Thermal-Electric Shell
SHELL157 Element Description
SHELL157 is a 3-D element having in-plane thermal and electrical conduction capability. The element has four nodes with two degrees of freedom, temperature and voltage, at each node. The element applies to a 3-D, steady-state or transient thermal analysis, although the element includes no transient electrical capacitance or inductance effects. The element requires an iterative solution to include the Joule heating effect in the thermal solution. See SHELL157 in the Mechanical APDL Theory Reference for more details about this element. If no electrical effects are present, the 3-D thermal shell (SHELL131) may be used.
If the model containing the thermal-electrical element is also to be analyzed structurally, replace the element with an equivalent structural element (such as SHELL181). If both in-plane and transverse thermal-electric conduction are needed, use a thermal-electric solid element (SOLID226 with KEYOPT(1) = 110).
SHELL157 Input Data
The geometry, node locations, and coordinate systems for this element are shown in Figure 157.1: SHELL157 Geometry. The element is defined by four nodes, four thicknesses, a material direction angle, and the orthotropic material properties.
The element may have variable thickness. The thickness is assumed to vary smoothly over the area of the element, with the thickness input at the four nodes. If the element has a constant thickness, you need to specify only TK(I). If the thickness is not constant, you must specify all four thicknesses.
Orthotropic material directions correspond to the element coordinate directions. The element coordinate system orientation is as described in Coordinate Systems. The element x-axis may be rotated by an angle THETA (in degrees). You can assign the specific heat and density any values for steady-state solutions. The electrical material property, RSV_, is the resistivity of the material. You can specify the resistivity, like any other material property, as a function of temperature. Properties not specified default as described in the Material Reference.
Specify the word VOLT for the Lab variable on the D command and the voltage input for the value. Specify the word AMPS for the Lab variable on the F command and the current into the node input for the value.
Element loads are described in Nodal Loading. Convection or heat flux (but not both) and radiation may be specified as surface loads at the element faces as shown by the circled numbers on Figure 157.1: SHELL157 Geometry. Because shell edge convection and flux loads are input on a per-unit-length basis, per-unit-area quantities must be multiplied by the shell thickness.
Heat generation rates may be specified 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). This rate is in addition to the Joule heat generated by the current flow.
"SHELL157 Input Summary" summarizes the element input. A general description of element input appears in Element Input.
SHELL157 Input Summary
- Nodes
I, J, K, L
- Degrees of Freedom
TEMP, VOLT
- Real Constants
TK(I) - Shell thickness at node I TK(J) - Shell thickness at node J; defaults to TK(I) TK(K) - Shell thickness at node K; defaults to TK(I) TK(L) - Shell thickness at node L; defaults to TK(I) THETA - Element X-axis rotation - Material Properties
MP command: KXX, KYY, DENS, C, ENTH, RSVX, RSVY
- Surface Loads
- Convection or Heat Flux (but not both) and Radiation (using Lab = RDSF)--
face 1 (I-J-K-L) (bottom, -Z side), face 2 (I-J-K-L) (top, +Z side), face 3 (J-I), face 4 (K-J), face 5 (L-K), face 6 (I-L)
- Body Loads
- Heat Generations --
HG(I), HG(J), HG(K), HG(L)
- Special Features
Birth and death - KEYOPT(2)
Evaluation of 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|
SHELL157 Output Data
The solution output associated with the element is in two forms:
Nodal temperatures and voltages included in the overall nodal solution
Additional element output as shown in Table 157.1: SHELL157 Element Output Definitions
Heat flowing out of the element is considered to be positive. The element output directions are parallel to the element coordinate system. The heat flow and the current flow into the nodes may be printed with the OUTPR command. The Joule heat generated this substep is used in the temperature distribution calculated for the next substep. A general description of solution output is given in Solution Output. See The General Postprocessor (POST1) in 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 157.1: SHELL157 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 |
| AREA | Convection face area | Y | Y |
| XC, YC, ZC | Location where results are reported | Y | 2 |
| 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 |
| EF:X, Y, SUM | Component electric fields and vector sum | Y | Y |
| JS:X, Y | Component current densities | Y | Y |
| JSSUM | Component current density vector sum | Y | - |
| JHEAT: | Joule heat generation per unit volume | Y | Y |
| FACE | Face label | 1 | 1 |
| AREA | Face area | 1 | 1 |
| NODES | Face nodes | 1 | 1 |
| HFILM | Film coefficient | 1 | 1 |
| TAVG | Average face temperature | 1 | 1 |
| TBULK | Fluid bulk temperature | 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 across face caused by input heat flux | - | 1 |
| HEAT RATE/AREA | Heat flow rate/area across face by convection | 1 | - |
| HEAT FLUX | Heat flux at each node of face | 1 | - |
Available only at centroid as a *GET item.
Table 157.2: SHELL157 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 157.2: SHELL157 Item and Sequence Numbers:
- Name
output quantity as defined in the Table 157.1: SHELL157 Element Output Definitions
- Item
predetermined Item label for ETABLE command
SHELL157 Assumptions and Restrictions
The element requires an iterative solution for electrical-thermal coupling.
Zero area elements are not allowed. This occurs most frequently when the elements are not numbered properly. The element must not taper down to a zero thickness at any corner. 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 for melting) within a coarse grid. If a current is specified at the same node that a voltage is specified, the current is ignored. The electrical and the thermal solutions are coupled through an iterative procedure.
No conversion is included between electrical heat units and mechanical heat units. The resistivity may be divided by a conversion factor, such as 3.415 BTU/Hr per watt, to get Joule heat in mechanical units. Current (input and output) should also be converted for consistent units.
This element may not be compatible with other elements with the VOLT degree of freedom. To be compatible, the elements must have the same reaction force (see Element Compatibility in the Low-Frequency Electromagnetic Analysis Guide).