1. GANDHINAGAR INSTITUTE OF TECHNOLOGY
SUBJECT : Heat Transfer
TOPIC : Extended Surfaces-Fins
Guided by :- Prof. Abhishek Swarnkar
Prepared By :- Bhatia Simranjeetsingh B. ( ) Babar Prashant ( )
Ashutosh Kumar ( )

2. Fin
Extended surfaces may exist in many situations but are commonly used as fins to enhance heat transfer by increasing the surface area available for convection (and/or radiation).
Some typical fin configurations:

3. Extended Surface AnalysisTb
P: the fin perimeter
Ac: the fin cross-sectional area x

4. Extended Surface Analysis(Cont.)

5. The Fin Equation
Assuming one-dimensional, steady-state conduction in an extended surface of constant conductivity and uniform cross-sectional area, with negligible generation and radiation , the fin equation is of the form:
or, with and the reduced temperature ,
The general solution of linear homogeneous second order differential equation is of the form :

6. Heat dissipation from an infinitely long fin
Temperature at the base of fin=Temperature of the surface to which the fin is attached
at x=0
Temperature at the end of an infinitely long fin=surroundings.
at x=
So estimate heat flow rate is given by,

7. Heat dissipation from a fin insulated at the tip
For this boundary conditions are:
at x=0
So net heat transfer is given by:
at x=0

8. Heat dissipation from a fin losing heat at the tip
The relevant boundary conditions are:
The fin is losing heat at the tip i.e. the heat conducted to the fin at x=l equals the heat convected from the end to the surroundings so,
at x=0

9. Performance of fin
It is ratio of actual heat transfer by fin to maximum heat is transfer where surface temperature is base temperature.
[for infinitely long fin]
[for insulated tip]

10. Effectiveness of the fin
It is the ratio of the fin heat transfer rate to the heat transfer rate that would exist without a fin.

11. FIN EFFECTIVENESS The fin effectiveness can be increased by
Increasing the thermal conductivity of material(k).
Decreasing the value of convective heat transfer co-efficient(h) .
By increasing the ratio of parameter to cross section area of the fins (P/A).
By extending the length of fin but in an optimum value.

12. Temperature distribution Convection heat transfer
Cases
Tip condition (x=L)
Temperature distribution
Fin heat transfer rate A
Convection heat transfer B
Adiabatic C
Constant Temperature D
Infinite Fin Length

13. REAL IMAGES OF FINS

14. References https://en.wikipedia.org/wiki/Fin_(extended_surfa ce)
+transfer+in+rectangular+fin
notes/fin-design.ppt
Heat and mass transfer by Dr. D.S.Kumar