Heat Sink Convection with Fins Calculator

FINS
 
 
 
 
 
 
 
 
 
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.
 
 
 
 
 
FINS-RECTANGULAR
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 =
 
 
 
 
Calculations
 
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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