3-D 10-Node Tetrahedral Thermal Solid

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SOLID87 Element Description

SOLID87 is well suited to model irregular meshes (such as produced from various CAD/CAM systems). The element has one degree of freedom, temperature, at each node.

The element is applicable to a 3-D, steady-state or transient thermal analysis. See SOLID87 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 the equivalent structural element (such as SOLID187). A 20-node thermal solid element, SOLID90, is also available.

Figure 87.1:  SOLID87 Geometry

SOLID87 Geometry

SOLID87 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 87.1: SOLID87 Geometry.

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 87.1: SOLID87 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.

For phase change problems, use KEYOPT(1) = 1 (diagonalized specific heat matrix). For convection regions with strong thermal gradients, use KEYOPT(5) = 1 (consistent convection matrix).

A summary of the element input is given in "SOLID87 Input Summary". A general description of element input is given in Element Input.

SOLID87 Input Summary


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

Degrees of Freedom


Real Constants


Material Properties

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

Surface Loads
Convection or Heat Flux (but not both) and Radiation (using Lab = RDSF) -- 

face 1 (J-I-K), face 2 (I-J-L), face 3 (J-K-L), face 4 (K-I-L)

Body Loads
Heat Generations -- 

HG(I), HG(J), HG(K), HG(L), HG(M), HG(N), HG(O), HG(P), HG(Q), HG(R)

Special Features

Birth and death


Specific heat matrix:

0 -- 

Consistent specific heat matrix

1 -- 

Diagonalized specific heat matrix


Surface convection matrix:

0 -- 

Diagonalized convection matrix

1 -- 

Consistent convection matrix

SOLID87 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. The element output directions are parallel to the element coordinate system. 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 87.1:  SOLID87 Element Output Definitions

ELElement NumberYY
NODESNodes - I, J, K, L, M, N, O, P, Q, RYY
MATMaterial numberYY
XC, YC, ZCLocation where results are reportedY2
HGENHeat generations HG(I), HG(J), HG(K), HG(L), HG(M), HG(N), HG(O), HG(P), HG(Q), HG(R)Y-
TG:X, Y, Z, SUMThermal gradient components and vector sum at centroidYY
TF:X, Y, Z, SUMThermal flux (heat flow rate/cross-sectional area) components and vector sum at centroidYY
FACEConvection face label1-
NODESConvection face corner nodes1-
AREAConvection face 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 if a surface load is input

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

Table 87.2: SOLID87 Item and Sequence Numbers lists output available through the ETABLE command using the Sequence Number method. See Creating an Element Table 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 87.2: SOLID87 Item and Sequence Numbers:


output quantity as defined in the Table 87.1: SOLID87 Element Output Definitions


predetermined Item label for ETABLE command


sequence number for solution items for element Face n

Table 87.2:  SOLID87 Item and Sequence Numbers

Output Quantity NameETABLE and ESOL Command Input

SOLID87 Assumptions and Restrictions

  • The element must not have a zero volume.

  • Elements may be numbered either as shown in Figure 87.1: SOLID87 Geometry or may have node L below the IJK plane.

  • 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.

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

  • A free surface of the element (i.e., not adjacent to another element and not subjected to a boundary constraint) is assumed to be adiabatic.

SOLID87 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 

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ANSYS Mechanical Premium 

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