1. LOGO Heat Exchanger with cooling fins Hyun Jae Kim EGEE 520, Mathematical Modeling

2. www.themegallery.com Company Logo Contents 3. Validation of Model using 1-D calculation 2.3. Solution 2.2. Formulation 2.1. Governing Equation 1. Introduction of Heat Exchanger with Fins 4. Parametric Study of Radiation and Convection 5. Conclusion

3. www.themegallery.com Company Logo 1. Introduction Heat Exchangers ? Commonly used in many fields of industry, which are composed of finned surfaces for dissipation of heat by convection and conduction. Fin ? Used to increase the cooling area of system available for heat transfer between metal walls and condu- cting fluid such as gases and liquids. In this Study.. To calculate the conduction of cooling fins in heat exchanging cataly- tic reactor system with FEM and direct calculation of LDE and compare each other

4. www.themegallery.com Company Logo 2. 1. Governing Equation The heat transfer within the fin is governed by the stationary heat equation. On the external boundaries of the fin, heat convection term is added. On the external boundaries of the wall is also governed by above equation. 1m 0.25m 8m 0.4m ReactantProduct Catalysts

5. www.themegallery.com Company Logo 2.2. Formulation ① ② ③

6. www.themegallery.com Company Logo 2.3. Solution

7. www.themegallery.com Company Logo 3. Validation,, Boundary Condition (2) (1) (2) (1) Boundary Condition By defining dimensionless variables, 1) T is a function of x(fin length) alone 2) No heat lost from the end or from the edge 3) Heat flux at surface is, where h=constant, T=T(x) 4) Radiation is not concerned in validation. Assumption 0.25 m 1.0m L 2B= 0.4m

8. www.themegallery.com Company Logo 4. Parametric Study Natural convection with radiation Forced convection with radiation Natural convection without radiation Forced convection without radiation

9. www.themegallery.com Company Logo 5. Conclusion 1 Heat exchange with fins was examined and we can find convection term is important factor in calculation of surface temperature. 2 Comparison between solution from FEMLAB and direct calculation of ODE indicates that the former might get the more exact estimated value than the latter which needs more assumptions 3 Even though consideration of radiation is important in the natural convection system, it can be easily ignored when convection becomes significant term.

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