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Slender Fins with Variable Cross-Sectional Area

Slender Fins with Variable Cross-Sectional Area. P M V Subbarao Professor Mechanical Engineering Department IIT Delhi. Geometry Decides the Volume of Material …. L. q b. x. b. x=b. x=0. LONGITUDINAL FIN OF TRIANGULAR PROFILE. The differential equation for temperature excess :.

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Slender Fins with Variable Cross-Sectional Area

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  1. Slender Fins with Variable Cross-Sectional Area P M V Subbarao Professor Mechanical Engineering Department IIT Delhi Geometry Decides the Volume of Material …

  2. L qb x b x=b x=0 LONGITUDINAL FIN OF TRIANGULAR PROFILE The differential equation for temperature excess :

  3. For a slender fin:

  4. Define Fin Factor m Define Temperature excess:

  5. The particular solution for is: The differential equation for temperature excess is a form of Bessel’s equation of 0th order: The fin heat dissipation is: The fin efficiency is:

  6. Optimum Shapes : Triangular Fin L=1 With profile area This makes

  7. For Least material

  8. Optimum Shapes Iterative solving yields bT=2.6188 and

  9. Performance of Optimally Designed TRIANGULAR PROFILE (L=1) Heat dissipated: For optimum fin width

  10. And solve for Ap

  11. Comparison of Strip Fins Rectangular Profile: Triangular Profile: For the same material, surrounding conditions and which is basically the user’s design requirement. Triangular profile requires only about 68.8% as much metal as rectangular profile.

  12. Selection of Material Rectangular Profile: Triangular Profile: Consider three materials: Steel Aluminum Copper 7249 2704 8895 43.3 202.5 389.4

  13. Comparison of Longitudinal Fin (cont.) Fin mass is proportional to Ap & r. Apis inversely proportional to thermal conductivity. For given h, qb, and qb:

  14. L qb x b x=b x=a=0 STRIP FIN OF CONCAVE PARABOLIC PROFILE The differential equation for temperature excess is an Euler Differential Equation

  15. nth Order Strip Fins

  16. L qb x b x=b x=a=0 Optimum Shape of Parabolic Profile Solution of Euler equation: The temperature excess is linear if p=1. For p=1:

  17. The heat dissipated will be: And the efficiency will be:

  18. Performance of Strip Fins h mb

  19. Size of A FinVs Number of Fins In both (strip and triangular) fins, profile area varies as : To double the heat flow make one fin eight times as large or you use two fins !!! In pin fin, profile volume varies as To double the heat flow, make one fin 3.17 times as large or use two fins. More number of small fins are better than …...

  20. Pentium III Pentium IV Pentium II

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