphase continuum, a version of this field function is created for each phase.

Temperature on External Side

The temperature of the external side of a boundary between the ambient environment and an internal domain. Available only when a convection condition is applied with non-zero thermal resistance.

Thermal Conductivity

Scalar value that reflects this material property according to the method that you defined for the physics continuum.

注	This field function is a scalar value and therefore not populated in regions where thermal conductivity is defined by an anisotropic tensor.

In a multiphase continuum, a version of this field function is created for each phase.

Thermal Resistance

Time Averaged Boundary Heat Flux

This field function provides the boundary heat flux, averaged over time, on the fluid side of a fluid-solid interface boundary, based on Sliding Sample Window Size and Sampling Delta Time properties of the Sliding Time Averaging Parameters node, or on the Sampling delay property of the Running Time Averaging Parameters node.

To make this field function available, select the Sliding Window Average or Running Average option for Time Averaging Option selected on solid side interface boundary. See Explicit Energy Coupling Thermal Boundary Conditions.

Total Energy

E

in Eqn. (1657).

In a multiphase continuum, a version of this field function is created for each phase.

Total Enthalpy

The total enthalpy

H

is the sum of static enthalpy plus kinetic energy:

H = h + \frac{{| v |}^{2}}{2}

where:

$h$ is the static enthalpy
$v$ is the velocity vector.

In a multiphase continuum, a version of this field function is created for each phase.

Field Functions for Fluid Energy Models

Boundary Advection Heat Flux

The magnitude of the advection heat flux vector normal to the boundary. The quantity includes the energy that is carried by the fluid across the domain boundary and is only defined at flow openings. Consistent with the other heat fluxes, the sign convention is positive for transfer out of the domain.

In a multiphase continuum, a version of this field function is created for each phase.

Boundary Advection Heat Transfer

The heat transferred by advection at the boundary. The quantity is essentially the rate that energy is advected into and out of the domain by the moving fluid. Consistent with the other heat transfer rates, the sign convention is positive for transfer leaving the domain.

In a multiphase continuum, a version of this field function is created for each phase.

Boundary Heat Flux Radiation Coefficient

The boundary heat flux radiation coefficient, defined by

σ ε

, where

σ

is the Stefan-Boltzmann constant and

ε

is the total emissivity. This quantity can be used in external CAE packages to express the radiative emission flux in terms of the boundary temperature:

${\dot{q} ″}_{r a d, e m i s s i o n} = {D T^{4}}_{w}$

where $D$ is the boundary heat flux radiation coefficient.

Energy Residual

This residual becomes available in simulations involving heat transfer for fluids alone when the energy solver has the Temporary Storage Retained property activated.

In a multiphase continuum, a version of this field function is created for each phase.

Flow Work Energy Source

The rate of viscous dissipation or viscous work done as fluid is moved through a boundary, the dot product of the viscous stress tensor and the velocity with the boundary area

(T \cdot v) \cdot a

. See Eqn. (666) and Eqn. (1907).

This field function is only available with Temporary Storage Retained activated in the Segregated Flow solver.

Heat Exchanger Energy Source

This field function is applicable for dual stream heat exchangers. It represents the local heat transfer rate between the cells connected by a Heat Exchanger Direct Region Interface. See Heat Exchanger Energy Source Option.

Heat Exchanger Temperature Difference

This field function is applicable for dual stream heat exchangers.

Heat Exchanger Temperature Jump

This field function is applicable for dual stream heat exchangers.

Nusselt Number

The non-dimensional heat transfer coefficient is calculated as:

N u = \frac{{\dot{q}}^{″}_{w a l l}}{T_{r e f} - T_{w a l l}} \frac{L_{r e f}}{k_{r e f}}

where:

${\dot{q}}^{″}_{w a l l}$ is the wall heat flux.
$T_{r e f}$ is the specified Reference Temperature.
$T_{w a l l}$ is the temperature at the wall.
$L_{ref}$ is the specified Reference Length.
$k_{r e f}$ is the specified Reference Thermal Conductivity.

Relative Total Enthalpy

In a multiphase continuum, a version of this field function is created for each phase.

Relative Total Temperature

The temperature obtained by isentropically bringing the flow to rest in the relative frame of motion.

In a multiphase continuum, a version of this field function is created for each phase.

Rothalpy

Rothalpy

I

is the relative total enthalpy less the kinetic energy due to the velocity of the relative frame:

I = h + \frac{1}{2} v_{rel}^{2} - \frac{1}{2} v_{g}^{2}

where $h$ is the static enthalpy, $v_{rel}$ is the velocity of the fluid in the relative frame, and $v_{g}$ is the velocity of the relative frame.

Specified Y+ Heat Transfer Coefficient

The specified Y+ heat transfer coefficient is calculated in the same way as the local heat transfer coefficient (see Eqn. (1666)), but at a user-specified

y^{+}

value instead of the value that is associated with the near-wall cell.

In a multiphase continuum, a version of this field function is created for each phase. These field functions are volume fraction weighted for each phase. The specified Y+ heat transfer coefficient is the sum of the specified Y+ heat transfer coefficients for each phase. This summation is valid because the phase-specific coefficients are already volume fraction weighted.

For harmonic balance cases, the value of the coefficient is a time-mean.

To make this field function available, the Turbulence models must be activated.

Specified Y+ Heat Transfer Reference Temperature

The specified Y+ heat transfer reference temperature as given by Eqn. (1667).

In a multiphase continuum, a version of this field function is created for each phase. These field functions are not volume fraction weighted for each phase.

For a multiphase fluid, the specified Y+ heat transfer reference temperature is given by:

$\sum_{}^{} (h_{i} \times T r_{i}) / \sum_{}^{} h_{i}$

where:

$h_{i}$ is the specified Y+ heat transfer coefficient of phase $i$ .
${T r}_{i}$ is the specified Y+ heat transfer reference temperature of phase $i$ .

For harmonic balance cases, the value of the temperature is a time-mean.

To make this field function available, the Turbulence models must be activated.

Static Enthalpy

The static enthalpy

h

is related to the total enthalpy as calculated by Eqn. (1659).

This field function is only available for the Segregated Fluid Enthalpy model.

Field Functions for Solid Energy Models

Density: The density of the solid material.
Thermal Conductivity Tensor <nn>: Any of six components of the symmetric tensor describing thermal conductivity of solids in anisotropic regions. <nn> can be XX, YY, ZZ, XY, XZ, or YZ.