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- 1. Thermal analysis and Design optimization using Pro Mechanica<br />CAD Applications (MAE 477/577) - Final Project<br />Sasi Bhushan # 35763829<br />Srikanth # 35762927<br />
- 2. Objective<br />Explore the capability of Mechanica to study the conduction/convection heat transfer analysis by considering simple examples and quantifying the ProM results with analytical calculations. <br />And the second part of the study involves exploring the design optimization capabilities of Mechanica.<br />The Game Plan<br /> For the first part of the study we consider simple geometries like:<br /><ul><li>Flat Plate
- 3. Long Cylinder
- 4. Two Cylinders of different cross sections </li></ul> For the second part of the study, we considered a Finned Plate and optimized its shape and size for a given set of constraints.<br />
- 5. Case Study 1: Flat Plate<br />Material: Copper<br />Dimensions: <br />l = 95 mm, b = 100 mm, t = 10 mm<br />heat transfer coefficient of air: <br />H = 0.01 N/mm Sec S<br />Thermal Conductivity of Copper: <br />K = 121.223 N/Sec C<br />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.<br />
- 6. Steady State Analysis<br />Analytical Calculations:<br />Temperature of hot surface: T1 = 100 C<br />Temperature of Surroundings: 25 C<br />Area of the plate: A = l*b = 9.5E-03 m^2<br />Heat flux across the plate:<br />q = k*A*(T1-T2)/t a) Conduction equation<br />Heat transfer to the environment:<br />q = h*A*(T2-Tatm) b) Convection equation<br />At steady state both conduction and convection should be equal. Solving the above two equations we get T2 = 99.9 C.<br />Temperature distribution in Flat Plate<br />
- 7. Analysis 2: Transient<br />One end maintained at 100 C and other end exposed to air at temp of 25 C through a convection heat transfer coefficient of 0.01 N/mm Sec C. <br />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.<br />
- 8. Analysis 3: Thermally Induced stresses<br />VonMises stresses induced<br />By fixing all degrees of freedom except displacement in X and Y direction on the hot surface we get : Maximum Stress: = 9.351600e+12 N/mm2<br />
- 9. Case Study 2: Cylindrical Rod<br />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.<br />
- 10. Analytical calculations for Flat Plate study:<br />Heat transfer coefficient of air :h = 0.01 N/mm Sec C<br />Specific heat capacity: 3.77186e+08 mm^2/sec^2<br />Thermal Conductivity: K =121.223 N/Sec C<br />Density : 8.21395e-06 kg/m^3<br />Poisson’s ratio: 0.35<br />At Surface 1 <br />Heat Flux Q: k*A*(T1-T2)/L a) (Conduction)<br />k= 121.223 N/Sec C<br />A = π*r^2 = 7.065E-04 m^2<br />At Surface 2 <br />Heat Flux Q: h*A*(T2-25)b) (Convection) <br />Q = 0.1 W<br />Therefore, solving the above two equations for T1 and T2 :<br />T1 = 39.5 C<br />T2 = 39.15 C<br />
- 11. ProM results: Steady State Analysis<br />Temperature distribution<br />Heat Flux<br />
- 12. Analysis 2: Transient<br />As expected the temperatures at both the ends come down to 25 C as the heat load is shut off. Time = 1.06896e+07 sec<br />
- 13. Analysis 3: Thermally Induced stresses<br />VonMises stresses induced<br />By fixing all degrees of freedom except displacement in X and Y direction on the hot surface we get : Maximum Stress: = 1.970081e+02 N/mm2<br />
- 14. Case Study 3: 2Cylindrical Rods with interface<br />The combined cylindrical rod is given a uniform heat flux of 100 mW on end and the other is exposed to convection to the atmospheric air.<br />
- 15. Steady State Analysis:<br /><ul><li>Convection Coefficient: h = 0.01 N/mm Sec C
- 16. Heat load: q = 100 mW
- 17. Area of Rod1: A1 = 7.065E-04 m^2
- 18. Area of Rod2: A2 =3.14E-04 m^2
- 19. Length of Rod1:L1 = 0.3 m
- 20. Length of Rod2:L2 = 0.4 m
- 21. Tatm = 25 C</li></ul>Steady state equations:<br />At surface 1:<br /><ul><li>q = k1*A1*(T1-T2)/L1 a)</li></ul>At Surface 2:<br /><ul><li>q = K2*A2*(T2-T3)/L2 b)</li></ul>At Surface 3:<br /><ul><li>q = h*A2*(T3-Tatm) c)</li></ul>Solving the above three equations we get,<br /><ul><li>T1 = 58.87 C
- 22. T2 = 57.89 C
- 23. T3 = 56.84 C </li></ul>Temperature distribution<br />
- 24. Analysis 2: Transient<br />Heat Load is turned on. And we want to find the time to reach the steady state temperatures.<br />
- 25. Analysis 3: Thermally Induced stresses<br />VonMises stresses induced<br />By fixing all degrees of freedom except displacement in X and Y direction on the hot surface we get : Maximum Stress: = 4.449016e+02<br />N/mm2<br />
- 26. Finned Plate<br />In this study we will add fins for the flat plate discussed earlier and determine the optimum height and thickness of the fins to maximize heat transfer and minimize mass along with the steady state and transient thermal analysis. <br />
- 27. Finned Plate<br />
- 28. Steady State Analysis<br />For the given boundary conditions the temperature distribution in the fin is given by the equation:<br />
- 29. Sensitivity Analysis<br />We run the global sensitivity analysis to determine the variation of Min Temperature and Mass with respect to the design variables.<br />Variation of temperature with respect to thickness and height of the fins<br />
- 30. Optimization Analysis<br />The optimization problem can be formulated as shown below:<br />Objective function: f = Mass<br />Constraints: g = Min Temp <= 80 C<br />Design variables:<br />height of the fins: 20<=h<=100<br />thickness: 2<=t<=8<br />Optimized vs. Initial Design<br />
- 31. Results<br />
- 32. Conclusions<br />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.<br />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 went 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.<br />

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