Steady-State Thermal Analysis Problems
This chapter contains thermal analysis problems and Thermal's results. In a steady-state thermal analysis, Thermal calculates the thermal response of your model to specified heat loads and subject to specified constraints. Thermal also automatically calculates all predefined measures that apply to a model.
This chapter contains the following models:
mvts001: 3D Cooling Fin with Beam Element
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Analysis Type:
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Steady-State Thermal
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Model Type:
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3D
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Comparison:
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ANSYS No. 95
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Reference:
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Kreith, F. Principles of Heat Transfer. 2nd ed. PA: International Textbook Co., 1959.
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Description:
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A cooling fin of square cross-sectional area is surrounded by fluid, with one end maintained at a certain temperature, and the other end insulated. Find the temperature at the insulated tip, B.
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Specifications
Element Type: | beam (1) | |
Units: | Hr Ft Btu  F | |
Dimensions: | length: 0.6666 | |
Beam Properties: | Area: 0.00694 IYY: 0 Shear FY: 0 CY: 0 | J: 0 IZZ: 0 Shear FZ: 0 CZ: 0 |
Material Properties: | Mass Density: 1 Cost Per Unit Mass: 0 Young's Modulus: 0 | Poisson's Ratio: 0 Thermal Expansion: 0 Conductivity: 25 |
Prescribed Temperatures: | Location/Magnitude: | |
therm_constr1 | placed on point A: 100 | |
Convection Conditions: | Location/ Film Coefficient: | Bulk Temperature: |
therm_constr1 | placed on curve A-B: 0.333332 | 0 |
Comparison of Results Data
Theory | ANSYS | Thermal | % Difference | |
|---|---|---|---|---|
Temperature at Tip B (m=tip_temp) | 68.594 | 68.618 | 68.582 | 0.0174% |
Convergence %: 0.0% on Local Temp and Energy Index | Max P: 5 | No. Equations: 5 | ||
mvts002: 2D Plate with Convection
Analysis Type: | Steady-State Thermal |
Model Type: | 2D Plate |
Reference: | NAFEMS, FEBSTA, No. T4 |
Description: | A plate with uniform thickness is insulated on one side and surrounded by fluid on two other sides. The fourth side is maintained at a certain temperature. Find the temperature at point E. |
Specifications
Element Type: | 2D plate (2) | |
Units: | Hr M W C | |
Dimensions: | length: 1.0 width: 0.6 | |
Material Properties: | Mass Density: 0.08 Cost Per Unit Mass: 0 Young's Modulus: 0 | Poisson's Ratio: 0 Thermal Expansion: 0 Conductivity: 52 |
Prescribed Temperatures: | Location/Magnitude: | |
therm_constr1 | placed on curve A-B: 100 | |
Convection Conditions: | Location/ Film Coefficient: | Bulk Temperature: |
therm_constr1 | placed on curves C-D, B-E, C-E: 750 | 0 |
Comparison of Results Data
Theory | Thermal | % Difference | |
|---|---|---|---|
Temperature at Point E (m=pt_e_temp) | 18.3 | 18.15 | 0.81% |
Convergence %: 2.0% on Local Temp and Energy Index | Max P: 9 | No. Equations: 84 | |
mvts003: 2D Axisymmetric Cylinder with Prescribed Flux
Analysis Type: | Steady-State Thermal |
Model Type: | 2D Axisymmetric |
Reference: | NAFEMS, BMTTA(S), No. 15(i) |
Description: | A cylinder has a prescribed heat flux around part of the boundary. The bottom side is maintained at a certain temperature and the top is insulated. Find the temperature at point E. |
Specifications
Element Type: | 2D solid (2) | |
Units: | Hr M W C | |
Dimensions: | inner radius: 0.0 outer radius: 0.1 height: 0.05 | |
Material Properties: | Mass Density: 7850 Cost Per Unit Mass: 0 Young's Modulus: 0 | Poisson's Ratio: 0 Thermal Expansion: 0 Conductivity: 52 |
Prescribed Temperatures: | Location/Magnitude: | |
therm_constr1 | placed on curve A-B: 0 | |
Heat Loads | Location/Magnitude | Distribution | Spatial Variation |
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therm_load1 | placed on curve C-E: 500000 | heat/time per unit area | uniform |
Comparison of Results Data
Theory | Thermal | % Difference | |
Temperature at Target Point E (m=target_pt_temp) | 213.6 | 213.82 | 0.1% |
Convergence %: 0.0% on Local Temp and Energy Index | Max P: 9 | No. Equations: 80 | |
mvts004: 2D Axisymmetric Hollow Cylinder with Central Heat Source
Analysis Type: | Steady-State Thermal |
Model Type: | 2D Axisymmetric |
Reference: | NAFEMS, BMTTA(S), No. 15 (iii) |
Description: | A hollow cylinder has a prescribed heat flux over the central part of the inner surface; the ends are insulated. The top, bottom, and outer surfaces are maintained at a uniform temperature. Find the temperature at point G. |
Specifications
Element Type: | 2D solid (2) | |
Units: | Hr M W C | |
Dimensions: | inner radius: 0.02 outer radius: 0.1 height: 0.14 | |
Material Properties: | Mass Density: 7850 Cost Per Unit Mass: 0 Young's Modulus: 0 | Poisson's Ratio: 0 Thermal Expansion: 0 Conductivity: 52 |
Prescribed Temperatures: | Location/Magnitude: | |
Therm_constr1 | placed on curves A-B, B-C, C-D: 0 | |
Heat Loads | Location/Magnitude | Distribution | Spatial Variation |
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Therm_load1 | placed on curve E-F: 500000 | hear/time per unit area | uniform |
Comparison of Results Data
Theory | Thermal | % Difference | |
Temperature at Target Point G (m=target_pt_temp) | 59.82 | 59.84 | 0.03% |
Convergence %: 0.0% on Local Temp and Energy Index | Max P: 9 | No. Equations: 133 | |
mvts005: 2D Unit Depth Two-Layer Wall Temperatures
Analysis Type: | Steady-State Thermal |
Model Type: | 2D Unit Depth |
Comparison: | ANSYS No. 92 |
Reference: | Kreith, F. Principles of Heat Transfer. 2nd ed. PA: International Textbook Co., 1959. |
Description: | A two-layer wall is surrounded by heated fluid on both the inner and outer surfaces; the ends are insulated. Find the temperatures at the inner and outer surfaces. |
Specifications
Element Type: | 2D solid (2) | |
Units: | Hr Ft Btu F | |
Dimensions: | thickness of layer 1: 0.75 thickness of layer 2: 0.416666 | |
Material Properties: | Mass Density: 1 Cost Per Unit Mass: 0 Young's Modulus: 0 | Poisson's Ratio: 0 Thermal Expansion: 0 Conductivity: • layer 1 (K1): 0.8 • layer 2 (K2): 0.1 |
Convection Conditions: | Location/Film Coefficient: | Bulk Temperature: |
Therm_constr1 | placed on curve A-B: 12 placed on curve C-D: 2 | 3000 80 |
Comparison of Results Data
Theory | ANSYS | Thermal | % Difference | |
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Temperature at Inner Surface (m=inner_temp_1) | 2957 | 2957.2 | 2957.2 | 0.006% |
Temperature at Outer Surface (m=outer_temp_1) | 336 | 336.7 | 336.7 | 0.2% |
Convergence %: 0.0% on Local Temp and Energy Index | Max P: 2 | No. Equations: 13 | ||
mvts006: 3D Cooling Fin with Solid Elements
Analysis Type: | Steady-State Thermal |
Model Type: | 3D |
Comparison: | ANSYS No. 96 |
Reference: | Kreith, F. Principles of Heat Transfer. 2nd ed. PA: International Textbook Co., 1959. |
Description: | A cooling fin of square cross-sectional area is surrounded by fluid with one end maintained at a certain temperature, and the other end insulated. Find the temperature at the insulated tip (surface EFGH). |
Specifications
Element Type: | solid (2) | |
Units: | Hr Ft Btu F | |
Dimensions: | length: 0.6666 width: 0.083333 height: 0.083333 | |
Material Properties: | Mass Density: 1 Cost Per Unit Mass: 0 Young's Modulus: 0 | Poisson's Ratio: 0 Thermal Expansion: 0 Conductivity: 25 |
Prescribed Temperatures: | Location/Magnitude: | |
thermal_constr1 | placed on surface ABCD: 100 | |
Convection Conditions: | Location/Magnitude: | Bulk Temperature: |
therm_constr1 | placed on all outer surfaces except surfaces ABCD and EFGH: 1 | 0 |
Comparison of Results Data
Theory | ANSYS | Thermal | % Difference | |
Temperature at Tip (m=tip_temp_1) | 68.592 | 68.618 | 68.533 | 0.09% |
Convergence %: 0.0% on Local Temp and Energy Index | Max P: 8 | No. Equations: 998 | ||
mvts007: 3D Solid Cylinder Temperature Distribution
Analysis Type: | Steady-State Thermal |
Model Type: | 3D |
Comparison: | ANSYS No. 101 |
Reference: | Schneider, P. J. Conduction Heat Transfer. 2nd ed. MA: Addison-Wesley Publishing Co., Inc., 1957. |
Description: | A short, solid cylinder is subjected to prescribed temperatures over all surfaces. Find the temperature distribution in the cylinder. |
Specifications
Element Type: | solid 1(2) | |
Units: | Hr Ft Btu F | |
Dimensions: | outer radius: 0.5 height: 0.5 | |
Material Properties: | Mass Density: 1 Cost Per Unit Mass: 0 Young's Modulus: 0 | Poisson's Ratio: 0 Thermal Expansion: 0 Conductivity: 1.0 |
Prescribed Temperatures: | Location/Magnitude: | |
therm_constr1 | placed on surface EMN (top): 40 placed on surfaces AKL (bottom) and KLMN (outer surface): 0 | |
Comparison of Results Data
Theory | ANSYS | Thermal | % Difference | |
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Point A (m=node_1_temp) | 0 | 0 | 0.0 | 0.0% |
Point B (m=node_11_temp) | 6.8 | 7.4427 | 6.8577 | 0.84% |
Point C (m=node_21_temp) | 15.6 | 16.361 | 15.4406 | 1% |
Point D (m=node_31_temp) | 26.8 | 27.411 | 26.4951 | 1.13% |
Point E (m=node_41_temp) | 40 | 40 | 40.0 | 0.0% |
Convergence %: 1.4% on Local Temp and Energy Index | Max P: 9 | No. Equations: 622 | ||
mvts008: 3D Shell with Prescribed Temperature
Analysis Type: | Steady-State Thermal |
Model Type: | 3D |
Reference: | NAFEMS, BMTTA(S), No. 9 (i) |
Description: | A plate has a prescribed temperature distributed evenly around its boundary. No internal heat is generated. Find the temperature at point E. |
Specifications
Element Type: | Shell (10) | |
Units: | Hr M W C | |
Dimensions: | length: 0.6 width: 0.4 thickness: 1 | |
Material Properties: | Mass Density: 7850 Cost Per Unit Mass: 0 Young's Modulus: 0 | Poisson's Ratio: 0 Thermal Expansion: 0 Conductivity: 52 |
Prescribed Temperatures: | Location/Magnitude: | |
therm_constr1 | placed on curve A-B: 1000 placed on curves A-D, C-D, B-C: 0 | |
Comparison of Results Data
Theory | Thermal | % Difference | |
Temperature at Target Point E (m=target_pt_temp) | 260.5 | 260.4192 | 0.03% |
Convergence %: 1.8 % on Local Temp and Energy Index | Max P: 9 | No. Equations: 341 | |