4.55 PLANE55 2-D Thermal Solid

4.55 PLANE55 2-D Thermal Solid (UP19980821 ) PLANE55 can be used as a plane element or as an axisymmetric ring element with a two-dimensional thermal conduction capability. The element has four nodes with a single degree of freedom, temperature, at each node.

The element is applicable to a two-dimensional, 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 PLANE42). A similar element, with mid-side node capability (PLANE77), is described in Section 4.77. A similar axisymmetric element which accepts nonaxisymmetric loading (PLANE75) is described in Section 4.75.

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 Section 14.55 of the ANSYS Theory Reference for more details about this element.

Figure 4.55-1 PLANE55 2-D Thermal Solid



4.55.1 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 4.55-1. 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 Section 2.3. Specific heat and density are ignored for steady-state solutions. Properties not input default as described in Section 2.4.

Element loads are described in Section 2.7. Convections or heat fluxes (but not both) may be input as surface loads at the element faces as shown by the circled numbers on Figure 4.55-1.

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 Section 14.70 of the ANSYS 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).

A summary of the element input is given in Table 4.55-1. A general description of element input is given in Section 2.1.

Table 4.55-1 PLANE55 Input Summary

Element Name

PLANE55

Nodes

I, J, K, L

Degrees of Freedom

TEMP

Real Constants

VX, VY if KEYOPT (8) > 0

Material Properties

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

Convections:
face 1 (J-I), face 2 (K-J), face 3 (L-K), face 4 (I-L)
Heat Fluxes:
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

KEYOPT(1)

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)

0 - Plane
1 - Axisymmetric

KEYOPT(4)

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)

0 - No mass transport effects
1 - Mass transport with VX and VY
2 - Same as 1 but also print mass transport heat flow

KEYOPT(9)

0 - Standard heat transfer element
1 - Nonlinear steady-state fluid flow analogy element (temperature degree of freedom interpreted as pressure)

4.55.2 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. Heat flowing out of the element is considered to be positive. 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 Section 2.2 and of postprocessing data in Section 2.8. See the ANSYS Basic Analysis Procedures Guide for ways to view results.

The following notation is used in Table 4.55-2:

A colon (:) in the Name column indicates the item can be accessed by the Component Name method [ETABLE, ESOL] (see Section 2.2.2). The O and R columns indicate the availability of the items in the file Jobname.OUT (O) or in the results file (R), a Y indicates that the item is always available, a number refers to a table footnote which describes when the item is conditionally available, and a - indicates that the item is not available.

Table 4.55-2 PLANE55 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
CENT: X, Y

Center location XC, YC, ZC

- Y
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 -
HEAT FLOW BY MASS TRANSPORT

Heat flow rate across face by mass transport

2 -
PRESSURE GRAD

Total pressure gradient and its X and Y components

3 -
MASS FLUX

Mass flow rate per unit cross-sectional area

3 -
FLUID VELOCITY

Total 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

Table 4.55-3 lists output available through the ETABLE command using the Sequence Number method. See Chapter 5 of the ANSYS Basic Analysis Procedures Guide and Section 2.2.2.2 of this manual for more information. The following notation is used in Table 4.55-3:

Table 4.55-3 PLANE55 Item and Sequence Numbers for the ETABLE and ESOL Commands

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

4.55.3 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 4.55-1 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 Section 2.8. 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.

If the thermal element is to be replaced by a PLANE42 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 (i.e., 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.

4.55.4 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/Thermal