> > 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
mvts002: 2D Plate with Convection
mvts003: 2D Axisymmetric Cylinder with Prescribed Flux
mvts004: 2D Axisymmetric Hollow Cylinder with Central Heat Source
mvts005: 2D Unit Depth Two-Layer Wall Temperatures
mvts006: 3D Cooling Fin with Solid Elements
mvts007: 3D Solid Cylinder Temperature Distribution
mvts008: 3D Shell with Prescribed Temperature
mvts001: 3D Cooling Fin with Beam Element
 Analysis Type: Steady-State Thermal Model Type: 3D Comparison: ANSYS No. 95 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, B.
Specifications
 Element Type: beam (1) Units: Hr Ft Btu F Dimensions: length: 0.6666 Beam Properties: Area: 0.00694IYY: 0Shear FY: 0CY: 0 J: 0IZZ: 0Shear FZ: 0CZ: 0 Material Properties: Mass Density: 1Cost Per Unit Mass: 0Young's Modulus: 0 Poisson's Ratio: 0Thermal Expansion: 0Conductivity: 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: 1.0width: 0.6 Material Properties: Mass Density: 0.08Cost Per Unit Mass: 0Young's Modulus: 0 Poisson's Ratio: 0Thermal Expansion: 0Conductivity: 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: 0.0outer radius: 0.1height: 0.05 Material Properties: Mass Density: 7850Cost Per Unit Mass: 0Young's Modulus: 0 Poisson's Ratio: 0Thermal Expansion: 0Conductivity: 52 Prescribed Temperatures: Location/Magnitude: therm_constr1 placed on curve A-B: 0
 Heat Loads Location/Magnitude Distribution Spatial Variation 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: 0.02outer radius: 0.1height: 0.14 Material Properties: Mass Density: 7850Cost Per Unit Mass: 0Young's Modulus: 0 Poisson's Ratio: 0Thermal Expansion: 0Conductivity: 52 Prescribed Temperatures: Location/Magnitude: Therm_constr1 placed on curves A-B, B-C, C-D: 0
 Heat Loads Location/Magnitude Distribution Spatial Variation 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: 0.75thickness of layer 2: 0.416666 Material Properties: Mass Density: 1Cost Per Unit Mass: 0Young's Modulus: 0 Poisson's Ratio: 0Thermal Expansion: 0Conductivity:• layer 1 (K1): 0.8• layer 2 (K2): 0.1 Convection Conditions: Location/Film Coefficient: Bulk Temperature: Therm_constr1 placed on curve A-B: 12placed on curve C-D: 2 300080
Comparison of Results Data
 Theory ANSYS Thermal % Difference 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: 0.6666width: 0.083333height: 0.083333 Material Properties: Mass Density: 1Cost Per Unit Mass: 0Young's Modulus: 0 Poisson's Ratio: 0Thermal Expansion: 0Conductivity: 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: 0.5height: 0.5 Material Properties: Mass Density: 1Cost Per Unit Mass: 0Young's Modulus: 0 Poisson's Ratio: 0Thermal Expansion: 0Conductivity: 1.0 Prescribed Temperatures: Location/Magnitude: therm_constr1 placed on surface EMN (top): 40placed on surfaces AKL (bottom) and KLMN (outer surface): 0
Comparison of Results Data
 Theory ANSYS Thermal % Difference 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: 0.6width: 0.4thickness: 1 Material Properties: Mass Density: 7850Cost Per Unit Mass: 0Young's Modulus: 0 Poisson's Ratio: 0Thermal Expansion: 0Conductivity: 52 Prescribed Temperatures: Location/Magnitude: therm_constr1 placed on curve A-B: 1000placed 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