Heat Sink Convection with Fins Calculator

Fins are used to increase heat transfer area
and provide a cooling effect.
However, if h*A / P*k is greater than 1.00
the fins will insulate and prevent heat flow.
h = air film convective coefficient
A = exposed surface area of the fins.
P = perimeter of the fins.
k = fin material conductivity coefficient.
Case 1. Fin, finite length, heat loss by convection at end.
Heat flow rate,  Q = (K*Ab*n*ΔT)*X1 / X2
Input Data
Temperature at fin base,  T1 = deg F
Room Temperature,  T2 = deg F
Fin width,  w = in
Fin thickness,  t = in  
Fin material thermal conductivity,  K = W/m*C
Convective heat transfer coefficient,  h = W / m^2*C
Fin length,  L = in
Number of fins,  N =
Fin width,  w = m
Fin thickness,  t = m
Fin base area,  A = w*t m^2
A = m^2
Temperature difference,  ΔT = T1 - T2
  ΔT = deg F
  ΔT = deg C
For thin fin,  n = (2*h/K*t)^.5
  n =
 h / n*K =
L = m
 n*L =
sinh(n*L) =
 cosh(n*L) =
X1 = [(sinh(n*L) + (h / n*K)*cosh(n*L)]
X1 =
X2 = [(cosh(n*L) + (h / n*K)*sinh(n*L)]
  X2 =
Q = N*(K*A*n*ΔT)*(X1 / X2))
Answer:  Q = Watts
Case 2. Fin, finite length (L) insulated end.
tanh(n*L) =
Heat flow rate,  Q = N*(K*A*n*ΔT)*tanh(n*L)
Answer:  Q = Watts
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