7.13.2.2. 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

$q = h(T) ( T_{s} - T_{b} )$

where $q$ is the heat flux per unit surface area, $h(T)$ is the surface heat transfer coefficient or convection coefficient, $T_{s}$ is the surface temperature and $T_{b}$ 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 $h(T)$ and $T_{b}$ 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 $h(T)$ and $T_{b}$ . Additionally module provides a catalog of heat transfer correlations.

7.13.2.2.1. 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: $q_n=h(T-T_r)$ . The convection coefficient, $h$ , and the reference temperature, $T_r$ , 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, $T_r$ , 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	–