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- 1. CAD APPLICATIONS Project 5 – Thermal Analysis and Design Optimization using ProMechanica Sasi Bhushan B # 35763829 Srikanth Avala # 35762927
- 2. Introduction The objective of this study is two folded: 1) Firstly, to explore the capability of Mechanica to study the conduction/convection heat transfer analysis by considering simple examples and quantifying the ProM results with the analytical calculations. 2) And the second part of the study involves exploring the design optimization capabilities of Mechanica. For the first part of the study we consider simple geometries like: a) Flat Plate b) Long Cylinder c) Two Cylinders of different cross sections And we perform the steady state thermal analysis, transient analysis and thermal stress analysis for the different models in different loading and boundary conditions. And the results are to be compared with the analytical results. For the second part of the study, we considered a Finned Plate and optimized its shape and size for a given set of constraints.
- 3. Case Study 1: Flat Plate Material Copper Dimensions l = 95 mm, b = 100 mm, t = 10 mm The flat plate is modeled in ProE and is shown in the figure below: Two dimensional drawings of Flat Plate The above plate is subjected to a uniform temperature of 100 C on one surface and the other surface is exposed to atmosphere at a temperature of 25 C. Therefore, there is convective heat transfer from the surface. heat transfer coefficient of air H = 0.01 N/mm Sec S Thermal Conductivity of Copper K = 121.223 N/Sec C Analysis: Steady State Analytical Calculations: Temperature of hot surface: T1 = 100 C
- 4. Temperature of Surroundings: 25 C Area of the plate: A = l*b = 9.5E-03 m^2 Heat flux across the plate: q = k*A*(T1-T2)/t a) Conduction equation Heat transfer to the environment: q = h*A*(T2-Tatm) b) Convection equation At steady state both conduction and convection should be equal. Solving the above two equations we get T2 = 99.9 C. ProM Results: Temperature distribution in Flat Plate Heat Flux
- 5. ProM Analytical Mass 7.80E-04 Max Temp 100 C Min Temp 99.93818 C 99.9 C Heat Flux 7.49E-01 0.749 We can clearly see that the analytical results match closely with the results we get from ProM. Analysis 2: Transient Initial temperature: 100 C One end maintained at 100 C and other end exposed to a air at temp of 25 C through a convection heat transfer coefficient of 0.01 N/mm Sec C. The primary question we want to answer is to find the eventual temperature of the cold end of the plate, and the time it takes to reach the steady state. Since the plate thickness in our case is very small it reaches the steady state almost instantaneously as shown in the figure above. Analysis3: Thermally Induced stresses For the same thermal conditions at steady state, we need to create displacement constraints. Fix all degrees of freedom on the cold surface. Fix all degrees of freedom except displacement in X and Y direction on the hot surface.
- 6. VonMises stresses induced Maximum Stress: = 9.351600e+12
- 7. Case Study 2: Cylindrical Rod Material Copper Dimensions Height h = 300 mm, diameter d = 30 mm The model of the cylindrical rod in ProE is as shown in the figure below: Two Dimensional drawing of Cylinder in ProE The above cylindrical rod is given a uniform heat flux of 100 mW on end and the other is exposed to convection to the atmospheric air. Material Cu Height 300 mm Diameter 30 mm Heat Source 100 mW Boundary Conditions h= 0.01 N/mm Sec C Analytical Calculations: Heat transfer coefficient of air: h = 0.01 N/mm Sec C Specific heat capacity: 3.77186e+08 mm^2/sec^2 Thermal Conductivity: K =121.223 N/Sec C
- 8. Density: 8.21395e-06 kg/m^3 Poisson’s ratio: 0.35 At Surface 1 Heat Flux Q: k*A*(T1-T2)/L a) (Conduction) k= 121.223 N/Sec C A = π*r^2 = 7.065E-04 m^2 At Surface 2 Heat Flux Q: h*A*(T2-25) b) (Convection) Q = 0.1 W Therefore, solving the above two equations for T1 and T2 : T1 = 39.5 C T2 = 39.15 C ProM Results: Temperature distribution
- 9. Heat Flux ProM Analytical Mass 1.75E-03 Max Temp 3.95E+01 39.5 Min Temp 3.91E+01 39.15 Max Heat Flux 1.47E-01 Transient Analysis: Heat Load is shut off. And we want to find the time for the cylinder to cool down to ambient temperature. As expected the temperatures at both the ends come down to 25 C as the heat load is shut off.
- 10. Time = 1.06896e+07 secs Thermally Induced stresses: For the same thermal conditions at steady state, we need to create displacement constraints. Fix all degrees of freedom on the cold surface. Fix all degrees of freedom except displacement in X and Y direction on the hot surface.
- 11. VonMises stresses induced Maximum Stress: = 1.970081e+02
- 12. Case 3: Two Cylindrical Rods Rod 1 Rod2 Material Steel Copper Height 300 mm 400 mm Diameter 30 mm 20 mm Heat Source 100 mW Boundary Conditions The ProE model is as shown in the figure below: ProE Model
- 13. Two Dimensional drawing h of air = 0.01 N/mm Sec C Rod1: Properties of Steel: Specific heat capacity: 4.73341e+08 mm^2/sec^2 Thermal Conductivity:k1 = 43.0125 N/Sec C Density : 7.82708e-06 kg/m^3 Poisson’s ratio: 0.27 Rod2: Properties of Copper: Specific heat capacity: 3.77186e+08 mm^2/sec^2 Thermal Conductivity: k2 =121.223 N/Sec C Density: 8.21395e-06 kg/m^3
- 14. Poisson’s ratio: 0.35 Steady State: Analysis Results: Young’s Modulus: 131000 Mpa Coefficient of thermal expansion: 113100 /C Analytical Calculations: Convection Coefficient: h = 0.01 N/mm Sec C Heat load: q = 100 mW Area of Rod1: A1 = 7.065E-04 m^2 Area of Rod2: A2 =3.14E-04 m^2 Length of Rod1:L1 = 0.3 m Length of Rod2:L2 = 0.4 m Tatm = 25 C Steady state equations: At surface 1: q = k1*A1*(T1-T2)/L1 a) At Surface 2: q = K2*A2*(T2-T3)/L2 b) At Surface 3: q = h*A2*(T3-Tatm) c) Solving the above three equations we get, T1 = 58.87 C T2 = 57.89 C T3 = 56.84 C
- 15. ProM results: ProM Analytical Mass Max Temp 5.89E+01 58.87 Interface Temp 5.76E+01 57.89 Min Temp 5.68E+01 56.84 Heat Flux Transient Analysis: Heat Load is turned on. And we want to find the time to reach the steady state temperatures. Time 3.99955e+06 secs
- 16. Max dynamic and Min dynamic temperatures Thermally Induced stresses: For the same thermal conditions at steady state, we need to create displacement constraints. Fix all degrees of freedom on the cold surface. Fix all degrees of freedom except displacement in X and Y direction on the hot surface.
- 17. VonMises stresses induced Maximum Stress: = 4.449016e+02
- 18. Finned Plate: For the second part of the study, we considered a Finned Plate and optimized its shape and size for a given set of constraints. In the study of heat transfer, a fin is a surface that extends from an object to increase the rate of heat transfer to or from the environment by increasing convection. The amount of conduction, convection, or radiation of an object determines the amount of heat it transfers. Increasing the temperature difference between the object and the environment, increasing the convection heat transfer coefficient, or increasing the surface area of the object increases the heat transfer. Sometimes it is not economical or it is not feasible to change the first two options. Adding a fin to an object, however, increases the surface area and can sometimes be an economical solution to heat transfer problems. In this study we will add fins for the flat plate discussed above and determine the optimum height and thickness of the fins to maximize heat transfer and minimize mass. The finned flat plate modeled in ProE is as shown in the figure below:
- 19. Two dimensional drawing of Finned Plate Dimensions of the plate l = 95 mm, b = 100 mm, t = 10 mm Dimensions of the Fins t= 5 mm, b = 100 mm, h = 5 mm Steady State Thermal Analysis: First a steady state thermal analysis is performed on the finned plate modeled in ProE. The Flat Surface of the plate is maintained at a temperature of 100C all the other surfaces are exposed to atmosphere at a temperature of 25. Analytical Calculations: For the given boundary conditions the temperature distribution in the fin is given by the equation:
- 20. From which the temperature at the tip the fin can be found. Using the above equation, we get minimum temperature by substituting x = L, Min Temp = 96.82 C ProM Results: The results are shown in the figures below: Temperature distribution Heat Flux
- 21. We can clearly see that the addition of fins has increased the heat flux. Analytical ProM Max Temperature 100 C 100 C Min Temperature 96.82C 95.6C Optimization: However, we would like to optimize the height and thickness of the fins such that we can minimize the minimum temperature in the model below 80 C and minimize the mass of the model. The optimization problem can be formulated as shown below: Objective function: f = Mass Constraints: g = Min Temp <= 80 C Design variables: height of the fins: 20<=h<=100 thickness: 2<=t<=8 We run the global sensitivity analysis to determine the variation of Min Temperature and Mass with respect to the design variables. The results are shown below: Variation of temperature with respect to thickness and height of the fins
- 22. Then we run the optimization problem posed above and obtain the optimum height and thickness of the fins. The results are compared to the initial design and are shown as below: Optimized vs. Initial Design Heat Flux Initial Design Optimized design Mass 2.83E-03 2.1783E-03 Max Temp 100E+02 100E+01 Minimum Temperature 9.56E+01 8.0000E+01 Optimized parameters: Fin height: h = 85.0972 mm Fin thickness: 2 mm
- 23. Conclusion: In this project, we explored the design optimization, thermal stress, conduction/convection heat transfer analysis capabilities of ProE.We went through this process by taking a few simple examples for steady state/transient analysis and validating the obtained ProM results with analytical calculations. We can infer from the coincidence of the final results that our analysis calculations are true and thus validate the overall process. The next step was taking up a more complex problem and exploring the design optimization capabilities of ProM. The finned plate problem is taken up and the whole previous process is gone through to obtain thermal analysis data, which is used for optimizing the plate design for particular parameters. The thermal analysis of the final optimized design shows the improved performance with better design parameters.
- 24. References: Wikipedia.org http://www.ptc.com/products/proengineer/ Fundamentals of Heat and Mass Transfer- Incropera http://www.me.uvic.ca/~mech410/proe_tutorials_files/Optimization%20in%20ProE. pdf http://www.cadcamguru.com/downloadPGDA_sept2008.pdf/Thermal%20Analysis% 20Of%20Heat%20Sink%20For%20Thyristor%20Controlled%20Systems%20Using%20 3-D%20ModelingAnd%20Finite%20Element%20Analysis..pdf

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