2. Double Pipe HEAT EXCHANGERS with Finned Inner Tube P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Ideas for Creation of Compact HX!!!

3.  NTU Curves: Counter flow NTU 

4. How to decide the height of fin for a Double Pipe HX ?

5. n th order Longitudinal Fins L x=a=0 b x=b x qbqb L b qbqb x=a=0 x

6. Effect of geometrical Order on Fin Effectiveness

7. Cost – Benefit Analysis of Fins The benefit of a fin is defined as effectiveness of a fin. An ideal fin will have highest value of effectiveness. An ideal fin is the one whose temperature is equal to temperature of the surface. This is possible only if the thermal conductivity of fin material is infinitely high. The effectiveness of an actual fin material is always lower than an ideal fin. The relative performance of a given fin is defined as efficiency of a fin. Provision of fins on a surface requires more material and hence more capital cost. A judicial decision is necessary to select correct factors of fin design. Best fin design should have higher benefits with a lower amount of material.

8. Performance of Least Material Strip Fin Optimum shape for a given q b &  b And solve for A p with [ tanh (1.4192) = 0.8894 ]

9. Comparison of Longitudinal Strip Fin profile area varies as the cube of To double the heat flow, you use two fins or make one fin eight times as large. There is a virtue in using short stubby fins.

10. Longitudinal Fin Of Triangular Profile The differential equation for temperature excess : L x=a=0 b x=b x qbqb

11. Longitudinal Fin Of Triangular Profile The differential equation for temperature excess is a form of Bessel’s equation: L x=a=0 b x=b x qbqb

12. Triangular Fin : Adiabatic Tip The particular solution foris: The fin heat dissipation is: The fin efficiency is:

13. Optimum Shape (Minimum Material) for Triangular Fin

14. Comparison of Longitudinal 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.

15. Comparison of Longitudinal Fin In both fins, profile area varies as the cube of To double the heat flow, you use two fins or make one fin eight times as large. There is a virtue in using short stubby fins.

16. Longitudinal Fin Of Concave Parabolic Profile The differential equation for temperature excess is an Euler equation: L b qbqb x=bx=a=0 x

17. The heat dissipated is: And the efficiency is: Optimum Shapes (Least Material) of Parabolic Profile

18. Double Pipe HX with finned inner Tube Equivalent diameter of annulus heat transfer, D e :

19. Longitudinally Welded fins

20. h, should be resulting heat transfer coefficient on annulus side. Fins with surface area, A fin, communicate as much as heat as an area of tube surface equal to  fin A fin. Therefore, the total annulus side effective area is A tube +  fin A fin. The ratio of total surface area to effective surface area is called as overall finned tube efficiency factor. Accounting of Heat Transfer due to strip Fins

21. Effective annulus side overall heat transfer coefficient: Overall Heat Transfer coefficient of finned Double tube HX:

22. More Ideas for Compact Double Pipe HXs The configuration should be similar to a straight double- pipe heat exchanger. But both the tubes are concentrically curved to take advantage of the space saving characteristics and through enhanced heat transfer coefficients. One such idea is double pipe Hx with the helical geometry. There are some distinct advantages from this type of design over hair pin DPHX. Firstly, the whole surface area of the coil will be exposed to moving fluid, eliminating the dead-zones that could be found in the outer tube of hair pin hx. Secondly, the flow in the outside tube will also experience secondary flows.

23. Helical Double-tube HX