2-D 8-Node Thermal Solid

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PLANE77 Element Description

PLANE77 is a higher order version of the 2-D, 4-node thermal element (PLANE55). The element has one degree of freedom, temperature, at each node. The 8-node elements have compatible temperature shapes and are well suited to model curved boundaries.

The 8-node thermal element is applicable to a 2-D, steady-state or transient thermal analysis. See PLANE77 in the Mechanical APDL Theory Reference for more details about this element. If the model containing this element is also to be analyzed structurally, the element should be replaced by an equivalent structural element (such as PLANE183). A similar axisymmetric thermal element which accepts nonaxisymmetric loading is PLANE78.

Figure 77.1:  PLANE77 Geometry

PLANE77 Geometry

PLANE77 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 77.1: PLANE77 Geometry. The element is defined by eight nodes and orthotropic material properties. A triangular-shaped element may be formed by defining the same node number for nodes K, L and O.

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 Nodal 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 77.1: PLANE77 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). If all corner node heat generation rates are specified, each midside node heat generation rate defaults to the average heat generation rate of its adjacent corner nodes.

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 summary of the element input is given in "PLANE77 Input Summary". A general description of element input is given in Element Input. For axisymmetric applications see Harmonic Axisymmetric Elements.

PLANE77 Input Summary


I, J, K, L, M, N, O, P

Degrees of Freedom


Real Constants


THK = Thickness (used only if KEYOPT(3) = 3)

Material Properties

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), HG(M), HG(N), HG(O), HG(P)

Special Features

Birth and death


Specific heat matrix:

0 -- 

Consistent specific heat matrix

1 -- 

Diagonalized specific heat matrix


Element behavior:

0 -- 


1 -- 


3 -- 

Plane with Z-depth, specified via real constant THK.

PLANE77 Output Data

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

The element output directions are parallel to the element coordinate system. 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. 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 77.1:  PLANE77 Element Output Definitions

ELElement NumberYY
NODESNodes - I, J, K, L, M, N, O, PYY
MATMaterial numberYY
XC, YCLocation where results are reportedY2
HGENHeat generations HG(I), HG(J), HG(K), HG(L), HG(M), HG(N), HG(O), HG(P)Y-
TG:X, Y, SUMThermal gradient components and vector sum at centroidYY
TF:X, Y, SUMThermal flux (heat flow rate/cross-sectional area) components and vector sum at centroidYY
FACEFace label1-
NODESFace nodes1-
AREAFace area11
HFILMFilm coefficient1-
TAVGAverage face temperature11
TBULKFluid bulk temperature1-
HEAT RATEHeat flow rate across face by convection11
HEAT RATE/AREAHeat flow rate per unit area across face by convection1-
HFAVGAverage film coefficient of the face-1
TBAVGAverage face bulk temperature-1
HFLXAVGHeat flow rate per unit area across face caused by input heat flux-1
HFLUXHeat flux at each node of face1-

  1. Output only if a surface load is input

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

Table 77.2: PLANE77 Item and Component Labels 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 77.2: PLANE77 Item and Component Labels:


output quantity as defined in the Table 77.1: PLANE77 Element Output Definitions


predetermined Item label for ETABLE command


sequence number for solution items for element Face n

Table 77.2:  PLANE77 Item and Component Labels

Output Quantity NameETABLE and ESOL Command Input

PLANE77 Assumptions and Restrictions

  • The area of the element must be positive.

  • The 2-D element must lie in an X-Y plane as shown in Figure 77.1: PLANE77 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 face with a removed midside node implies that the temperature varies linearly, rather than parabolically, along that face. See Quadratic Elements (Midside Nodes) in the Modeling and Meshing Guide for more information about the use of midside nodes.

  • The specific heat and enthalpy are evaluated at each integration point to allow for abrupt changes (such as melting) within a coarse grid.

  • If the thermal element is to be replaced by a PLANE183 structural element with surface stresses requested, the thermal element may be oriented such that face IJ and/or face KL is 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 require a fine mesh at the surface.

PLANE77 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.

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