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Infinitely Long Fins

A turbine bla...

Question

A turbine blade $4.5 c m^{2}$ cross sectional area and 10 cm perimeter is made of stainless steel of thermal conductivity $25 W / m K .$ If the surface heat transfer coefficient is $275 W / m^{2} K .$ What is length of fin required assume the given fin as effectively long fin?

A

5 cm

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B

20 cm

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C

10 cm

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D

2 cm

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Solution

The correct option is A 5 cm
To assume the given fin as long fin tanh(mL) should be equal to one.

$Then m L = 5 \sqrt{\frac{h P}{K A}} \times L = 5 \sqrt{\frac{275 \times 0.1}{25 \times 4.5 \times 10^{- 4}}} \times L = 5 49.44 \times L = 5 L = 10.11 c m$

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