An array of eight 2024 T6 aluminum alloy rectangular fins each 3 mm wide x 0.4 mm thick and 40 mm long is used to cool a transistor. When the base is 340 K and the ambient air is 300 K, how much power does the array dissipate? Take the combined convection and radiation heat transfer coefficient to be 8.0 W/m^2 K.

total heat dissipated from the array is 0.60 Watt

Explanation:

No. of fins 8

Given that:

Wdth (b) = 3 mm = 0.003 m

thickness (t) = 0.4 mm = 0.0004 m

length (L) = 40 mm

combined convection and radiation heat transfer coefficient to be = 8.0 W/m² K.

Tb = 340 K, Tw = 300 K

First we compute for area of  fins A = 0.003 m × 0.00004 = 1.2 × 10⁻⁶ m²

Perimeter of Fin P = 2( 0.003 m + 0.00004 m ) = 0.0068 = 6.8 × 10⁻³  

for 2024 T6 aluminium alloy K = 151 W/m-k from table

Now

m = √ ( hp/ka) = √[( 8 × 6.8 × 10⁻³  ) / (151 × 1.2 × 10⁻⁶ m²)] = 17.327

Lc = L + t/2 = 40 + 0.4/2 = 40.2 mm = 40.2 × 10⁻³

Now heat transfer from on fin :

Q = √( hpKA) × (Tb-Tw) × Tanh(mLc)

= √( 8×6.8 × 10⁻³×151×1.2 × 10⁻⁶) × (340-300) × tanh (0.6965)

= 3.13963 × 40 × 0.602144

= 0.075620 Watt

So total heat dissipated from array of 8 fins = 8 ×0.075620 = 0.60 Watt

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