2-D Thermal Solid

Compatible Products: – | Pro | Premium | Enterprise | Ent PP | Ent Solver | –

PLANE55 Element Description

PLANE55 can be used as a plane element or as an axisymmetric ring element with a 2-D thermal conduction capability. The element has four nodes with a single degree of freedom, temperature, at each node.

The element is applicable to a 2-D, steady-state or transient thermal analysis. The element can also compensate for mass transport heat flow from a constant velocity field. 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).

A similar element with midside node capability is PLANE77. A similar axisymmetric element which accepts nonaxisymmetric loading is PLANE75.

An option exists that allows the element to model nonlinear steady-state fluid flow through a porous medium. With this option the thermal parameters are interpreted as analogous fluid flow parameters. See PLANE55 in the Mechanical APDL Theory Reference for more details about this element.

Figure 55.1:  PLANE55 Geometry

PLANE55 Geometry

PLANE55 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 55.1: PLANE55 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 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 55.1: PLANE55 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).

A mass transport option is available with KEYOPT(8). With this option the velocities VX and VY must be input as real constants (in the element coordinate system). Also, temperatures should be specified along the entire inlet boundary to assure a stable solution. With mass transport, you should use specific heat (C) and density (DENS) material properties instead of enthalpy (ENTH).

The nonlinear porous flow option is selected with KEYOPT(9) = 1. For this option, temperature is interpreted as pressure and the absolute permeabilities of the medium are input as material properties KXX and KYY. Properties DENS and VISC are used for the mass density and viscosity of the fluid. See the Mechanical APDL Theory Reference for a description of the properties C and MU, which are used in calculating the coefficients of permeability, with reference to the Z terms ignored. Temperature boundary conditions input with the D command are interpreted as pressure boundary conditions, and heat flow boundary conditions input with the F command are interpreted as mass flow rate (mass/time).

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 "PLANE55 Input Summary". A general description of element input is given in Element Input. For axisymmetric applications see Harmonic Axisymmetric Elements.

PLANE55 Input Summary


I, J, K, L

Degrees of Freedom


Real Constants


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

VX = Mass transport velocity in X (used only if KEYOPT(8) > 0)

VY = Mass transport velocity in Y (used only if KEYOPT(8) > 0)

Material Properties

MP command: KXX, KYY, DENS, C, ENTH, VISC, MU (VISC and MU used only if KEYOPT (9) = 1.

Do not use ENTH with KEYOPT(8) = 1 or 2.

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)

Special Features

Birth and death


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|


Element behavior:

0 -- 


1 -- 


3 -- 

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


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.


Mass transport effects:

0 -- 

No mass transport effects

1 -- 

Mass transport with VX and VY

2 -- 

Same as 1 but also print mass transport heat flow


Nonlinear fluid flow option:

0 -- 

Standard heat transfer element

1 -- 

Nonlinear steady-state fluid flow analogy element (temperature degree of freedom interpreted as pressure)

PLANE55 Output Data

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

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. If KEYOPT(9) = 1, the standard thermal output should be interpreted as the analogous fluid flow output. 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 number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.

Table 55.1:  PLANE55 Element Output Definitions

ELElement NumberYY
NODESNodes - I, J, K, LYY
MATMaterial numberYY
XC, YCLocation where results are reportedY 4
HGENHeat generations HG(I), HG(J), HG(K), HG(L)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 label 1 -
AREAFace area 1 1
NODESFace nodes 1 1
HFILMFilm coefficient at each node of face 1 -
TBULKBulk temperature at each node of face 1 -
TAVGAverage face temperature 1 1
HEAT RATEHeat flow rate across face by convection 1 1
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
HEAT RATE/AREAHeat flow rate per unit area across face by convection 1 -
HFLUXHeat flux at each node of face 1 -
HEAT FLOW BY MASS TRANSPORTHeat flow rate across face by mass transport 2 -
PRESSURE GRADTotal pressure gradient and its X and Y components 3 -
MASS FLUXMass flow rate per unit cross-sectional area 3 -
FLUID VELOCITYTotal fluid velocity and its X and Y components 3 -

  1. If a surface load is input

  2. If KEYOPT(8) = 2

  3. If KEYOPT(9) = 1

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

Table 55.2: PLANE55 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 55.2: PLANE55 Item and Sequence Numbers:


output quantity as defined in the Table 55.1: PLANE55 Element Output Definitions


predetermined Item label for ETABLE command


sequence number for solution items for element Face n

Table 55.2:  PLANE55 Item and Sequence Numbers

Output Quantity Name ETABLE and ESOL Command Input

PLANE55 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 55.1: PLANE55 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.

  • 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.

  • 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 KEYOPT(8) > 0, unsymmetric matrices are produced.

  • When mass flow is activated (KEYOPT(8) = 1 or 2), the element Peclet number should be less than 1:

    Where L is an element length scale based on the flow direction and element geometry. See PLANE55 in the Mechanical APDL Theory Reference for more details.

PLANE55 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 

  • This element does not have the mass transport or fluid flow options. KEYOPT(8) and KEYOPT(9) default to 0 and cannot be changed.

  • Birth and death is not available.

ANSYS Mechanical Premium 

  • This element does not have the mass transport or fluid flow options. KEYOPT(8) and KEYOPT(9) default to 0 and cannot be changed.

  • Birth and death is not available.

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