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Fin, finite length, heat loss by convection at end.
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Heat flow rate,
Q = (K*Ab*n*ΔT)*X1 / X2
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Input Data
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Temperature at fin base,
T1 =
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deg F
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Room Temperature, T2 =
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deg F
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Fin width, w =
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in
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Fin thickness, t =
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in
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Fin material thermal conductivity, K =
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W/m*C
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Convective heat transfer coefficient, h =
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W / m2*C
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Fin length, L =
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in
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Number of fins, N =
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Calculations
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Case 1
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Fin width, w =
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m
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Fin thickness, t =
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m
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Fin base area, A =
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w*t
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m2
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A =
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m2
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Temperature
difference, ΔT =
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T1 - T2
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ΔT =
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deg F
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ΔT =
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deg C
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For thin fin, n =
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(2*h/K*t)1/2
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n =
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h / n*K =
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L =
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m
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n*L =
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sinh(n*L) =
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cosh(n*L) =
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X1 =
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[(sinh(n*L) + (h /
n*K)*cosh(n*L)]
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X1 =
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X2 =
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[(cosh(n*L) + (h /
n*K)*sinh(n*L)]
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X2 =
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Q =
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N*(K*A*n*ΔT)*(X1 / X2))
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Answer: Q =
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Watts
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Case 2. Fin, finite length (L) insulated end.
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tanh(n*L) =
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Heat flow
rate, Q =
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N*(K*A*n*ΔT)*tanh(n*L)
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Answer: Q =
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Watts
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