Page 141 - Mechanical Engineer's Data Handbook

130 MECHANICAL ENGINEER’S DATA HANDBOOK

Heat flow from fin figure where L=fin length=(r,-r,) and A=cross-
Fin efficiency q = sectional area = tL.
Heat flow if fin all at t,
- 4 Hyperbolic section circular fins: curves are given for
-
hPL(t, - t.) hyperbolic fins using the appropriate values of A, and
A.
If fin has constant cross-section and is insulated at the
end:
tanh mL
Efficiency q =-
mL
Temperature profile along fin:
Temperature at distance x from root
cosh m(L - x)
t, = t, + (t, - t,)
cosh mL I I I I
ob 1 2 3 4
Fins on a circular pipe
Constant thickness:
Straight fins

Similar efficiency curves are given in the figures for
straight fins of various shapes.

Constant thickness Triangular
‘2
Constant thickness

where: A,=surface area=n(r:-r?)+2ar2t.

Efficiency is plotted against the function

Parabolic (convex)
Parabolic (concave)