PLANE292

2D 4-Node Thermal Solid

PLANE292 Element Description

PLANE292 can be used as a plane element or as an axisymmetric ring element with a 2D thermal conduction capability. The element has four nodes with a single degree of freedom, temperature, at each node.

The element is applicable to a 2D, steady-state or transient thermal analysis. The element can also account for heat transfer by a mass flow with a prescribed velocity field (see Mass Transport (Advection) in the Theory Reference). If the model containing the temperature element is also to be analyzed structurally, the element should be replaced by an equivalent structural element (such as PLANE182). For more details about this element, see PLANE292 - 2D 4-Node Thermal Element in the Theory Reference.

A similar element with midside node capability is PLANE293.

Figure 292.1: PLANE292 Geometry

PLANE292 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 292.1: PLANE292 Geometry. The element is defined by four nodes and the orthotropic material properties. Orthotropic material directions correspond to the element coordinate directions. The element coordinate system orientation is as described in Coordinate Systems. Specific heat and density are ignored for steady-state solutions. Properties not input default as described in the Material Reference.

Element loads are described in Element Loading. Convection or heat flux (but not both) and radiation may be input as surface loads at the element faces as shown by the circled numbers on Figure 292.1: PLANE292 Geometry.

Heat generation rates may be input as element body loads at the nodes. If the node I heat generation rate HG(I) is input, and all others are unspecified, they default to HG(I).

This element can also have a Z-depth specified by KEYOPT(3) and real constant THK. Be careful when using this option with other physics, especially radiation. Radiation view factors will be based on a unit Z-depth (only).

A mass transport option is available with KEYOPT(8). With this option, you specify the velocity components VX and VY by issuing BF,,VELO,VX,VY. There is no restriction on the element Peclet number (Pe) for this element, and it offers the Streamline Upwind Petrov-Galerkin (SUPG) formulation and Discontinuity Capturing (DC) terms that enable convergence for high Pe conditions (see Galerkin or Streamline Upwind Petrov-Galerkin (SUPG) Formulation in the Thermal Analysis Guide). You can control the settings that activate the SUPG formulation and include one of three DC terms to smooth spurious oscillations if they arise in your solution by setting real constants with the R and RMORE commands as detailed in the table below. With mass transport, temperatures should be specified along the entire inlet boundary to assure a stable solution, and you should use specific heat (C) and density (DENS) material properties instead of enthalpy (ENTH). For more detais, see Mass Transport (Advection) in the Theory Reference and Mass Transport (Advection) in the Thermal Analysis Guide.

A summary of the element input is given in "PLANE292 Input Summary". A general description of element input is given in Element Input.

PLANE292 Input Summary

Nodes

I, J, K, L

Degrees of Freedom

TEMP

Real Constants

No. ^[a]	Name	Default ^[b]	Description
1	THK	none	Thickness (used only if KEYOPT(3) = 3)
Real Constants Used for Mass Transport (if KEYOPT (8) = 1 or 2) to Activate the Streamline Upwind Petrov-Galerkin (SUPG) Formulation and One of Three Discontinuity Capturing (DC) Terms ^[c]
2	`SUPG`	1.0	Acts as a multiplier on the stabilizing term of the SUPG formulation and enables you to choose also a DC term to smooth oscillations. To activate the Galerkin Formulation, use a small number(1.e-12), as an exact zero value reverts back to 1.0 internally and enables SUPG formulation.
3	`TGRADMAG`	1.0e-6	Thermal gradient threshold value, above which the DC term that you select will be applied. If the thermal gradient is less than the value you specify for `TGRADMAG`, the DC term is not applied, and vice versa, if it is greater, the nonlinear stabilizing DC term will be applied.
5	`DC1` ^[d]	0.0	Any non-zero value (typically 1.0) selects the DC1 term to be added to your analysis and acts as a multiplier on this stabilizing term.
6	`DC2` ^[d]	0.0	Any non-zero value (typically 1.0) selects the DC2 term to be added to your analysis and acts as a multiplier on this stabilizing term.
7	`DC3` ^[d]	0.0	Any non-zero value (typically 1.0) selects the DC3 term to be added to your analysis and acts as a multiplier on this stabilizing term.

^[a]Refers to the real constant values defined by issuing the R and RMORE commands.

^[b]If you do not specify any real constants, the mass transport solution will be based on the SUPG formulation without any DC terms.

^[c]The SUPG formulation and DC terms can be used to smooth oscillations that may arise in conditions of high Pe. For details, see Galerkin or Streamline Upwind Petrov-Galerkin (SUPG) Formulation in the Thermal Analysis Guide.

^[d]Activating more than one DC term at a time will produce an error message.

Material Properties

TB command: See Element Support for Material Models for this element.

MP command: KXX, KYY, DENS, C, ENTH

Surface Loads

Convection or Heat Flux (but not both) and Radiation (using Lab = RDSF) --: face 1 (J-I), face 2 (K-J), face 3 (L-K), face 4 (I-L)

Body Loads

Heat Generations --

HG(I), HG(J), HG(K), HG(L)

Velocity for Mass Transport (KEYOPT(8) = 1 or 2) --

Specify the velocity components VX and VY by issuing BF,,VELO,VX,VY

Special Features

Birth and death

KEYOPT(1)

How to evaluate film coefficient:

0 --: Evaluate film coefficient (if any) at average film temperature, (TS + TB)/2
1 --: Evaluate at element surface temperature, TS
2 --: Evaluate at fluid bulk temperature, TB
3 --: Evaluate at differential temperature, |TS - TB|

KEYOPT(3)

Element behavior:

0 --: Plane
1 --: Axisymmetric
3 --: Plane with Z-depth, specified via real constant THK.

KEYOPT(4)

Element coordinate system:

0 --: Element coordinate system is parallel to the global coordinate system
1 --: Element coordinate system is based on the element I-J side.

KEYOPT(8)

Mass transport effects:

0 --: Do not include mass transport in the analysis.
1 --: Include mass transport with Diffusive Flux (Dflux) Neumann boundary condition. You may want to choose the Dflux Neumann boudary condition if you are not interested in an energy balance as it is easier to specify compared to the Tflux boundary condition (see Diffusive Flux and Total Flux Neumann Boundary Conditions in the Theory Reference for details).
2 --: Include mass transport with Total Flux (Tflux) Neumann boundary condition. The Tflux Neumann boundary condition will satisfy an energy balance with the PRRSOL command, but setting up its Neumann boundary condition is slightly more complex than the Dflux option (see Diffusive Flux and Total Flux Neumann Boundary Conditions in the Theory Reference for details).

Note: Do not create models that have some elements with a value of 1 and others with a value of 2 for KEYOPT(8). On the other hand, it is possible to have combinations of elements with KEYOPT(8) = 0 and 2 as well as KEYOPT(8) = 0 and 1 in the same model.

KEYOPT(11)

Film coefficient matrix:

0 --: Program determines whether to use a diagonal or consistent film coefficient matrix.
1 --: Use a diagonal film coefficient matrix (default).
2 --: Use a consistent film coefficient matrix.

Note: If THOPT,QUASI has been issued, the only valid choice for KEYOP(11) is 0.

KEYOPT(15)

Specific heat matrix:

0 --: Program determines whether to use a diagonal or consistent specific heat matrix (default). For details on default behavior, see Assumptions and Restrictions.
1 --: Use a diagonal specific heat matrix.
2 --: Use a consistent specific heat matrix.

KEYOPT(16)

Evaluation of material properties:

0 --: Evaluate material properties at centroid (default).
1 --: Evaluate material properties at each integration point.

Note: If THOPT,QUASI has been issued, KEYOPT(16) is ignored and material properties are evaluated at the centroid.

PLANE292 Output Data

The solution output associated with the element is in two forms:

Nodal temperatures included in the overall nodal solution
Additional element output as shown in Table 292.1: PLANE292 Element Output Definitions

For an axisymmetric analysis the face area and the heat flow rate are on a full 360° basis. Convection heat flux is positive out of the element; applied heat flux is positive into the element. The element output directions are parallel to the element coordinate system. A general description of solution output is given in Solution Output and of postprocessing data in Degenerated Shape Elements. See the Basic Analysis Guide for ways to view results.

The Element Output Definitions table uses the following notation:

A colon (:) in the Name column indicates that the item can be accessed by the Component Name method (ETABLE, ESOL). The O column indicates the availability of the items in the file jobname.out. The R column indicates the availability of the items in the results file.

In either the O or R columns, “Y” indicates that the item is always available, a letter or number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.

Table 292.1: PLANE292 Element Output Definitions

Name	Definition	O	R
EL	Element Number	Y	Y
NODES	Nodes - I, J, K, L	Y	Y
MAT	Material number	Y	Y
VOLU:	Volume	Y	Y
XC, YC	Location where results are reported	Y	2
HGEN	Heat generations HG(I), HG(J), HG(K), HG(L)	Y	-
TG:X, Y, SUM	Thermal gradient components and vector sum at centroid	Y	Y
TF:X, Y, SUM	Thermal flux (heat flow rate/cross-sectional area) components and vector sum at centroid	Y	Y
FACE	Face label	1	-
AREA	Face area	1	1
NODES	Face nodes	1	1
HFILM	Film coefficient at each node of face	1	-
TBULK	Bulk temperature at each node of face	1	-
TAVG	Average face temperature	1	1
HEAT RATE	Heat flow rate across face by convection	1	1
HFAVG	Average film coefficient of the face	-	1
TBAVG	Average face bulk temperature	-	1
HFLXAVG	Heat flow rate per unit area across face caused by input heat flux	-	1
HEAT RATE/AREA	Heat flow rate per unit area across face by convection	1	-
HFLUX	Heat flux at each node of face	1	-

If a surface load is input
Available only at centroid as a *GET item.

Table 292.2: PLANE292 Item and Sequence Numbers lists output available through the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table of this reference for more information. The following notation is used in Table 292.2: PLANE292 Item and Sequence Numbers:

Name: output quantity as defined in the Table 292.1: PLANE292 Element Output Definitions
Item: predetermined Item label for ETABLE command
FCn: sequence number for solution items for element Face n

Table 292.2: PLANE292 Item and Sequence Numbers

Output Quantity Name	ETABLE and ESOL Command Input
Output Quantity Name	Item	FC1	FC2	FC3	FC4
AREA	NMISC	1	7	13	19
HFAVG	NMISC	2	8	14	20
TAVG	NMISC	3	9	15	21
TBAVG	NMISC	4	10	16	22
HEAT RATE	NMISC	5	11	17	23
HFLXAVG	NMISC	6	12	18	24

PLANE292 Assumptions and Restrictions

The element must not have a negative or a zero area.
The element must lie in an X-Y plane as shown in Figure 292.1: PLANE292 Geometry and the Y-axis must be the axis of symmetry for axisymmetric analyses. An axisymmetric structure should be modeled in the +X quadrants.
A triangular element may be formed by defining duplicate K and L node numbers as described in Degenerated Shape Elements.
Because the element is linear, the heat flux distribution is piecewise constant and, hence, the accuracy is low if the mesh is too coarse. This becomes more pronounced for axisymmetric elements (KEYOPT(3) =1) in which radial variation of heat flux is expected. To obtain a more accurate heat flux, increase the mesh density.
If the thermal element is to be replaced by a PLANE182 structural element with surface stresses requested, the thermal element should be oriented with face IJ or face KL as a free surface. A free surface of the element (that is, not adjacent to another element and not subjected to a boundary constraint) is assumed to be adiabatic.
Thermal transients having a fine integration time step and a severe thermal gradient at the surface will also require a fine mesh at the surface.
If enthalpy is defined, density and specific heat will be ignored.

The default for KEYOPT(15) depends on whether or not mass transport is included in the analysis:

If mass transport is not included in the analysis (KEYOPT (8) = 0), the default is to use a diagonal specific heat matrix.

If mass transport is included in the analysis (KEYOPT (8) = 1 or 2), the default is to use a consistent specific heat matrix.

PLANE292 Product Restrictions

When used in the product(s) listed below, the stated product-specific restrictions apply to this element in addition to the general assumptions and restrictions given in the previous section.

Ansys Mechanical Pro —

Birth and death is not available.