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Convection for Straight Fin Formulae and Calculator

Heat Transfer Engineering

Heat Transfer Convection for Straight Fin Equations and Calculator

For a straight fin with uniform cross section (assuming negligible heat transfer from tip),

Preview Convection for Straight Fin Calculator

Eq. 1

${\displaystyle Q=\sqrt{hPk{A}_c}(T_b-<!--\; -\; -->T_{\mathrm{\infty <!--\; \infty \; -->}})tanh(m{L}_c)}$

Eq. 2

${\displaystyle m=\sqrt{\frac{hP}{k{A}_c}}}$

Corrected length of fin (m)
Eq. 3

${\displaystyle L_c=L+\frac{A_c}{P}}$

where

Q = rate of heat transfer (W)
h = convection heat-transfer coefficient of the fluid [W/(m²·K)]
P = perimeter of exposed fin cross section (m)
k = fin thermal conductivity [W/(m·K)]
A_c = fin cross-sectional area (m²)
T_b = temperature at base of fin (K)
T_∞ = fluid temperature (K)
w = width (m)
L = length (m)
t = thickness (m)
D = diameter (m)

Figure 1, Rectangular Fin

Figure 2, Pin Fin

Reference:

Incropera, Frank P. and David P. DeWitt, Introduction to Heat Transfer, 4th ed., John Wiley and Sons

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