2-D Thermal Surface Effect

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SURF151 Element Description

SURF151 may be used for various load and surface effect applications. It may be overlaid onto a face of any 2-D thermal solid element (except axisymmetric harmonic elements PLANE75 and PLANE78). The element is applicable to 2-D thermal analyses. Various loads and surface effects may exist simultaneously. See SURF151 in the Mechanical APDL Theory Reference for more details about this element.

Figure 151.1:  SURF151 Geometry

SURF151 Geometry

SURF151 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 151.1: SURF151 Geometry. The element is defined by two to five node points and by the material properties. The nodes for this element must share the nodes of the underlying solid element. An extra node (away from the base element) may be used for convection or radiation effects. Two extra nodes (away from the base element) may be used to more accurately capture convection effects.

The mass, volume, and heat generation calculations use the in-plane element thicknesses at nodes I and J (real constants TKI and TKJ, respectively). Thickness TKI defaults to 0.0, and thickness TKJ defaults to TKI. If KEYOPT(3) = 3, the out-of-plane thickness is input as the real constant TKPS (defaults to 1.0). The mass calculation uses the density (material property DENS).

See Nodal Loading for a description of element loads. Convections or heat fluxes may be input as surface loads on the element.

The convection surface conductivity matrix calculation uses the film coefficient (input on the SFE command with KVAL = 0 and CONV as the label). If the extra node option is used, its temperature becomes the bulk temperature. If the extra node is not used, the CONV value input with KVAL = 2 becomes the bulk temperature. The convection surface heat flow vector calculation uses the bulk temperature. On a given face, either a heat flux or a convection may be specified, but not both simultaneously.

For the extra node option (KEYOPT(5) = 1), film effectiveness and free stream temperatures may also be input for convection surface loads (input on the SFE command with the CONV label and KVAL = 3 and 4, respectively). If film effectiveness is input, bulk temperature is ignored.

Setting KEYOPT(7) = 1 multiplies the evaluated film coefficient by the empirical term ITS-TBIn, where TS is the element surface temperature, TB is the fluid bulk temperature, and n is an empirical coefficient (real constant ENN).

Convections and heat fluxes are multiplied by an area to obtain the heat flows. KEYOPT(12) determines whether the current area or the original area is selected for the calculation.

If KEYOPT(5) = 1 and flow information is available from FLUID116 with KEYOPT(2) = 1, the bulk temperature may be adjusted to the adiabatic wall temperature using KEYOPT(6) = 1, real constants OMEG (rotational speed) and NRF (recovery factor), and the logic described in the Mechanical APDL Theory Reference. For this adjustment, the global Y Cartesian coordinate axis is used as the axis of rotation (KEYOPT(3) = 1). When using the OMEG real constant, you can specify either numerical values or table inputs. If specifying table inputs, enclose the table name in % signs (for example, %tabname%). Rotational speed (OMEG) can vary with time and location. Use the *DIM command to dimension the table and identify the variables. For more information and examples on using table inputs, see Array Parameters of the ANSYS Parametric Design Language Guide, Applying Loads Using TABLE Type Array Parameters in the Basic Analysis Guide and Doing a Thermal Analysis Using Tabular Boundary Conditions in the Thermal Analysis Guide, as well as the description of *DIM in the Command Reference.

A film coefficient specified by the SFE command may be modified by activating the user subroutine USERCV with the USRCAL command. USERCV may be used to modify the film coefficient of a surface element with or without an extra node. It may be used if the film coefficient is a function of temperature and/or location.

If the surface element has an extra node (KEYOPT(5) = 1), the bulk temperature and/or the film coefficient may be redefined in a general way by user programmable routine USRSURF116. USRSURF116 may be used if the bulk temperature and/or the film coefficient is a function of fluid properties, velocity and/or wall temperature. If a bulk temperature is determined by USRSURF116, it overrides any value specified by SFE or according to KEYOPT(6). Also, if a film coefficient is determined by USRSURF116, it overrides any values specified by SFE or USRCAL, USERCV. USRSURF116 calculation are activated by modifying the USRSURF116 subroutine and creating a customized version of ANSYS; there will be no change in functionality without modifying USRSURF116. For more information, see User-Programmable Features (UPFs) in the Mechanical APDL Advanced Analysis Guide.

Heat generation rates are input on a per unit volume basis and may be input as an element body load at the nodes, using the BFE command. Element body loads are not applied to other elements connected at the same nodes. The node I heat generation HG(I) defaults to zero. The node J heat generation defaults to HG(I). The heat generation load vector calculation uses the heat generation rate values.

As an alternative to using the BFE command, you can specify heat generation rates directly at the nodes using the BF command. For more information on body loads, see Body Loads in the Basic Analysis Guide.

SURF151 allows for radiation between the surface and the extra node. The emissivity of the surface (input as material property EMIS for the material number of the element) is used for the radiation surface conductivity matrix. The form factor FORMF and the Stefan-Boltzmann constant SBCONST are also used for the radiation surface conductivity matrix. The form factor can be either input as a real constant (defaults to 1) using KEYOPT(9) = 1 or it can be calculated automatically as a cosine effect using KEYOPT(9) = 2 or 3. For information on how the cosine effect depends on basic element orientation and the extra node location, see the Mechanical APDL Theory Reference. There is no distance effect included in the cosine effect. For axisymmetric analyses, the automatic form factor calculation is used only with the extra node on the Y-axis. The Stefan-Boltzmann constant defaults to 0.119x10-10 (Btu/hr*in2* °R4).

When KEYOPT(4) = 0, an edge with a removed midside node implies that the temperature varies linearly, rather than parabolically, along that edge. See Quadratic Elements (Midside Nodes) in the Modeling and Meshing Guide for more information about the use of midside nodes.

If a single PLANE element lies beneath SURF151, you can automatically set the element behavior (plane stress, axisymmetric, or plane stress with thickness [including TKPS if applicable]) to that of the underlying solid element using KEYOPT(3) =10. This option is valid only when a single PLANE element lies beneath the SURF element. For example, if you apply a SURF151 element over a PLANE77 (thermal) element whose nodes are also used in the definition of a PLANE183 (structural) element, a warning appears and the load is not applied to the element.

A summary of the element input is given in "SURF151 Input Summary". A general description of element input is given in Element Input. For axisymmetric applications see Harmonic Axisymmetric Elements.

SURF151 Input Summary

I, J if KEYOPT (4) = 1, and KEYOPT (5) = 0
I, J, K if KEYOPT (4) = 1, and KEYOPT(5) = 1
I, J, K, L if KEYOPT (4) = 1, and KEYOPT(5) = 2
I, J, K if KEYOPT (4) = 0, and KEYOPT(5) = 0
I, J, K, L if KEYOPT (4) = 0, and KEYOPT(5) = 1
I, J, K, L, M if KEYOPT (4) = 0, and KEYOPT(5) = 2
Degrees of Freedom


Real Constants
TKI, TKJ, (Blank), (Blank), (Blank), TKPS,
See Table 151.1: SURF151 Real Constants for a description of the real constants
Material Properties
MP command: DENS (density), EMIS (emissivity) if KEYOPT(9) > 0)
Surface Loads
Convections -- 

face 1 (I-J) if KEYOPT(8) > 1

Heat Fluxes -- 

face 1 (I-J) if KEYOPT(8) = 1

Body Loads
Heat Generation -- 

HG(I), HG(J); also HG(K) if KEYOPT(4) = 0

Special Features

Birth and death


Adiabatic wall temperature option:

0, 1, 2 -- 

See Adiabatic Wall Temperature as Bulk Temperature for information on these options.


Recovery factor (FR) option:

0, 1, or 2 -- 

See Adiabatic Wall Temperature as Bulk Temperature for information on these options.


Element behavior:

0 -- 


1 -- 


3 -- 

Plane with thickness input (TKPS)

10 -- 

Use the element behavior--plane, axisymmetric, or plane with thickness input (including TKPS if applicable)--of the underlying solid element.


Midside nodes:

0 -- 

Has midside node

1 -- 

No midside node


Extra node for radiation and/or convection calculations:

0 -- 

No extra nodes

1 -- 

Has extra node (optional if KEYOPT(8) > 1; required if KEYOPT(9) > 0)

2 -- 

Two extra nodes (optional if KEYOPT (8) > 1). Valid only for convection calculations using FLUID116. Use this option if the bulk temperature is unknown. The extra nodes get bulk temperatures from the two nodes of a FLUID116 element. This is generally more accurate than the one extra node option.

KEYOPT(6) (used only if KEYOPT(5) = 1 and KEYOPT(8) > 1)

Use of bulk temperatures:

0 -- 

Extra node temperature used as bulk temperature

1 -- 

Adiabatic wall temperature used as bulk temperature


Empirical term:

0 -- 

Do not multiply film coefficient by empirical term.

1 -- 

Multiply film coefficient by empirical term |TS-TB|n.


Heat flux and convection loads:

0 -- 

Ignore heat flux and convection surface loads (if any)

1 -- 

Include heat flux, ignore convection

Use the following to include convection (ignore heat flux):

2 -- 

Evaluate film coefficient hf (if any) at average film temperature, (TS +TB)/2

3 -- 

Evaluate hf at element surface temperature, TS

4 -- 

Evaluate hf at fluid bulk temperature, TB

5 -- 

Evaluate hf at differential temperature, | TS - TB |


Radiation form factor calculation:

0 -- 

Do not include radiation

1 -- 

Use radiation with the form factor real constant

2 -- 

Use radiation with cosine effect computed as an absolute value (ignore real constant)

3 -- 

Use radiation with cosine effect computed as zero if negative (ignore real constant)


Area to use for the heat-flow calculation:

0 -- 

Current area (default)

1 -- 

Original area


Film coefficient matrix key:

0 -- 

Program determines whether to use diagonal or consistent film coefficient matrix (default).

1 -- 

Use a diagonal film coefficient matrix.

2 -- 

Use a consistent matrix for the film coefficient.

Table 151.1:  SURF151 Real Constants

1FORMFForm factor
2SBCONTStefan-Boltzmann constant
4OMEGAAngular velocity
5NRFRecovery factor
6VABSAbsolute value of fluid velocity (KEYOPT(1) = 0)
7TKIIn-plane thickness at node I
8TKJIn-plane thickness at node J (defaults to TKI)
12TKPSOut-of-plane thickness (if KEYOPT(3) = 3)
13ENNEmpirical coefficient
14GCGravitational constant used for units consistency
15JCJoule constant used to convert work units to heat units

SURF151 Output Data

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

Convection heat flux is positive out of the element; applied heat flux is positive into the element. A general description of solution output is given in Solution Output. 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 number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.

Table 151.2:  SURF151 Element Output Definitions

ELElement NumberYY
EXTRA NODEExtra node (if present)YY
MATMaterial numberYY
AREASurface areaYY
XC, YCLocation where results are reportedY7
VN(X, Y)Components of unit vector normal to center of element-Y
MASSMass of Element-1
HGENHeat generations HG(I), HG(J), HG(K)2-
HEAT GEN. RATEHeat generation rate over entire element (HGTOT)22
HFLUXInput heat flux at nodes I, J3-
HEAT FLOW RATEInput heat flux heat flow rate over element surface area (HFCTOT)33
HFILMFilm coefficient at each face node44
TBULKBulk temperature at each face node or temperature of extra node44
TAVGAverage surface temperature44
TAWAdiabatic wall temperature55
RELVELRelative velocity55
SPHTFLSpecific heat of the fluid55
RECFACRecovery factor55
CONV. HEAT RATEConvection heat flow rate over element surface area (HFCTOT)44
CONV. HEAT RATE/AREAAverage convection heat flow rate per unit area4-
EMISSURAverage emissivity of surface (for element material number)66
EMISEXTEmissivity of extra node66
TEMPSURAverage temperature of surface66
TEMPEXTTemperature of extra node66
FORM FACTORAverage form factor of element66
RAD. HEAT RATERadiation heat flow rate over entire element (HRTOT)66
RAD. HEAT RATE/AREAAverage radiation heat flow rate per unit area6-

  1. If dens > 0

  2. If heat generation load is present

  3. If KEYOPT(8) = 1

  4. If KEYOPT(8) > 1

  5. If KEYOPT(6) = 1 and KEYOPT(8) > 1

  6. If KEYOPT(9) > 0

  7. Available only at centroid as a *GET item.

Table 151.3: SURF151 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 in this reference for more information. The following notation is used in Table 151.3: SURF151 Item and Sequence Numbers:


output quantity as defined in Table 151.2: SURF151 Element Output Definitions


predetermined Item label for ETABLE command


sequence number for single-valued or constant element data


sequence number for data at nodes I and J

Table 151.3:  SURF151 Item and Sequence Numbers

Output Quantity NameETABLE and ESOL Command Input

SURF151 Assumptions and Restrictions

  • The element must not have a zero length.

  • If KEYOPT(9) > 0 (radiation is used):

    • element is nonlinear and requires an iterative solution

    • extra node must be present.

    • if KEYOPT(4) = 0, midside nodes may not be dropped.

  • If real constants TKI, TKJ (in-plane thicknesses), and TKPS (out-of-plane thickness) are defined for the element, the element volume is greater than zero. If BF, BFE, or BFUNIF commands are issued under this circumstance, heat generation loads are activated. However, the damping matrix is not activated even though the element volume is greater than zero.

SURF151 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.

ANSYS Mechanical Premium 

  • Birth and death is not available.

Release 18.2 - © ANSYS, Inc. All rights reserved.