VM321
VM321
Steady-State Radiation Between a Fixed Plate and a Moving Plate
Overview
| Reference: | Lienhard IV, John H. & Lienhard V, John H. (2008). A heat transfer textbook, (3rd ed.). Phlogiston Press. |
| Analysis Type(s): | Steady-State Thermal (ANTYPE = 0) |
| Element Type(s): |
2D 4-Node Coupled-Field Solid (PLANE222) 2D Radiosity Surface (SURF251) |
| Input Listing: |
vm321.dat VM321 requires a supplemental .cdb input file which is too long to include full input listings. This file must be downloaded and placed in your working directory for the test case to run properly. Additionally, the geometry and mesh should be regenerated. Download link: MAPDL Test Case Files for 2024 R2 vm321.cdb |
Test Case
Two plates of height H and thickness t are at an initial distance X from each other. Plate 1 is fixed, and plate 2 is moved in the positive X direction and given a displacement of D. Plate 1 is also maintained at a constant temperature of T1. Radiation is specified on the surfaces of plates 1 and 2 that see each other. Each surface is given an emissivity of 1. The space node associated with this enclosure is kept at a temperature of Tinf. A constraint is applied on all nodes of plate 2 to maintain a constant temperature across the body. Determine the temperature of plate 2 and the flux emanating from plate 1. The analytical solution for the temperature of plate 2, flux emanating from plate 1 and heat lost by the enclosure is given below:
 | (321–1) |
 | (321–2) |
 | (321–3) |
where
 is the view factor (proportion of radiation that leaves surface  that strikes surface  ). |
 is the net heat flux emanating from surface 1. |
 is the area of the radiating surface of plate 1. |
| Geometric Properties | Loading |
|---|---|
|
Height H = 10 m Thickness t = 1 m |
Temperature T1 = 1000°C Displacement D = 10 m |
Analysis Assumptions and Modeling Notes
Two plates are modeled using PLANE222 with thermal and structural degrees of freedom (KEYOPT(1) = 11). KEYOPT(1) = 1 is specified for the SURF251 elements generated after the RSURF command to enable view factor updates. This must be specified in conjunction with the VFUP command to set the required frequency of view factor updates. A steady-state thermal analysis determines the temperature variation of plate 2, which is then compared with the analytical solution.
Results Comparison
| Temperature of Plate 2 | |||
|---|---|---|---|
| Distance D (m) | Target (°C) | Mechanical APDL (°C) | Ratio |
| 6 | 858.95 | 858.95 | 1.00 |
| 7 | 840.71 | 840.71 | 1.00 |
| 8 | 823.89 | 823.89 | 1.00 |
| 9 | 808.41 | 808.41 | 1.00 |
| 10 | 794.16 | 794.15 | 1.00 |
| 11 | 781.03 | 781.03 | 1.00 |
| 12 | 768.93 | 768.93 | 1.00 |
| 13 | 757.75 | 757.75 | 1.00 |
| 14 | 747.42 | 747.42 | 1.00 |
| 15 | 737.84 | 737.84 | 1.00 |
| Heat flux from Plate 1 | |||
|---|---|---|---|
| Distance D (m) | Target (W/m2) | Mechanical APDL (W/m2) | Ratio |
| 6 | 87412.86 | 87412.86 | 1.00 |
| 7 | 93779.98 | 93779.98 | 1.00 |
| 8 | 98936.78 | 98936.79 | 1.00 |
| 9 | 103137.75 | 103137.75 | 1.00 |
| 10 | 106582.50 | 106582.54 | 1.02 |
| 11 | 109426.84 | 109426.84 | 1.00 |
| 12 | 111792.15 | 111792.15 | 1.00 |
| 13 | 113773.10 | 113773.10 | 1.00 |
| 14 | 115443.72 | 115443.72 | 1.00 |
| 15 | 116862.12 | 116862.12 | 1.00 |
| Heat Balance | |||
|---|---|---|---|
| Distance D (m) | Target (W) | Mechanical APDL (W) | Ratio |
| 6 | 874128.58 | 874128.59 | 1.00 |
| 7 | 937799.81 | 937799.81 | 1.00 |
| 8 | 989367.85 | 989367.86 | 1.00 |
| 9 | 1031377.49 | 1031377.48 | 1.00 |
| 10 | 1065825.00 | 1089300.39 | 0.98 |
| 11 | 1094268.37 | 1094268.38 | 1.00 |
| 12 | 1117921.50 | 1117921.48 | 1.00 |
| 13 | 1137731.01 | 1137731.02 | 1.00 |
| 14 | 1154437.16 | 1154437.16 | 1.00 |
| 15 | 1168621.23 | 1168621.23 | 1.00 |