# 7.14.2.2. Convection Heat Transfer

A broad class of thermal applications involve heat transfer between a solid volume and a surrounding fluid. In numerical simulations these interactions are modeled using various surface boundary conditions depending upon the detail to which the fluid flow is resolved. If both heat transfer in the solid model and fluid flow are explicitly modeled then it is often appropriate to solve the conjugate heat transfer problem. However, in many cases the expense of this calculation may not be justified and one reverts to alternative methods of modeling these effects.

In many situations it may be appropriate to simply characterize a bulk behavior of the fluid and employ a convective flux boundary condition of the form

where $q$ is the heat flux per unit surface area, is the surface heat transfer coefficient or convection coefficient, is the surface temperature and is the bulk fluid temperature. Many of the engineering models based upon experimental data for given configurations include variations of the values that enter into the expression above. In particular the values of and are often linked to representative fluid flow conditions.

For quick estimates of heat transfer, textbooks provide a tabulated range of surface heat transfer coefficients for general conditions. Furthermore, heat transfer handbooks provide a collection of heat transfer correlations from which convective coefficients can be computed. These correlations include empirical constants and are functions dimensionless numbers which characterize the bulk fluid flow and the bulk fluid temperature.

The Sierra Thermal module includes a number of different ways for specifying and . Additionally module provides a catalog of heat transfer correlations.

## 7.14.2.2.1. Convective Flux Boundary Condition

Scope

  Aria Region, Equation System, Explicit Equation System, Root Finder Equation System

Summary

  This command block specifies heat transfer on a boundary surface that can be modeled using Newton’s law of cooling.

Description

  Newton’s law of cooling specifies that the heat flux normal to a surface is proportional to the difference between the unknown temperature of the surface and some reference temperature of the fluid in which the surface is immersed: . The convection coefficient, , and the reference temperature, , may be specified in several ways as explained in detail below. In particular, note that the reference temperature is usually a known quantity, because the fluid with which it is associated is modeled as an infinite reservoir. However, if the size of this reservoir is finite, then its temperature can be affected by the energy transfer across the surface in question. This situation can be modeled by the bulk fluid element, wherein the energy of the reservoir is determined by a finite volume conservation equation.

  You must specify exactly one convection coefficient, and either exactly one reference temperature or exactly one bulk fluid element name.

    begin Convective Flux Boundary Condition Name

       Add Surface SurfaceList...

       Convective Coefficient {=} Value

       Convective Coefficient Fortran Subroutine {=} Name

       Convective Coefficient Node Variable {=} Name

       Convective Coefficient Scale Factor {=} Magnitude

       Convective Coefficient Subroutine {=} Name

       Convective Coefficient Temperature Function {=} NName

       Convective Coefficient Time Function {=} Name

       Equation {=} EquationName

       Ignore Flux Coverage

       Integer Data Values...

       Integrated Flux Output VariableName

       Integrated Power Output VariableName

       Real Data Values...

       Ref Temp Convective Coefficient Subroutine {=} Name [ UsingRefTemp  ]

       Reference Temperature {=} Value

       Reference Temperature Fortran Subroutine {=} Name

       Reference Temperature Global Variable {=} GlobalVariableName

       Reference Temperature Node Variable {=} Name

       Reference Temperature Subroutine {=} Name

       Reference Temperature Temperature Function {=} FunctionName

       Reference Temperature Time Function {=} FunctionName

       Scaled Convective Coefficient Subroutine {=} Name FieldName {=} Field

       Scaled Ref Temp Convective Coefficient Subroutine {=} Name FieldName {=} Field

       Uq Flux Multiplier {=} Value

       Use Advective Bar Name [ BulkNodes  ]

       Use Bulk Element Name

       Use Correlation Convection Model Name

       Use Data Block Name

       Use Enclosure Name

       Use Toggle Block ToggleName [ {on} ElementBlockList...  ]

       User Field Mask {=} Name [ Threshold {=} Value  ]

       User Field Scaling {=} Name

    end Convective Flux Boundary Condition Name

### Line Commands

###### Add Surface

Syntax

  Add Surface SurfaceList…

Summary

  Adds surfaces, by name, to a boundary condition’s extent.

Description

  This line command is used to add surfaces to the extent of a boundary condition. In Exodus II, surfaces are specified as side sets, that have a global integer identifier. For example, side set 12 would be added by this line command using the surface name surface_12. Note that in SIERRA, each element of an array of strings must be separated by whitespace.

Parameter | Value | Default
--- | --- | ---
SurfaceList | string… | –

###### Convective Coefficient

Syntax

  Convective Coefficient {=} Value

Summary

  Specify a constant convective coefficient for this boundary condition.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Value | real | –

###### Convective Coefficient Fortran Subroutine

Syntax

  Convective Coefficient Fortran Subroutine {=} Name

Summary

  Specify the name of a FORTRAN user subroutine that will be used to calculate the convective coefficient for this boundary condition.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Name | string | –

###### Convective Coefficient Node Variable

Syntax

  Convective Coefficient Node Variable {=} Name

Summary

  Specify the name of the node variable to use for the convective coefficient that is associated with this boundary condition.

Description

  The indicated node variable must be a legal Aria variable. Typically, this variable is defined by the user in the user definition command block. The node variable is interpolated to the integration points during the integration of the flux term. Typically, this variable would be calculated in another SIERRA region, e.g., Fuego, and transferred to Aria.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Name | string | –

###### Convective Coefficient Scale Factor

Syntax

  Convective Coefficient Scale Factor {=} Magnitude

Summary

  Specify that the convective coefficient is to be computed using sideset distribution factors that must be defined in the mesh database.

Description

  The coefficient on each face is computed by interpolating the distribution factors to the Gauss points and then multiplying the result by the given magnitude. Distribution factors do not currently work with h–adaptivity, since their values are not currently interpolated to the new nodes.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Magnitude | real | –

###### Convective Coefficient Subroutine

Syntax

  Convective Coefficient Subroutine {=} Name

Summary

  Specify the name of a user subroutine that is to be used to calculate the convective coefficient for this boundary condition.

  If the user subroutine employs a user specified reference temperature model to compute the heat transfer coefficient then optional arguments USING_REF_TEMP must also appear at the end of the command line.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Name | string | –

###### Convective Coefficient Temperature Function

Syntax

  Convective Coefficient Temperature Function {=} NName

Summary

  Specify the name of a temperature-dependent function that is to be used to calculate the convective coefficient for this boundary condition.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
NName | string | –

###### Convective Coefficient Time Function

Syntax

  Convective Coefficient Time Function {=} Name

Summary

  Specify the name of a time-dependent function that is used to calculate the convective coefficient for this boundary condition.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Name | string | –

###### Equation

Syntax

  Equation {=} EquationName

Summary

  This command can be used to apply the Convective Flux conditions for an equation other than the ENERGY equation.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
EquationName | string | –

###### Ignore Flux Coverage

Syntax

  Ignore Flux Coverage

Summary

  This command causes the code to ignore the flux coverage Field when contact is present. Thus the flux will be applied even if the BC is being set on a contact surface.

###### Integer Data

Syntax

  Integer Data Values…

Summary

  List of integer data values to be used by the FORTRAN user subroutine. Copies of these values are provided to the subroutine hence changes to these values within the subroutine are not saved.

Parameter | Value | Default
--- | --- | ---
Values | integer… | –

###### Integrated Flux Output

Syntax

  Integrated Flux Output VariableName

Summary

  Calculate the average flux associated with this flux boundary condition.

Description

  This line command specifies that, as a postprocess, the normal flux associated with this boundary condition be integrated over the surface to obtain the total power. This power is then divided by the total area of the surface to obtain the average flux on the surface, and stored in a global variable named “VariableName”. This global variable may then be output to history files, or accessed in user subroutines, etc.

Parameter | Value | Default
--- | --- | ---
VariableName | string | –

###### Integrated Power Output

Syntax

  Integrated Power Output VariableName

Summary

  Calculate the total power associated with this flux boundary condition.

Description

  This line command specifies that, as a postprocess, the normal flux associated with this boundary condition be integrated over the surface to obtain the total power which is then stored into a global variable named “VariableName”. This global variable may then be output to history files, or accessed in user subroutines, etc.

Parameter | Value | Default
--- | --- | ---
VariableName | string | –

###### Real Data

Syntax

  Real Data Values…

Summary

  List of real data values to be used by the FORTRAN user subroutine. Copies of these values are provided to the subroutine hence changes to these values within the subroutine are not saved.

Parameter | Value | Default
--- | --- | ---
Values | real… | –

###### Ref Temp Convective Coefficient Subroutine

Syntax

  Ref Temp Convective Coefficient Subroutine {=} Name [ UsingRefTemp ]

Summary

  Specify the name of a user subroutine that is to be used to calculate the convective coefficient for this boundary condition. Use of this command line will enable the reference temperature to be supplied to the subroutine interface.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Name | string | –

###### Reference Temperature

Syntax

  Reference Temperature {=} Value

Summary

  Specify a constant reference temperature for this boundary condition.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Value | real | –

###### Reference Temperature Fortran Subroutine

Syntax

  Reference Temperature Fortran Subroutine {=} Name

Summary

  Specifies the name of a FORTRAN user-defined subroutine that will be used to calculate the reference temperature associated with this boundary condition.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Name | string | –

###### Reference Temperature Global Variable

Syntax

  Reference Temperature Global Variable {=} GlobalVariableName

Summary

  Specify a global variable to be used for reference temperature.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
GlobalVariableName | string | –

###### Reference Temperature Node Variable

Syntax

  Reference Temperature Node Variable {=} Name

Summary

  Specify the name of the node variable to use for the reference temperature that is associated with this boundary condition.

Description

  The indicated node variable must be a legal Aria variable. Typically, this variable is defined by the user in the user definition command block. The node variable is interpolated to the integration points during the integration of the flux term. Typically, this variable would be calculated in another SIERRA region, e.g., Fuego, and transferred to Aria.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Name | string | –

###### Reference Temperature Subroutine

Syntax

  Reference Temperature Subroutine {=} Name

Summary

  Specifies the name of a user-defined subroutine that is to be used to calculate the reference temperature associated with this boundary condition.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Name | string | –

###### Reference Temperature Temperature Function

Syntax

  Reference Temperature Temperature Function {=} FunctionName

Summary

  Specifies the name of the temperature-dependent function that is to be used to calculate the reference temperature associated with this boundary condition.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
FunctionName | string | –

###### Reference Temperature Time Function

Syntax

  Reference Temperature Time Function {=} FunctionName

Summary

  Specify the name of a time-dependent function for the reference temperature for this boundary condition.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
FunctionName | string | –

###### Scaled Convective Coefficient Subroutine

Syntax

  Scaled Convective Coefficient Subroutine {=} Name FieldName {=} Field

Summary

  Specify the name of a user subroutine that is to be used to calculate the scaled convective coefficient for this boundary condition. The interpolated scaling Field is supplied directly to the user subroutine.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Name | string | –
FieldName | string | –
{=} | {= | are | is} | –
Field | string | –

###### Scaled Ref Temp Convective Coefficient Subroutine

Syntax

  Scaled Ref Temp Convective Coefficient Subroutine {=} Name FieldName {=} Field

Summary

  Specify the name of a user subroutine that is to be used to calculate the scaled convective coefficient for this boundary condition. Use of this command will enable the reference temperature to be supplied to the user subroutine. Additionally interpolated values of the scaling Field will be delivered to the subroutine.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Name | string | –
FieldName | string | –
{=} | {= | are | is} | –
Field | string | –

###### Uq Flux Multiplier

Syntax

  Uq Flux Multiplier {=} Value

Summary

  Specify constant scaling of the convective flux.

Description

  Intended use of this scaling parameter is primarily for evaluation of model sensitivities.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Value | real | 1.0

###### Use Advective Bar

Syntax

  Use Advective Bar Name [ BulkNodes ]

Summary

  Use the named advective bar to model the reference temperature.

Description

  This line command specifies the name of an advective bar that has been defined using the advective bar command block. The temperature of the advective bar is used as the reference temperature, , for the convective heat transfer and this is computed based on a geometric coupling algorithm. Note that it is illegal to specify both a reference temperature and an advective bar.

Parameter | Value | Default
--- | --- | ---
Name | string | –

###### Use Bulk Element

Syntax

  Use Bulk Element Name

Summary

  Use the named bulk element to model the reference temperature.

Description

  This line command specifies the name of a bulk fluid element that has been defined using the bulk fluid command block. The temperature of the bulk fluid element is used as the reference temperature, $T_r$, for the convective heat transfer.

  Note

  It is illegal to specify both a reference temperature and a bulk element.

Parameter | Value | Default
--- | --- | ---
Name | string | –

###### Use Correlation Convection Model

Syntax

  Use Correlation Convection Model Name

Summary

  Specifies correlation model for convection coefficient

Parameter | Value | Default
--- | --- | ---
Name | string | –

###### Use Data Block

Syntax

  Use Data Block Name

Summary

  Reference to predefined data to be used by the user subroutine. These values may be changed by the user subroutine.

Parameter | Value | Default
--- | --- | ---
Name | string | –

###### Use Enclosure

Syntax

  Use Enclosure Name

Summary

  Use the named enclosure to define the surface list and possibly model the reference temperature using the MBL bulk node of the enclosure.

Description

  This line command specifies the name of an enclosure that has been defined using the enclosure definition command block. The list of surfaces for this convective BC is taken from the enclosure surfaces and it is illegal to specify both an enclosure and a surface list. If the enclosure has the Mean Beam Length (MBL) model activated, then this convective BC is linked to the bulk fluid element associated with the MBL model. The temperature of the bulk fluid element is used as the reference temperature, $T_r$, for the convective heat transfer.

  Note

  It is illegal to specify both a reference temperature and an enclosure with an MBL bulk element.

Parameter | Value | Default
--- | --- | ---
Name | string | –

###### Use Toggle Block

Syntax

  Use Toggle Block ToggleName [ {on} ElementBlockList… ]

Summary

  Specification for toggling entities in the computational model based on Toggle Block parameters. When used at the region level, the list of element blocks to be toggled must be provided. Otherwise a listing of entities is not needed as the Toggle Block will be associated with the command line or the enclosing command block.

Parameter | Value | Default
--- | --- | ---
ToggleName | string | –

###### User Field Mask

Syntax

  User Field Mask {=} Name [ Threshold {=} Value ]

Summary

  Specify that the convective boundary condition is to be masked by nonzero values of a user defined Field.

Description

  The convective boundary condition is applied in a conventional manner but then masked by nonzero values of an interpolated user defined Field. In most cases the user Field is transferred to Aria but it could also be computed. Default threshold for the masked value is 0.0, i.e. mask value equals 1.0 for values greater than zero.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Name | string | –

###### User Field Scaling

Syntax

  User Field Scaling {=} Name

Summary

  Specify that the convective boundary condition is to be scaled by a user defined Field.

Description

  The convective boundary condition is applied in a conventional manner but then scaled by an interpolated user defined Field. In most cases the user Field is transferred to Aria and acts as a weighting of the flux condition.

Parameter | Value | Default
--- | --- | ---
{=} | {= | are | is} | –
Name | string | –